From jdgall84 at gmail.com Wed Jan 11 17:05:09 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Wed Jan 11 17:05:54 2017 Subject: [Alta-Logic] Peripatetic Kickoff! Message-ID: Speaker: JS Lemay Location: ICT 616 Friday 12:15 pm Title: Universal Rota-Baxter Modules in Calculus Categories Abstract: In classical algebra, all algebras have a universal differential module. Constructing the universal Rota-Baxter module, the integral analogue, for an arbitrary algebra has been much more challenging. In this talk we construct a universal Rota-Baxter module in a calculus category where a certain coequalizer exists. In particular, this construction gives the universal Rota-Baxter module for the free symmetric algebra over a vector space. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170111/443b4f09/attachment.html From jdgall84 at gmail.com Thu Jan 19 18:40:05 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Jan 19 18:40:52 2017 Subject: [Alta-Logic] peripatetic seminar Message-ID: Greetings, There is a meeting of the peripatetic seminar tomorrow; two talks are scheduled. Location: MS 371 at 12:15 pm - 2 pm on Friday January 20 Talk 1: Speaker: JS Lemay Title: The universal Rota-Baxter construction part II Talk 2: Speaker: Jonathan Gallagher Title: Coherently closed tangent categories and their differential objects part I Hope to see you all there! -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170119/bfb83cda/attachment.html From jdgall84 at gmail.com Thu Jan 26 14:33:06 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Jan 26 14:33:51 2017 Subject: [Alta-Logic] peripatetic seminar and cs theory talk tomorrow Message-ID: Greetings, There are three talks tomorrow that you may be interested in! *Peripatetic Seminar. Location ICT 616 at 12:00 pm, Friday January 27* Speaker 1: Geoff Vooys *Title: A Categorical Introduction to the Theory of Witt Vectors, Part I* Abstract: The theory of Witt vectors is traditionally used to lift commutative rings with identity in positive characteristic to commutative rings with identity in characteristic zero in a way that extends to a functor from the opposite category of affine schemes to the category of commutative rings with identity. However, the constructions that define the ring operations on the ring of Witt vectors are frequently too complicated to work with in practice, and many of the properties of Witt vectors useful in arithmetic geometry are frustratingly difficult to derive. In this talk we will provide an alternative, more categorical, development of Witt vectors that will make the theory cleaner and clearer, as well as show that many of the properties of Witt vectors are simple consequences of the categorical perspective that we will provide. In particular, we will show that the Witt vector functor arises as a left Kan extension and that the ring of Ghost components associated a ring of Witt vectors comes from a natural transformation induced by the universal property of left Kan extensions. Speaker 2: Jonathan Gallagher *Title: Tangent categories are strong, but still need to be a little coherent* Abstract: We will show that the structural natural transformations that define a tangent category are strong transformations with respect to appropriate strengths. We will see that this strength gives almost enough coherence to ensure that the category of differential objects is a differential $\lambda$-category; and we will introduce the notion of coherent differential structure which ensures that differential objects are a differential $\lambda$-category. *CS Theory Seminar. Location ICT 616 at 2:00 pm, Friday January 27* Speaker: J?r?me Fortier (University of Ottawa) *Title: Restriction lambda-calculus * One of the most general, and therefore nicest, families of models for the notion of partiality (as in partial functions: functions that may be undefined sometimes) in categorical terms is the notion of a restriction category. That is: we put a focus on the idea of restricting morphisms to the domain of other morphisms via a restriction operator. There is also a notion of a cartesian closed restriction category (CCRC), analogous to the regular notion of a CCC. This work is an attempt to prove the Curry-Howard property for CCRC's, by developing the corresponding syntax. Our solution is something like simply typed lambda-calculus, with a restriction operator. The resulting logic turns out to be substructural, and therefore very nice! Hope to see you all there!! -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170126/2a3e5bd0/attachment.html From jdgall84 at gmail.com Thu Feb 2 22:54:07 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Feb 2 22:56:31 2017 Subject: [Alta-Logic] peripatetic seminar tomorrow Message-ID: There is a peripatetic seminar meeting tomorrow. Where and when: ICT 616 Friday, Feb 3 at 12:15 p.m. Speaker 1: Geoff Vooys Title: A Categorical Introduction to the Theory of Witt Vectors, Part II Abstract: The theory of Witt vectors is traditionally used to lift commutative rings with identity in positive characteristic to commutative rings with identity in characteristic zero in a way that extends to a functor from the opposite category of affine schemes to the category of commutative rings with identity. However, the constructions that define the ring operations on the ring of Witt vectors are frequently too complicated to work with in practice, and many of the properties of Witt vectors useful in arithmetic geometry are frustratingly difficult to derive. In this talk we will provide an alternative, more categorical, development of Witt vectors that will make the theory cleaner and clearer, as well as show that many of the properties of Witt vectors are simple consequences of the categorical perspective that we will provide. In particular, we will show that the Witt vector functor arises as a left Kan extension and that the ring of Ghost components associated a ring of Witt vectors comes from a natural transformation induced by the universal property of left Kan extensions. Speaker 2: TBA We look forward to seeing you tomorrow! -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170202/1b1a2c9d/attachment.html From jdgall84 at gmail.com Fri Feb 3 08:50:28 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Fri Feb 3 08:51:41 2017 Subject: [Alta-Logic] peripatetic seminar update Message-ID: Regarding today's 12:15 peripatetic meeting, our second speaker will be Cole Comfort. Speaker 2: Cole Comfort Title: The Category CNOT: a Categorical Approach to Quantum Computing -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170203/69ef2dbe/attachment.html From jdgall84 at gmail.com Thu Feb 9 23:24:12 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Feb 9 23:25:01 2017 Subject: [Alta-Logic] peripatetic seminar Friday Message-ID: Peripatetic seminar notice: *Location ICT 616 at 12:15 pm Friday, Feb. 10* Speaker 1: Geoff Vooys *Title: A Categorical Introduction to the Theory of Witt Vectors, Part III* Speaker 2: Cole Comfort *Title: CNOT, a category for quantum computing* -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170209/5e4ff840/attachment.html From bauerk at ucalgary.ca Fri Feb 10 09:49:34 2017 From: bauerk at ucalgary.ca (Kristine Bauer) Date: Fri Feb 10 09:49:36 2017 Subject: [Alta-Logic] peripatetic seminar Friday In-Reply-To: References: Message-ID: Hi all, There is a funding announcement for BIRS at 10am on the third floor of EEEL. I understand the minister of education will be here and would like to hear from students, in particular. Stop by if you have something to say... it's a rare opportunity. Cheers, Kristine Sent from my iPhone On Feb 9, 2017, at 11:25 PM, Jonathan Gallagher > wrote: Peripatetic seminar notice: Location ICT 616 at 12:15 pm Friday, Feb. 10 Speaker 1: Geoff Vooys Title: A Categorical Introduction to the Theory of Witt Vectors, Part III Speaker 2: Cole Comfort Title: CNOT, a category for quantum computing _______________________________________________ This message was sent to all subscribers of alta-logic-l To unsubscribe, see instructions at: http://www.ucalgary.ca/it/email/mailman E-mail: alta-logic-l@mailman.ucalgary.ca Homepage: http://mailman.ucalgary.ca/mailman/listinfo/alta-logic-l -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170210/691398cf/attachment.html From jdgall84 at gmail.com Mon Feb 13 11:57:21 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Mon Feb 13 11:58:09 2017 Subject: [Alta-Logic] peripatetic seminars this week Message-ID: Greetings, We will have two talks this Friday in the peripatetic seminar! Location: ICT 616 When: Friday 12:15 p.m. Geoff Vooys will give the construction of Witt vectors and Cole Comfort will wrap up his seminar on CNOT. Speaker 1: Geoff Vooys *Title: A Categorical Introduction to the Theory of Witt Vectors* Speaker 2: Cole Comfort *Title: CNOT a categorical approach to quantum computing* -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170213/796113f6/attachment.html From rzach at ucalgary.ca Mon Feb 13 17:34:49 2017 From: rzach at ucalgary.ca (Richard Zach) Date: Mon Feb 13 17:35:12 2017 Subject: [Alta-Logic] Save the Date: The Calgary Mathematics & Philosophy Lecture March 16: Emily Grosholz Message-ID: Theory Reduction, Algebraic Number Theory, and the Complex Plane Emily Grosholz Pennsylvania State University Thursday, March 16, 2017, 3:30 pm ICT 121 (Lecture Theatre Five) How does mathematical knowledge grow? According to an influential formulation due to philosopher Ernest Nagel, when a scientific theory "reduces" another, the reduced theory is deductively subsumed under the reducing theory: thus for example chemistry is deduced from quantum mechanics, and molecular biology from chemistry. Recent critics, using examples from science, argue that Nagel's criteria for theory reduction are both too strict, and too weak. Prof. Grosholz reviews Nagel's model and its difficulties, and argues that theory reduction faces similar problems in mathematics. Certain proofs of Fermat's conjectures about whole number solutions of quadratic and cubic polynomials, by means of the alliance of number theory with complex analysis, lead not deductively but abductively (adding content) to the study of algebraic number fields, and class field theory. This extension of number theory is at once too strong and too weak to look like Nagelian theory reduction, which is precisely why it turns out to be so fruitful. *Emily Grosholz* is Edwin Erle Sparks Professor of Philosophy at the Pennsylvania State University. She is the author of monographs on Descartes, Leibniz and the role of "productive ambiguity" in mathematics and the sciences. She edited a collection of essays on Leibniz, time and history, as a special issue of /Studia Leibnitiana/ (44 / 1 2012), as well as collection of essays on modern cosmology and time as a special issue of /Studies in the History and Philosophy of Modern Physics/ (52 / Part A 2015). Her new philosophy book /Starry Reckoning: Reference and Analysis in Mathematics and Cosmology/ is just out from Springer in the SAPERE series edited by Lorenzo Magnani. Next year, Springer will publish her book on poetry and mathematics, /Great Circles: The Transits of Mathematics and Poetry/ in a new series, Mathematics, Culture and the Arts, edited by Margerie Senechal, Jeremy Gray and Jed Buchwald. / This talk is the third annual Calgary Mathematics & Philosophy Lecture , co-sponsored by PIMS , the Pacific Institute for the Mathematical Sciences, the Department of Philosophy, and the /Department of Mathematics /. The Mathematics & Philosophy Lectures aim to introduce topics at the intersection of mathematics and philosophy to a general academic audience. The event is free & open to the public; a reception follows/ -------------- next part -------------- Skipped content of type multipart/related From rzach at ucalgary.ca Tue Feb 28 08:48:54 2017 From: rzach at ucalgary.ca (Richard Zach) Date: Tue Feb 28 08:49:05 2017 Subject: [Alta-Logic] Fwd: [PT] Call for Scholarship Applications: Logic Mentoring Workshop (LMW) '17 In-Reply-To: <3223fd07-b1fa-e9f8-0452-e23afe5eb230@gmail.com> References: <3223fd07-b1fa-e9f8-0452-e23afe5eb230@gmail.com> Message-ID: <74dba34c-f0d6-7192-9b37-cb1dc48cbe83@ucalgary.ca> Please note FIRST CALL FOR SCHOLARSHIP APPLICATIONS 2nd LOGIC MENTORING WORKSHOP Reykjavik, Iceland Sunday 18 June 2017 http://lics.rwth-aachen.de/lics17/lmw.html Colocated with LICS 2017 The 2nd Logic Mentoring Workshop (LMW) invites applications from students (undergraduate, master's and PhD), in all areas of logic for scholarships to attend the Logic in Computer Science (LICS) conference this year. Attending a conference such as LICS can be a transformative experience. It exposes participants to cutting-edge research and can open up new research avenues and collaboration opportunities. However many students do not get the opportunity to attend a conference such as LICS, and its participation often underrepresents women and minorities. For this reason, women and members of minority groups are especially encouraged to apply. Scholarships will be generously funded by our sponsors (see below) and covers registration to LMW and the main LICS conference, and possibly travel and accommodation. The LMW will focus on the technical and practical aspects of a career in logic research, including talks and panel sessions from leaders in the subject. LMW '17 builds on the success of the first edition which took place last year, also colocated with LICS. Last year's programme can be found here: . SCHOLARSHIP APPLICATIONS Applications should be made via the online form: http://bit.ly/2lLnRq5 Please note that a letter of recommendation is required and should be sent directly by your referee to Valeria Vignudelli . Further details are on the form. The deadline for applications is *31 March 2017*. Notification will be made shortly thereafter. CONFIRMED SPEAKERS Yuri Gurevich (University of Michigan, Microsoft Research) Valeria de Paiva (Nuance Communications) Prakash Panangaden (McGill University) (more TBA) ORGANISING COMMITTEE Anupam Das (co-chair) Eric Koskinen Valeria Vignudelli (co-chair) Fabio Zanasi (co-chair) SPONSORS Icelandic Centre of Excellence in Theoretical Computer Science (ICE-TCS) National Science Foundation (NSF) ACM Special Interest Group on Logic and Computation (SIGLOG) From jdgall84 at gmail.com Wed Mar 1 21:10:31 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Wed Mar 1 21:12:11 2017 Subject: [Alta-Logic] peripatetic seminars this Friday Message-ID: There are two very special peripatetic seminars this Friday, March 3! Details below. The first is *Chad Nester*'s graduate seminar. *Title:* Turing Categories and Realizability *Location:* ICT 616 at 12:30 pm on March 3 *Abstract:* Realizability is an interesting way to relate computation to logic. In a realizability model for a system of logic, a proposition is provable in case there is a computable function witnessing this in a constructive sense. Notions of computation have historically been defined in terms of partial functions on sets, but need not be. Turing categories present computation in a very general categorical framework, allowing us to study computation more abstractly. This raises the question of how realizability works in the more abstract setting. We approach this question through a generalization of the category of assemblies. In addition to being of independent interest, these generalized assemblies allow us to construct realizability toposes more abstractly, and in the presence of less structure than classical set-based constructions. Second, Richard Zach has a visitor,* Matthias Baaz*, from the Vienna University of Technology. Matthias has agreed to speak at a joint peripatetic-CS theory seminar. *Title:* Unsound inferences make proofs shorter (joint work with Juan.P.Aguilera) *Location: *ICT 616 at 2pm on March 3 *Abstract:* We give examples of analytic sequent calculi that extend Gentzen's sequent calculus LK by unsound quantifier rules in such a way that (i) derivations lead only to true sequents and (ii) cut free proofs may be non-elementary shorter than cut free LK proofs. This research is based on properties of Hilbert's epsilon calculus and part of efforts to complement Hilbert's stepwise concept of proof by useful global concepts. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170301/59460580/attachment.html From rzach at ucalgary.ca Mon Mar 13 19:26:07 2017 From: rzach at ucalgary.ca (Richard Zach) Date: Mon Mar 13 19:27:06 2017 Subject: [Alta-Logic] THIS THURSDAY: Emily Grosholz gives the Calgary Mathematics & Philosophy Lecture, 3:30pm Message-ID: <6822b04f-ab11-19dc-bc7f-d19e36401bd2@ucalgary.ca> Skipped content of type multipart/alternative-------------- next part -------------- A non-text attachment was scrubbed... Name: Calgaryhandout021817.pdf Type: application/x-pdf Size: 175107 bytes Desc: not available Url : http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170313/236d1988/Calgaryhandout021817.bin From jdgall84 at gmail.com Thu Mar 23 19:55:18 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Mar 23 19:56:04 2017 Subject: [Alta-Logic] peripatetic seminar tomorrow Message-ID: Tomorrow the peripatetic seminar will host two introductory talks on microlinearity and representable tangent structure respectively. Location: ICT 616 Time: Friday at 12:15 pm Speaker 1: Ben MacAdam Title: The micro linear spaces of SDG Speaker 2: Jonathan Gallagher Title: Representable Tangent Categories See you all there! -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170323/0208e275/attachment.html From jdgall84 at gmail.com Fri Apr 7 01:51:34 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Fri Apr 7 01:52:21 2017 Subject: [Alta-Logic] peripatetic seminar today (Friday, April 7) Message-ID: JS Lemay is giving a practice thesis defense seminar, and also a research talk. Location ICT 616 at 12:15 pm Title: Deriving transformations for bialgebra modalities Abstract: For a bialgebra modality, deriving transformations which satisfy the nabla-rule are induced by codereliction maps. The problem is: not all deriving transformations satisfy the nabla-rule. In this talk, we will show that for an additive bialgebra modality, all deriving transformation satisfy the nabla rule. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170407/0f7132e4/attachment.html From bauerk at ucalgary.ca Thu Apr 20 13:36:02 2017 From: bauerk at ucalgary.ca (Kristine Bauer) Date: Thu Apr 20 13:36:05 2017 Subject: [Alta-Logic] Fwd: Two Colloquia this Friday (April 21) References: <10E27C1F-08C0-447A-A7A8-CBD625F58288@ucalgary.ca> Message-ID: <27AE5163-AFDA-4055-A196-626CAE8BF52F@ucalgary.ca> Hello all, You might be interested in one or both of the talks advertised by Karen in the message below. Cheers, Kristine Begin forwarded message: From: Karen Seyffarth > Subject: Two Colloquia this Friday (April 21) Date: April 20, 2017 at 1:27:46 PM MDT To: "dept@math.ucalgary.ca" > Date & Time: Friday, April 21, 2017 from 13:00 to 13:50 Location: MS 431 The Winter 2017 Fejes Toth Lecture will be delivered by Dr. Peter Pivovarov (University of Missouri) Title: Empirical Forms of Isoperimetric Inequalities in Convex Geometry The talk will be followed by coffee and cookies in the lounge. Once you?ve had your caffeine and sugar boost, please join us for Title: The First Calculus Textbook: The Marquis de l'Hospital and the "Analyse des infiniments petits? Speaker: Dr. Thomas Kucera (University of Manitoba) Time: 15:00 to 15:50. Location: MS 319 (please note the room number) All are welcome! ?Karen ------------------------------------------ Dr. K. Seyffarth Dept. of Math. & Stat. University of Calgary kseyffar@math.ucalgary.ca Phone: 403-220-6311 ------------------------------------------ -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170420/c2eb74c5/attachment.html From jdgall84 at gmail.com Thu Apr 20 17:08:43 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Apr 20 17:09:28 2017 Subject: [Alta-Logic] peripatetic seminar tomorrow Message-ID: JS Lemay will be giving a talk tomorrow in the peripatetic seminar: Where: ICT 616 at 12:00 pm Title: Additive Linear Categories Abstract: In this talk, I will introduce additive linear categories and explain how I already introduced them last time when I introduced additive bialgebra modalities. We will also discuss the Seely isomorphisms and the biproduct completion. Given time, we will look at some of the compatibility between the additive linear structure and the differential structure. This time cuts close with the math colloquia tomorrow afternoon, so feel free to come and leave early. Hope to see you there! -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170420/76ee8762/attachment.html From rzach at ucalgary.ca Sat Apr 29 11:58:41 2017 From: rzach at ucalgary.ca (Richard Zach) Date: Sat Apr 29 11:58:47 2017 Subject: [Alta-Logic] =?utf-8?q?Logic_=26_Philosophy_of_Mathematics_at_SE?= =?utf-8?b?UCDiiKcgU1NIQVAsIE1heSA1LTEw?= Message-ID: <53e7e6dd-70f5-1756-c91a-1c6919d0258a@ucalgary.ca> The Department of Philosophy is sponsoring two conferences from May 5-10 in Science A. There will be lots of talks on logic, history of logic, and the philosophy of mathematics. Faculty and students are welcome to attend (no registration necessary). The SEP meeting is here: http://www.phil.ufl.edu/SEP/meeting/2017/index.html The SSHAP meeting is here: http://sshap.org/2017/04/22/sshap-2017-program-and-registration/ Room numbers will be posted shortly, but everything will take place in Science A, and there will be programs available in SA 147. -- Richard Zach ......http://www.ucalgary.ca/rzach/ Professor, Department of Philosophy University of Calgary, Calgary AB T2N 1N4, Canada From jdgall84 at gmail.com Wed May 17 15:27:18 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Wed May 17 15:28:03 2017 Subject: [Alta-Logic] peripatetic seminar Monday at 1 pm Message-ID: There are two talks on Monday in the peripatetic seminar: Time: Monday May 22, 2017 at 1 pm Location: ICT 616 Talk 1: Speaker: Ben MacAdam Title: Indexed linear systems of maps Abstract: Indexed linear systems of maps will be introduced, and used to explore some linear-logical aspects of \topological vector bundles. Talk 2: Speaker: Jonathan Gallagher Title: Path object categories and fibrations Abstract: We will introduce path objects and the cloven weak factorization systems they imply. We will develop their display system of type theoretic fibre bunldes with a slant towards connecting these to tangent categories. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170517/08156c21/attachment.html From jdgall84 at gmail.com Sun May 21 22:34:37 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Sun May 21 22:35:30 2017 Subject: [Alta-Logic] talk time correction Message-ID: I previously posted talk times for Monday -- which is a holiday. The two talks advertised will be on Wednesday at 11:30 am. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170521/3a3636dc/attachment.html From jdgall84 at gmail.com Wed May 24 09:17:04 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Wed May 24 09:17:50 2017 Subject: [Alta-Logic] peripatetic seminars today Message-ID: Time: Monday May 24, 2017 at 11:30 am Location: MS431 Talk 1: Speaker: Ben MacAdam Title: Indexed linear systems of maps Abstract: Indexed linear systems of maps will be introduced, and used to explore some linear-logical aspects of \topological vector bundles. Talk 2: Speaker: Jonathan Gallagher Title: Path object categories and fibrations Abstract: We will introduce path objects and the cloven weak factorization systems they imply. We will develop their display system of type theoretic fibre bunldes with a slant towards connecting these to tangent categories. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170524/7c886eaf/attachment.html From jdgall84 at gmail.com Wed Jun 21 12:37:53 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Wed Jun 21 12:38:39 2017 Subject: [Alta-Logic] peripatetic seminar this Friday Message-ID: Speaker: Ben MacAdam Title: Characterizing the simple fibration Abstract: The simple fibration on a cartesian category, and its generalization to the simple fibration above a fibration with fibered products are explored. Following the work of Hermida and Street, the simple fibration is characterized on a cartesian objects in a bicategory with weak products. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170621/75791a1f/attachment.html From jdgall84 at gmail.com Wed Jun 21 12:40:55 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Wed Jun 21 12:41:40 2017 Subject: [Alta-Logic] peripaetic seminar this Friday Message-ID: Sorry ... I hit send by accident. Below are the relevant details. Location: ICT 616 on Friday at 11:30 am. Speaker: Ben MacAdam Title: Characterizing the simple fibration Abstract: The simple fibration on a cartesian category, and its generalization to the simple fibration above a fibration with fibered products are explored. Following the work of Hermida and Street, the simple fibration is characterized on a cartesian objects in a bicategory with weak products -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170621/77f76bfd/attachment.html From bauerk at ucalgary.ca Mon Jun 26 15:43:20 2017 From: bauerk at ucalgary.ca (Kristine Bauer) Date: Mon Jun 26 15:43:26 2017 Subject: [Alta-Logic] website, seminar time Message-ID: Hi all, Next year, we are very lucky to have funding to bring about one visitor a month to the Peripatetic seminar. I?d like to have posters printed for the Peripatetic for the fall, including the names and dates of all of our visitors. For this it would be nice to have an idea of when the seminar could meet, together with a website where we can offer concrete details like titles and abstracts of the talks as they become available. Does anyone have access to either of these two websites: http://www.ucalgary.ca/logic/cprglct http://pages.cpsc.ucalgary.ca/%7Erobin/CPRGLCT/CPRGLCT.html If so, we could use one of these sites to update our seminar series. If not, we can ask PIMS to host a new site. Unless there another site that I?ve missed? Second, I would like to pick a meeting time/place for the seminar. Does anyone have conflicts (yet) at 2pm on Wednesdays? If not, would you please block off this time? Thanks, Kristine -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170626/fe0bdaa1/attachment.html From robin at ucalgary.ca Mon Jun 26 16:33:23 2017 From: robin at ucalgary.ca (Robin Cockett) Date: Mon Jun 26 16:33:26 2017 Subject: [Alta-Logic] Re: website, seminar time In-Reply-To: References: Message-ID: OK it seems I have the second of these on my website!! So I do have access ... This may not help as I am useless with web things ... -robin ________________________________ From: Kristine Bauer Sent: Monday, June 26, 2017 3:43 PM To: Robin Cockett; Jonathan Gallagher; Chad Mitchell Nester; Prashant Kumar; priyaa Srinivasan; Benjamin MacAdam Cc: alta-logic-l@mailman.ucalgary.ca Subject: website, seminar time Hi all, Next year, we are very lucky to have funding to bring about one visitor a month to the Peripatetic seminar. I?d like to have posters printed for the Peripatetic for the fall, including the names and dates of all of our visitors. For this it would be nice to have an idea of when the seminar could meet, together with a website where we can offer concrete details like titles and abstracts of the talks as they become available. Does anyone have access to either of these two websites: http://www.ucalgary.ca/logic/cprglct http://pages.cpsc.ucalgary.ca/%7Erobin/CPRGLCT/CPRGLCT.html If so, we could use one of these sites to update our seminar series. If not, we can ask PIMS to host a new site. Unless there another site that I?ve missed? Second, I would like to pick a meeting time/place for the seminar. Does anyone have conflicts (yet) at 2pm on Wednesdays? If not, would you please block off this time? Thanks, Kristine -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170626/ca2f3369/attachment.html From jdgall84 at gmail.com Thu Jun 29 14:23:36 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Jun 29 15:24:38 2017 Subject: [Alta-Logic] peripatetic seminar: Friday (tomorrow) at 3pm Message-ID: Speaker: Ben MacAdam Location: ICT 616 at 3pm Friday on June 30 Title: Fibred Linear Maps Abstract: We complete the characterization of the simple fibration in an arbitrary 2-category and apply it to define a fibered system of linear maps. Applications to abstract differential geometry and string calculi will be discussed. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170629/e93e0dd8/attachment.html From jdgall84 at gmail.com Wed Jul 5 15:53:41 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Wed Jul 5 15:54:27 2017 Subject: [Alta-Logic] peripatetic seminar this Friday Message-ID: Speaker: JS Lemay Where: ICT 616 at 12:30 pm, July 7 TITLE: Integral Category Structure of Smooth Functions ABSTRACT: In this talk, I will explain how line integration from classical vector calculus gives an integral combinator on the category of real smooth functions. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170705/5dcdbe33/attachment.html From bauerk at ucalgary.ca Fri Jul 7 14:32:34 2017 From: bauerk at ucalgary.ca (Kristine Bauer) Date: Fri Jul 7 14:32:37 2017 Subject: [Alta-Logic] special seminar next week Message-ID: Dear colleagues, Next week there will be a special meeting of the Peripatetic Seminar on Wednesday, July 12 at 1pm in MS 431. Dr. Rory Lucyshyn-Wright from Mount Allison University is visiting for the week and will talk about his work related to the structure of differential geometry. The talk may be of broad interest. The title and abstract are below. Many thanks, Kristine Title: Simplicial calculus of higher-order differentials Introduced by J. E. White in 1982, sector forms are certain real-valued functions on the n-fold iterated tangent bundle of a manifold, and they can be seen as generalized differential forms. In joint work with Geoffrey Cruttwell, we showed that sector forms on a given manifold constitute a symmetric cosimplicial abelian group, and in fact we proved a similar result in an arbitrary tangent category. As a corollary, sector forms constitute a cochain complex, with a subcomplex of alternating elements. The latter subcomplex is isomorphic to the usual de Rham complex, so that the familiar exterior derivative is canonically induced by the cosimplicial structure on sector forms. This talk will be an introduction to sector forms on manifolds, including a local description of sector forms on a given chart, as well as a comparison with the familiar description of differential forms via exterior algebra. We shall see that sector n-forms constitute a locally free sheaf whose rank is related to the combinatorics of partitions, and we shall exhibit a specific basis on each chart. The resulting local description makes it clear how sector forms provide a generalization of differential n-forms in which one finds not only first-order differentials and their n-th degree skew-symmetric products, but also higher-order differentials. In particular, the cosimplicial structure on sector forms includes operations that capture the higher-order iterated partial derivatives of smooth functions, in coordinate-free form. References: G. S. H. Cruttwell and R. B. B. Lucyshyn-Wright, A simplicial foundation for de Rham cohomology in tangent categories, arXiv:1606.09080 (2016). J. E. White, The method of iterated tangents with applications in local Riemannian geometry, Pitman, 1982. From bauerk at ucalgary.ca Tue Jul 11 10:00:10 2017 From: bauerk at ucalgary.ca (Kristine Bauer) Date: Tue Jul 11 10:00:13 2017 Subject: [Alta-Logic] CUMC festival on Friday Message-ID: Dear colleagues, I would like to invite you to preview the Calgary contributions to the Canadian Undergraduate Math Conference which will take place next week in Montreal. The five students who are giving talks have agreed to give their talks locally in Calgary first, and will do so on Friday afternoon. I will provide written feedback forms which can be used to record comments to help the students improve their talks, and there will be time for questions and comments between the talks and following the session. The talks are 20 minutes each and we will offer them in parallel sessions, as in the schedule below. Please drop in as you would like! It will be a really good opportunity to see what kind of things our undergraduates are doing in math outside the classroom. Cheers, Kristine Session 1: MS 319 2:30 pm Speaker: Vanessa Pizante Title: The Mean Variance Hedging Problem for a Contingent Claim in a Two Dimensional Binomial Model Abstract: In this presentation, we will specifically find the mean variance hedging portfolio for an exchange option in a two period, two dimensional binomial model. The problem of or finding the mean variance hedging portfolio for any contingent claim involves an incomplete market, meaning there is no replicating portfolio corresponding to the claim. Equivalently, there does not exist a unique risk neutral probability corresponding to the model. We utilize dynamical programming to find the optimal replicating strategy for the exchange option in this market. We then use the optimal policy to find a price for the exchange option. 3:00pm Speaker: Aiden Huffman Title: SIC(K) Measurements Abstract: Measurements lay at the heart of how we interpret quantum mechanics. One class of measurements of interest are SIC-POVMs, Positive Operator Valued Measurements which are both Symmetric and Informationally Complete. This class of measurements gives a nice framework for understanding finite dimensional quantum states probabilistically. In this talk we will introduce the SIC representation of quantum states and their relationship to the Bloch sphere, we will also investigate how quantum channels can be viewed in this representation. Session 2: MS 371 2:30pm Speaker: Ethan White Title: Different Necklaces Abstract: At the 2000 World Puzzle Championship Bernardo Santos asked if the integers 1 to 15 could be arranged in a chain such that adjacent numbers summed to squares. This problem has inspired many variations, including the generalization to arbitrary length, and examination of square differences, instead of sums. With Renate Scheidler, Richard Guy and I answered this question, and began to investigate necklaces where any two differences are allowed. The numbers of such necklaces always seems to satisfy a linear recurrence relation, but a proof of this result appears elusive for all but the smallest difference values. 3:00 pm Speaker: Reginald Lybbert Title: Blowing Up Singularities: A Foray into Algebraic Geometry Abstract: Algebraic geometry is the study of solution sets to multivariate polynomial equations via algebraic methods. These solution sets are known as algebraic varieties. Oftentimes, we will run into special points on these varieties, known as singularities. We desire to find other varieties, which are 'nearly' isomorphic to these singular varieties, but which lack any singularities. This is known as resolving the singularities. In this talk, we will introduce these concepts and discuss the process of blowing up singularities, through which they can be resolved. From bauerk at ucalgary.ca Tue Jul 11 14:56:37 2017 From: bauerk at ucalgary.ca (Kristine Bauer) Date: Tue Jul 11 14:56:40 2017 Subject: [Alta-Logic] CUMC festival on Friday In-Reply-To: References: Message-ID: <173E2719-AEFF-4AE6-AFEF-0E48AFDC49D0@ucalgary.ca> Hello all, Thanks to everyone who pointed out the conflict between the CUMC talks and Lauren DeDieu?s talk on Friday. We are working on resolving this conflict, so please stay tuned and I will send an adjusted schedule. Also, I seem to have made a cut-and-paste error. There is indeed a 5th CUMC talk, whose title and abstract are below. My apologies to Adam Humeniuk for the oversight! Cheers, Kristine Speaker: Adam Humeniuk Title: Rings of Functions and the Gelfand Transform: an Intro to C*-algebras Abstract: The set $C(X)$ of continuous complex-valued functions on a space $X$ is simultaneously a commutative ring, a vector space, and a topological space (a commutative Banach algebra). Algebraic properties of this ring encode geometric properties of the space, e.g. ideals correspond naturally to closed subspaces. Consider a dual problem: given a commutative Banach algebra $\mathcal{A}$, can we build a space $X$ on which $\mathcal{A}$ is the ring of functions $C(X)$? I will sketch how to do so; this is called the Gelfand transform. I'll identify the class of algebras for which $\mathcal{A}\cong C(X)$. These are the commutative C*-algebras. Time permitting, I'll give a categorical perspective of the Gelfand transform. > On Jul 11, 2017, at 10:00 AM, Kristine Bauer wrote: > > > > Dear colleagues, > > I would like to invite you to preview the Calgary contributions to the Canadian Undergraduate Math Conference which will take place next week in Montreal. The five students who are giving talks have agreed to give their talks locally in Calgary first, and will do so on Friday afternoon. I will provide written feedback forms which can be used to record comments to help the students improve their talks, and there will be time for questions and comments between the talks and following the session. The talks are 20 minutes each and we will offer them in parallel sessions, as in the schedule below. Please drop in as you would like! It will be a really good opportunity to see what kind of things our undergraduates are doing in math outside the classroom. > > Cheers, > Kristine > > > Session 1: MS 319 > > 2:30 pm > Speaker: Vanessa Pizante > Title: The Mean Variance Hedging Problem for a Contingent Claim in a Two Dimensional Binomial Model > > Abstract: In this presentation, we will specifically find the mean variance hedging portfolio for an exchange option in a two period, two dimensional binomial model. The problem of or finding the mean variance hedging portfolio for any contingent claim involves an incomplete market, meaning there is no replicating portfolio corresponding to the claim. Equivalently, there does not exist a unique risk neutral probability corresponding to the model. We utilize dynamical programming to find the optimal replicating strategy for the exchange option in this market. We then use the optimal policy to find a price for the exchange option. > > 3:00pm > Speaker: Aiden Huffman > Title: SIC(K) Measurements > Abstract: Measurements lay at the heart of how we interpret quantum mechanics. One class of measurements of interest are SIC-POVMs, Positive Operator Valued Measurements which are both Symmetric and Informationally Complete. This class of measurements gives a nice framework for understanding finite dimensional quantum states probabilistically. In this talk we will introduce the SIC representation of quantum states and their relationship to the Bloch sphere, we will also investigate how quantum channels can be viewed in this representation. > > Session 2: MS 371 > > 2:30pm > Speaker: Ethan White > Title: Different Necklaces > Abstract: At the 2000 World Puzzle Championship Bernardo Santos asked if the integers 1 to 15 could be arranged in a chain such that adjacent numbers summed to squares. This problem has inspired many variations, including the generalization to arbitrary length, and examination of square differences, instead of sums. With Renate Scheidler, Richard Guy and I answered this question, and began to investigate necklaces where any two differences are allowed. The numbers of such necklaces always seems to satisfy a linear recurrence relation, but a proof of this result appears elusive for all but the smallest difference values. > > 3:00 pm > Speaker: Reginald Lybbert > Title: Blowing Up Singularities: A Foray into Algebraic Geometry > Abstract: Algebraic geometry is the study of solution sets to multivariate polynomial equations via algebraic methods. These solution sets are known as algebraic varieties. Oftentimes, we will run into special points on these varieties, known as singularities. We desire to find other varieties, which are 'nearly' isomorphic to these singular varieties, but which lack any singularities. This is known as resolving the singularities. In this talk, we will introduce these concepts and discuss the process of blowing up singularities, through which they can be resolved._______________________________________________ > This message was sent to all subscribers of alta-logic-l > To unsubscribe, see instructions at: > http://www.ucalgary.ca/it/email/mailman > > E-mail: alta-logic-l@mailman.ucalgary.ca > Homepage: http://mailman.ucalgary.ca/mailman/listinfo/alta-logic-l From bauerk at ucalgary.ca Wed Jul 12 16:57:16 2017 From: bauerk at ucalgary.ca (Kristine Bauer) Date: Wed Jul 12 16:57:20 2017 Subject: [Alta-Logic] CUMC festival on Friday In-Reply-To: References: Message-ID: <1B20D4C6-C759-412D-94A1-121CD1900226@ucalgary.ca> Dear colleagues, We have rescheduled the CUMC talks on Friday, which will now begin at 3:00 pm. To remind you, the five undergraduate students from our department who are giving talks have agreed to preview their talks for us on Friday afternoon. I'll provide written feedback forms so that you can offer suggestions and encouragement for their talks. The talks are 20 minutes each, in parallel sessions, as below. Cheers, Kristine Session 1: MS 319 3:00 pm Speaker: Vanessa Pizante Title: The Mean Variance Hedging Problem for a Contingent Claim in a Two Dimensional Binomial Model Abstract: In this presentation, we will specifically find the mean variance hedging portfolio for an exchange option in a two period, two dimensional binomial model. The problem of or finding the mean variance hedging portfolio for any contingent claim involves an incomplete market, meaning there is no replicating portfolio corresponding to the claim. Equivalently, there does not exist a unique risk neutral probability corresponding to the model. We utilize dynamical programming to find the optimal replicating strategy for the exchange option in this market. We then use the optimal policy to find a price for the exchange option. 3:30pm Speaker: Aiden Huffman Title: SIC(K) Measurements Abstract: Measurements lay at the heart of how we interpret quantum mechanics. One class of measurements of interest are SIC-POVMs, Positive Operator Valued Measurements which are both Symmetric and Informationally Complete. This class of measurements gives a nice framework for understanding finite dimensional quantum states probabilistically. In this talk we will introduce the SIC representation of quantum states and their relationship to the Bloch sphere, we will also investigate how quantum channels can be viewed in this representation. Session 2: MS 371 3:00pm Speaker: Ethan White Title: Different Necklaces Abstract: At the 2000 World Puzzle Championship Bernardo Santos asked if the integers 1 to 15 could be arranged in a chain such that adjacent numbers summed to squares. This problem has inspired many variations, including the generalization to arbitrary length, and examination of square differences, instead of sums. With Renate Scheidler, Richard Guy and I answered this question, and began to investigate necklaces where any two differences are allowed. The numbers of such necklaces always seems to satisfy a linear recurrence relation, but a proof of this result appears elusive for all but the smallest difference values. 3:30 pm Speaker: Reginald Lybbert Title: Blowing Up Singularities: A Foray into Algebraic Geometry Abstract: Algebraic geometry is the study of solution sets to multivariate polynomial equations via algebraic methods. These solution sets are known as algebraic varieties. Oftentimes, we will run into special points on these varieties, known as singularities. We desire to find other varieties, which are 'nearly' isomorphic to these singular varieties, but which lack any singularities. This is known as resolving the singularities. In this talk, we will introduce these concepts and discuss the process of blowing up singularities, through which they can be resolved. 4:00 pm Speaker: Adam Humeniuk Title: Rings of Functions and the Gelfand Transform: an Intro to C*-algebras Abstract: The set $C(X)$ of continuous complex-valued functions on a space $X$ is simultaneously a commutative ring, a vector space, and a topological space (a commutative Banach algebra). Algebraic properties of this ring encode geometric properties of the space, e.g. ideals correspond naturally to closed subspaces. Consider a dual problem: given a commutative Banach algebra $\mathcal{A}$, can we build a space $X$ on which $\mathcal{A}$ is the ring of functions $C(X)$? I will sketch how to do so; this is called the Gelfand transform. I'll identify the class of algebras for which $\mathcal{A}\cong C(X)$. These are the commutative C*-algebras. Time permitting, I'll give a categorical perspective of the Gelfand transform. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170712/c020ee2c/attachment.html From jdgall84 at gmail.com Wed Aug 9 13:34:53 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Wed Aug 9 13:35:38 2017 Subject: [Alta-Logic] peripatetic seminar Friday, August 11, at 2pm Message-ID: Speaker: Jonathan Gallagher Location: ICT 616 @ 2 pm on Friday, August 11 Title: Scott, Koymans, and Beyond Abstract: Dana Scott, in "Relating theories of the lambda calculus" sought to show that the same techniques for modelling the simply typed lambda calculus can be used to model the untyped lambda calculus. He essentially constructed an adjunction between lambda theories T and cartesian closed categories X with a chosen reflexive object U: CL(T) ---> (X,U) ----------------------- T ---> Th(X,U) with the property that Th(CL(T)) \simeq T In other words, every lambda theory T has a model M, whose theory is equivalent to T. This is now called the Scott-Koymans theorem. In this talk, we will give a modern presentation of the classifying category of a lambda theory, and the theory of a model, using Turing categories with an extra property called canonical codes (or perhaps latently closed), and use this to reconstruct the Scott-Koymans theorem. Footnote: Koymans' contribution was to characterize the difference between lambda-algebras and lambda-models. One can make a subtle mistake about substitutional properties when interpreting into points via a pseudostructure on X(1,U). Koymans' contribution is vital, but we will steer around issues with points. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170809/ab957b98/attachment.html From bauerk at ucalgary.ca Mon Aug 14 12:47:01 2017 From: bauerk at ucalgary.ca (Kristine Bauer) Date: Mon Aug 14 12:47:04 2017 Subject: [Alta-Logic] Fwd: Seminar by Dr. Rick Churchill - Tuesday, August 15 References: Message-ID: Begin forwarded message: From: Karen Seyffarth > Subject: Seminar by Dr. Rick Churchill - Tuesday, August 15 Date: 11 August, 2017 1:55:49 PM MDT To: "faculty@math.ucalgary.ca" >, Richard c Churchill > Cc: Robin Cockett > Date & time: Tuesday, August 15, 2017 from 14:00 to 15:00 Location: MS 319 Speaker: Dr. R.C. Churchill (Hunter College and Graduate Center, CUNY, and the University of Calgary) Title: What are the ``Models'' of Model Theory? Abstract: Model theory, which often appears to reside midway between mathematics and formal logic, has recently made significant contributions to pure mathematics; in particular to number theory and differential algebra. In this talk I will define ``theories?' and their associated ``models'' in purely set-theoretic terms in an attempt to open the subject up to a wider audience. All are welcome! ?Karen -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170814/3b9718a7/attachment.html From jdgall84 at gmail.com Mon Aug 14 15:03:11 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Mon Aug 14 15:03:56 2017 Subject: [Alta-Logic] peripatetic seminar this wednesday! Message-ID: Location: Wednesday, August 16th, in ICT 616 at 2pm Speaker: Brenda Johnson (Union) Title: Functor Calculus and Precalculus Abstract: Functor calculi have been developed in a variety of forms and contexts for use in algebraic topology and homological algebra. Examples include the manifold calculus of Tom Goodwillie and Michael Weiss, Goodwillie's calculus of homotopy functors, Weiss' orthogonal calculus, and the discrete calculi for abelian and simplicial model categories developed with Kristine Bauer and Randy McCarthy. After reviewing common features of these calculi, I will show how the discrete calculus tower is constructed and describe work in progress with Kathryn Hess to identify a general framework, inspired by the discrete calculus, that can be used to generate functor calculi. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170814/e9a63dd9/attachment.html From jdgall84 at gmail.com Mon Aug 14 16:02:01 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Mon Aug 14 16:02:46 2017 Subject: [Alta-Logic] peripatetic (tutorial) seminar tomorrow Message-ID: Location: Tuesday, August 15th, at 12:15 pm, in ICT 616 Location note: Feel free to bring your lunch and your notebook! Speaker: Jonathan Gallagher Title: A tutorial on the Scott--Koymans [*] theorem part 2 Abstract: We will continue our investigation into the modernization of the Scott-Koymans theorem. This theorem says, roughly, that the semantics of the untyped lambda calculus into CCCs with a reflexive object, is sound and complete -- in fact it says: Theorem: Every lambda theory T, has a model M, whose theory is equivalent to T. Moroever, these models are always are given by a reflexive object in a CCC. Last time we stopped at the definition of the category of lambda theories. This time we will continue the investigation by considering the "semantic part", and move towards constructing the adjunction between syntax and semantics. Footnote: Really, [*] = [1-5] 1) Scott (`80) "Relating theories of the lambda calculus" 2) Hindey and Longo (`80) "Lambda-calculus models and extensionality" 3) Meyer (`82) "What is a model of the lambda calculus?" 4) Barendregt and Koymans (`80) "Comparing some classes of lambda calculus models" 5) Koymans (`82) "Models of the lambda calculus" -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170814/54e685b1/attachment.html From jdgall84 at gmail.com Tue Aug 15 15:19:16 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Tue Aug 15 15:20:01 2017 Subject: [Alta-Logic] peripatetic seminars this week Message-ID: Just a reminder, Brenda Johnson is speaking *tomorrow* at *2pm* in *ICT 616* on Functor Calculus and Precalculus. Also, on Thursday, there will be another peripatetic seminar on the models of the untyped lambda calculus, and the modernization of the Scott-Koymans theorem. This will again be a lunchtime talk: *Thursday 12:15 pm *in *ICT 616.* The title and abstract are the same as today's talk. And again, bring your lunch. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170815/08b3f0be/attachment.html From bauerk at ucalgary.ca Tue Aug 22 16:08:32 2017 From: bauerk at ucalgary.ca (Kristine Bauer) Date: Tue Aug 22 16:08:34 2017 Subject: [Alta-Logic] Homotopy Theory Course this fall Message-ID: <623053A7-6EB3-4DD0-B27B-EFC020CE0FCC@ucalgary.ca> Hello, This fall, Rick Jardine from UWO is offering his homotopy theory course remotely via the magic of the internet. At least two of us in math plan to attend the course remotely. If you are interested in joining us, please let me know so that I reserve a large enough room (we'll get a room with a shared screen to promote discussion following lectures). For details about the course, please see: http://uwo.ca/math/faculty/jardine/courses/homth/homotopy_theory.html The course is based on the Goerss-Jardien simplicial homotopy theory book. You can also participate individually by installing the software on your own computer or laptop - if you are interested in doing so please contact Rick directly. He can be reached at the address: jardine@uwo.ca. The course is tentatively scheduled for MWF @ 3pm. This is subject to change, though, so please check in with me! Cheers, Kristine -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170822/cb6f1f31/attachment.html From jdgall84 at gmail.com Tue Aug 29 01:19:19 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Tue Aug 29 01:20:04 2017 Subject: [Alta-Logic] peripatetic seminar wednesday Message-ID: There is a peripatetic seminar this Wednesday at a special time. Location: ICT 616 at 12 pm (noon) on Wednesday August 30 Speaker: Daniel Satanove Title: Internal Full Subcategories Abstract: This talk will introduce the notion of an internal category as a certain kind of object in a category. The goal of this talk is to examine what it means for a category in X to be a full subcategory of X. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170829/443d71e0/attachment.html From pvsriniv at gmail.com Wed Aug 30 09:14:19 2017 From: pvsriniv at gmail.com (Priyaa Varshinee Srinivasan) Date: Wed Aug 30 09:14:26 2017 Subject: [Alta-Logic] peripatetic seminar wednesday In-Reply-To: References: Message-ID: <1CE67870-8FDD-4DD3-AA41-4E2FAAC7841E@gmail.com> Lets please start at 12:15 pm. My bro is leaving Calgary today and I want to take him out for lunch. Hayley can?t join us after the seminar. Will appreciate if the seminar could be postponed by 15 mins. Thanks Priyaa > On Aug 29, 2017, at 1:19 AM, Jonathan Gallagher wrote: > > There is a peripatetic seminar this Wednesday at a special time. > > Location: ICT 616 at 12 pm (noon) on Wednesday August 30 > Speaker: Daniel Satanove > Title: Internal Full Subcategories > Abstract: > This talk will introduce the notion of an internal category as > a certain kind of object in a category. The goal of this > talk is to examine what it means for a category in X to > be a full subcategory of X. > _______________________________________________ > This message was sent to all subscribers of alta-logic-l > To unsubscribe, see instructions at: > http://www.ucalgary.ca/it/email/mailman > > E-mail: alta-logic-l@mailman.ucalgary.ca > Homepage: http://mailman.ucalgary.ca/mailman/listinfo/alta-logic-l -------------- next part -------------- A non-text attachment was scrubbed... Name: signature.asc Type: application/pgp-signature Size: 801 bytes Desc: Message signed with OpenPGP using GPGMail Url : http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170830/8ec40516/signature.bin From bauerk at ucalgary.ca Sat Sep 2 23:48:40 2017 From: bauerk at ucalgary.ca (Kristine Bauer) Date: Sat Sep 2 23:48:55 2017 Subject: [Alta-Logic] UWO homotopy theory course Message-ID: <50D20F31-5514-4445-A12E-AE4C659B9231@ucalgary.ca> Hello all, Just a short note to let you know that the homotopy theory course at the University of Western Ontario (which we had planned to host locally by internet connection) will be delayed until the winter term due to local scheduling issues. Thanks, Kristine From jdgall84 at gmail.com Tue Sep 5 18:37:18 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Tue Sep 5 18:38:04 2017 Subject: [Alta-Logic] peripatetic seminar tomorrow Message-ID: We are kicking the peripatetic seminar off, tomorrow, at 2pm with a talk by a new postdoc in our group -- Matthew Burke. Details below. Location: ICT 616 at 2pm on Wednesday Sept. 6 Speaker: Matthew Burke Title: Lie?s Third Theorem using an Intuitionistic Double Negation Abstract: In this talk we will describe the construction of a local approximation of a category in a certain well adapted model of synthetic differential geometry. This approximation is analogous to the germ of a local Lie group and is constructed using an intuitionistic double negation. After giving the basic definitions we will sketch a proof of Lie?s third theorem in this context. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170905/67012845/attachment.html From jdgall84 at gmail.com Tue Sep 12 15:31:01 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Tue Sep 12 15:31:47 2017 Subject: [Alta-Logic] talk tomorrow Message-ID: Location: ICT 616 at 12:15 pm. Wednesday, Sept. 13. Speaker: Priyaa Srinivasan *Title*: Environment structures for dagger compact closed categories *Abstract*: In this talk, I will introduce environment structure for a dagger compact closed category and purification for an environment structure. I will provide an example environment structure in the category of Hilbert spaces and completely positive maps. I will also prove the following theorem: Suppose C is a dagger compact closed category and C_{pure} is dagger compact closed subcategory of C. (C,C_{pure}) has an environment structure with purification. Then, there exists a dagger functor from a subcategory of C_{pure} - whose objects are endomorphism algebras and completely positive maps - to C. Moreover, the functor is left invertible up to equivalence. Environment structures are used in the construction and verification of protocols in the category of finite-dimensional Hilbert spaces and completely positive maps. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170912/ebd4503b/attachment.html From jdgall84 at gmail.com Tue Sep 19 17:46:53 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Tue Sep 19 17:47:38 2017 Subject: [Alta-Logic] talk: Friday at 11:15 am in ICT 616 Message-ID: There is a talk this Friday! Details below. *Location*: ICT 616 *Date*: Friday at 11:15 am. September 22. *Speaker*: Matthew Burke *Title*: Sites of Smooth Affine Schemes *Abstract*: In this talk we will sketch the construction of a few well-adapted models of synthetic differential geometry. Then we will recall the definition of an intuitionistic order relation and show how to define one in the Dubuc topos. Finally we will formulate Lie?s third theorem in a manner appropriate to this setup. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170919/e2eeac7f/attachment.html From bauerk at ucalgary.ca Fri Sep 22 15:12:28 2017 From: bauerk at ucalgary.ca (Kristine Bauer) Date: Fri Sep 22 15:12:31 2017 Subject: [Alta-Logic] Peripatetic Seminar Thursday September 28 Message-ID: <16761CC5-15E5-49BC-B550-4CC9681393B2@ucalgary.ca> Next Thursday, Ben Williams from UBC will be visiting Calgary as part of the Peripatetic Seminar Lecture Series. The details for his talk follow this message. If you are interested in meeting Dr. Williams or joining us for dinner, please let me know. Cheers, Kristine Date & Time: Thursday, September 28 @ 11am Place: MS 431 Speaker: Ben Williams Title: Motivic homotopy groups and a conjecture of Suslin Abstract: Fix an infinite field k. Associated to the group GL_n(F), one can form the +-construction of the classifying space BGL_n(F)^+. As n increases, both the homotopy groups and homology groups of this space stabilize; the homotopy groups give the higher algebraic K-theory of F, whereas the cokernel of the stabilization map in homology was proved by Suslin in the 1980s to give the Milnor K-theory of the field F, an older invariant of the field. There is a Hurewicz map relating homotopy to homology, and therefore a comparison map from algebraic K_n(F) to the Milnor K-group K^M_n(F). A longstanding conjecture of Suslin is that the image of this map is the subgroup (n-1)! K^M_n(F). By recasting this as a problem in motivic homotopy theory, we can borrow intuition and results from the calculation of the unstable homotopy groups of spheres and BU_n, and this allows us to settle the conjecture in the case n=5. This is joint work with Aravind Asok and Kirsten Wickelgren. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170922/fd61ed25/attachment.html From bauerk at ucalgary.ca Thu Sep 28 09:32:02 2017 From: bauerk at ucalgary.ca (Kristine Bauer) Date: Thu Sep 28 09:32:06 2017 Subject: Fwd: [Alta-Logic] Peripatetic Seminar Thursday September 28 References: <16761CC5-15E5-49BC-B550-4CC9681393B2@ucalgary.ca> Message-ID: <44B93A85-FF0B-4FAC-B209-A03A3DFEA23F@ucalgary.ca> Just a reminder about today's Peripatetic Seminar at 11am in MS 431. Ben Williams from UBC will give a talk title "Motivic homotopy groups and a conjecture of Suslin". Cheers, Kristine Begin forwarded message: From: Kristine Bauer > Subject: [Alta-Logic] Peripatetic Seminar Thursday September 28 Date: 22 September, 2017 3:12:28 PM MDT To: "dept@math.ucalgary.ca" >, "alta-logic-l@mailman.ucalgary.ca" > Next Thursday, Ben Williams from UBC will be visiting Calgary as part of the Peripatetic Seminar Lecture Series. The details for his talk follow this message. If you are interested in meeting Dr. Williams or joining us for dinner, please let me know. Cheers, Kristine Date & Time: Thursday, September 28 @ 11am Place: MS 431 Speaker: Ben Williams Title: Motivic homotopy groups and a conjecture of Suslin Abstract: Fix an infinite field k. Associated to the group GL_n(F), one can form the +-construction of the classifying space BGL_n(F)^+. As n increases, both the homotopy groups and homology groups of this space stabilize; the homotopy groups give the higher algebraic K-theory of F, whereas the cokernel of the stabilization map in homology was proved by Suslin in the 1980s to give the Milnor K-theory of the field F, an older invariant of the field. There is a Hurewicz map relating homotopy to homology, and therefore a comparison map from algebraic K_n(F) to the Milnor K-group K^M_n(F). A longstanding conjecture of Suslin is that the image of this map is the subgroup (n-1)! K^M_n(F). By recasting this as a problem in motivic homotopy theory, we can borrow intuition and results from the calculation of the unstable homotopy groups of spheres and BU_n, and this allows us to settle the conjecture in the case n=5. This is joint work with Aravind Asok and Kirsten Wickelgren. _______________________________________________ This message was sent to all subscribers of alta-logic-l To unsubscribe, see instructions at: http://www.ucalgary.ca/it/email/mailman E-mail: alta-logic-l@mailman.ucalgary.ca Homepage: http://mailman.ucalgary.ca/mailman/listinfo/alta-logic-l -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20170928/cc106293/attachment.html From jdgall84 at gmail.com Thu Oct 5 15:36:23 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Oct 5 15:37:07 2017 Subject: [Alta-Logic] two talks tomorrow Message-ID: There are two talks tomorrow: The peripatetic seminar will begin tomorrow at *11:15 am* in *ICT 616, Oct 6.* *Talk 1:* *Speaker: *Matthew Burke *Title*: Sites of Smooth Affine Schemes *Abstract*: In this talk we will sketch the construction of a few well-adapted models of synthetic differential geometry. Then we will recall the definition of an intuitionistic order relation and show how to define one in the Dubuc topos. Finally we will formulate Lie?s third theorem in a manner appropriate to this setup. *Talk 2:* *Speaker*: Ben MacAdam *Title*: Linear/Non-Linear models in a 2-category: Part 1 *Abstract*: A linear/non-linear model is a monoidal adjunction between a cartesian category and symmetric monoidal category. Such an adjunction gives rise to a coalgebraic modality which in turn a model of MELL. Birkedal showed that these results translate easily to fibred monoidal categories -- here one obtains a model in each fiber category. We show that many of these results can be further generalized to pseudomonoids in 2-categories with suitable universal properties. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20171005/2d298e8e/attachment.html From jdgall84 at gmail.com Thu Oct 12 17:13:49 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Oct 12 17:14:33 2017 Subject: [Alta-Logic] peripatetic seminar tomorrow Message-ID: *Location: *ICT 616 *Time: *Friday the 13th at 11:15 am *Speaker: *Matthew Burke *Title*: Sites of Smooth Affine Schemes *Abstract*: In this talk we will sketch the construction of a few well-adapted models of synthetic differential geometry. Then we will recall the definition of an intuitionistic order relation and show how to define one in the Dubuc topos. Finally we will formulate Lie?s third theorem in a manner appropriate to this setup. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20171012/9a443f86/attachment.html From jdgall84 at gmail.com Thu Oct 19 14:26:29 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Oct 19 14:27:13 2017 Subject: [Alta-Logic] talk tomorrow Message-ID: The next meeting of the peripatetic seminar will be held tomorrow, *October 20*, at *11:15* am in *ICT 616*. *Speaker*: Jonathan Gallagher *Title*: Ditching squares for triangles -- confluence in under an hour *Abstract*: In this talk, we will give a proof of the Church-Rosser theorem for the lambda-calculus that is due to Takahashi 1995. Takashi used a property of developments -- that they are always developing towards a 'goal' -- to give the shortest known proof of confluence for the lambda calculus. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20171019/bace6ba9/attachment.html From jdgall84 at gmail.com Thu Oct 26 11:50:44 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Oct 26 11:51:27 2017 Subject: [Alta-Logic] peripatetic seminar tomorrow Message-ID: The next meeting of the peripatetic seminar will be held tomorrow. Details below! *Where and When: *ICT 616 11:15 am Friday, October 27 *Who: *Ben MacAdam and Priyaa Srinivasan *What and why:* *Talk 1 - Ben MacAdam* *Title*: Linear/Non-Linear models in a 2-category: Part 1 *Abstract*: A linear/non-linear model is a monoidal adjunction between a cartesian category and symmetric monoidal category. Such an adjunction gives rise to a coalgebraic modality which in turn a model of MELL. Birkedal showed that these results translate easily to fibred monoidal categories ? here one obtains a model in each fiber category. We show that many of these results can be further generalized to pseudomonoids in 2-categories with suitable universal properties. *Talk 2 - Priyaa Srinivasan* *Title: Structures for decoherent* *Abstract:* This talk will introduce and develop the structure required for studying decoherence in certain monoidal categories. Our driving example is a decoherence structure in CP*[FHilb] Our goal is to move towards understanding the following: Theorem: Let C be a dagger compact closed category and C_{pure} be a subcategory of C that inherits the dagger and compact closed structure. Suppose C_{pure} has a decoherence structure with purification, then there exists an invertible dagger functor from CP*[C_{pure}] -> C such that F(f \otimes g) = F(f) \otimes F(g). -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20171026/f52710b6/attachment.html From jdgall84 at gmail.com Thu Oct 26 11:54:30 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Oct 26 11:55:14 2017 Subject: [Alta-Logic] peripatetic seminar tomorrow Message-ID: The details for the seminar can also be found on our website at http://peripatetic-seminar.cpsc.ucalgary.ca/wp/?event=ben-macadam-and-priyaa-srinivasan -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20171026/5cbc89f1/attachment.html From rzach at ucalgary.ca Thu Oct 26 13:18:08 2017 From: rzach at ucalgary.ca (Richard Zach) Date: Thu Oct 26 13:18:17 2017 Subject: [Alta-Logic] Modal Logic in W18 Message-ID: <4143a64e-aeaf-a8db-7445-76fa345f8178@ucalgary.ca> Just FYI, I'm teaching a 500/600 level course on Modal Logic (including intuitionistic logic) next term. -- Richard Zach ...... http://www.ucalgary.ca/rzach/ Professor, Department of Philosophy University of Calgary, Calgary AB T2N 1N4, Canada From jdgall84 at gmail.com Thu Nov 2 16:18:35 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Nov 2 16:19:19 2017 Subject: [Alta-Logic] peripatetic seminar tomorrow Message-ID: The next meeting of the peripatetic seminar will be held tomorrow *Friday, November 3, *at* 11:15 am* in *ICT 616*. *Speaker*: Jonathan Gallagher *Title*: Differentiation is progressive *Abstract*: The Takahashi triangle property for abstract rewriting systems contrasts 'good' and 'bad' developments of a simultaneous set of rewrites: for every bad development, there is a better development that converts the result into the result of the good development. Takahashi used the triangle property to study the confluence and standardization theorems of the lambda calculus at the same time. In this talk, we will show that the equational theory of differentiation can be cast in terms of rewriting modulo equations, and that moreover developments in this rewriting system have a version of the triangle property that is applicable to rewriting modulo equations. In particular, this rewriting system has the Church-Rosser modulo property. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20171102/a93cc7a1/attachment.html From jdgall84 at gmail.com Mon Nov 6 09:55:39 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Mon Nov 6 09:56:24 2017 Subject: [Alta-Logic] Peripatetic Seminar Invited Lecture Series Message-ID: We are pleased to announce that the next speaker in the Peripatetic Seminar Invited Lecture Series is Geoff Cruttwell, speaking tomorrow at 5pm in ICT 616. Details below. *Speaker*: Geoff Cruttwell *Title*: Affine spaces in a tangent category *Location*: ICT 616, November 6 at 5 pm. *Abstract*: Affine manifolds are smooth manifolds with a particular choice of charts such that each transition function is affine. In addition to being interesting in their own right, recent work of Jubin showed that the category of affine manifolds has a wide variety of monads and comonads on it, with many distributive laws relating these monads and comonads. In this talk, we shall see how to work with affine manifolds in a tangent category. A key result of Auslander and Markus shows that an affine structure on a smooth manifold M is equivalent to giving a flat, torsion-free connection on the tangent bundle of M; this we take as the definition of an affine object in a tangent category. We give several alternate characterizations of such connections (some of which appear to be new in differential geometry), show how to extend Jubin's results on the existence of monads and comonads to this setting, and find additional distributive laws between these monads and comonads that Jubin did not discover. This is joint work Rick Blute and Rory Lucyshyn-Wright. See also http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20171106/aea864a6/attachment.html From jdgall84 at gmail.com Thu Nov 9 18:59:08 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Nov 9 19:00:12 2017 Subject: [Alta-Logic] peripatetic seminar tomorrow Message-ID: Details can be found here: http://peripatetic-seminar.cpsc.ucalgary.ca/wp/?event=ben-macadam-and-priyaa-srinivasan-2 Alternatively see below. *Where*: ICT616 *When*: 11:15 am on Friday, Nov. 10 *Talk 1 - Ben MacAdam* *Title*: Linear/Non-Linear models in a 2-category: Part 1 *Abstract*: A linear/non-linear model is a monoidal adjunction between a cartesian category and symmetric monoidal category. Such an adjunction gives rise to a coalgebraic modality which in turn a model of MELL. Birkedal showed that these results translate easily to fibred monoidal categories ? here one obtains a model in each fiber category. We show that many of these results can be further generalized to pseudomonoids in 2-categories with suitable universal properties. *Talk 2 - Priyaa Srinivasan* *Title: Structures for decoherent* *Abstract:* This talk will introduce and develop the structure required for studying decoherence in certain monoidal categories. Our driving example is a decoherence structure in CP*[FHilb] Our goal is to move towards understanding the following: Theorem: Let C be a dagger compact closed category and C_{pure} be a subcategory of C that inherits the dagger and compact closed structure. Suppose C_{pure} has a decoherence structure with purification, then there exists an invertible dagger functor from CP*[C_{pure}] -> C such that F(f \otimes g) = F(f) \otimes F(g). -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20171109/33c9cba9/attachment.html From jdgall84 at gmail.com Thu Nov 16 13:18:41 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Nov 16 13:19:26 2017 Subject: [Alta-Logic] peripatetic seminar tomorrow Message-ID: See http://peripatetic-seminar.cpsc.ucalgary.ca/wp/?event=cole-comfort for details about tomorrow's talk. The peripatetic seminar will meet: Where: ICT 616 When: Friday, November 17, 2017 at 11:15 Why: Cole Comfort is speaking Title: A Complete Classification of the Toffoli Gate with Ancillary bits Abstract: The Toffoli gate is a universal gate for classical reversible computation. This means that if we are allowed to fix the values of certain inputs and outputs (called ancillary bits), we can simulate any Boolean function from $\mathbb{Z}_2^n\to\mathbb{Z}_2^m$ with a circuit from $n\to m+k$ wires consisting only of Toffoli gates (with $k$ extra ignored outputs). Iwama found a complete set of identities for circuits solely consisting of Toffoli gates. I present a complete set of identities for the symmetric monoidal category generated by the Toffoli gate \emph{and ancillary bits}. I also provide a normal form for these circuits and prove an equivalence of categories into a subcategory of $\mathsf{PInj}$ -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20171116/997650eb/attachment.html From jdgall84 at gmail.com Thu Nov 23 15:37:56 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Nov 23 15:38:41 2017 Subject: [Alta-Logic] peripatetic seminar tomorrow Message-ID: *Location:* ICT 616, Friday November 24 at 11:15 am See http://peripatetic-seminar.cpsc.ucalgary.ca/wp/?event=cole-comfort-and-priyaa-srinivasan-or-priyaa-and-cole Or below for details: *Speaker: *Cole *Title*: A Complete Classification of the Toffoli Gate with Ancillary bits *Abstract*: The Toffoli gate is a universal gate for classical reversible computation. This means that if we are allowed to fix the values of certain inputs and outputs (called ancillary bits), we can simulate any Boolean function from $\mathbb{Z}_2^n\to\mathbb{Z}_2^m$ with a circuit from $n\to m+k$ wires consisting only of Toffoli gates (with $k$ extra ignored outputs). Iwama found a complete set of identities for circuits solely consisting of Toffoli gates. I present a complete set of identities for the symmetric monoidal category generated by the Toffoli gate \emph{and ancillary bits}. I also provide a normal form for these circuits and prove an equivalence of categories into a subcategory of $\mathsf{PInj}$ *Speaker: *Priyaa *Title: *Structures for decoherence *Abstract:* This talk will introduce and develop the structure required for studying decoherence in certain monoidal categories. Our driving example is a decoherence structure in CP*[FHilb] Our goal is to move towards understanding the following: Theorem: Let C be a dagger compact closed category and C_{pure} be a subcategory of C that inherits the dagger and compact closed structure. Suppose C_{pure} has a decoherence structure with purification, then there exists an invertible dagger functor from CP*[C_{pure}] -> C such that F(f \otimes g) = F(f) \otimes F(g). -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20171123/78525935/attachment.html From jdgall84 at gmail.com Thu Nov 30 19:46:24 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Nov 30 19:47:09 2017 Subject: [Alta-Logic] peripatetic seminar tomorrow Message-ID: We are pleased to announce that the peripatetic seminar will meet tomorrow at 11:15 am. *Location*: ICT 616 at 11:15 am on Friday December 1 *Speaker*: Priyaa Srinivasan *Title*: Structures for decoherence *Abstract:* The goal is this talk is to prove the following theorem about decoherence structures that have been introduced in my earlier talk: Theorem: Suppose a compact dagger category $\mathbb{C}$ comes with a compact dagger subcategory $\mathbb{C}_{Pure}$ and a decoherence structure with purification, then there is an isomorphism of categories between CP*[\mathbb{C}_{pure}] between \mathbb{C}. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20171130/fb730c92/attachment.html From jdgall84 at gmail.com Mon Dec 11 15:10:15 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Mon Dec 11 15:11:01 2017 Subject: [Alta-Logic] a very special peripatetic seminar Message-ID: Join us for the penultimate peripatetic seminar tomorrow at 2pm! http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ or *Speaker:* Kristine Bauer *Location: *ICT 616 on Tuesday December 12, 2 pm *Title: *Abelian functor calculus, derivatives, and operads *Abstract: *The first chain rules in functor calculus were established by Arone-Ching and Klein-Rognes, who considered functors of spaces or spectra. The Arone-Ching chain rule stemmed from earlier work of M. Ching, in which he established that the derivatives of the identity functor form an operad, whose homology is the classical Lie operad. The chain rule, in conjunction with Ching's earlier work, lead to a classification theorem for all functors of spaces or spectra. That is, it explained how you could produce a functor from its derivatives. However, Arone-Ching's work was quite complicated and difficult. One of the motivations for establishing a chain rule for abelian functor calculus was to try to look for a simplification of their work. Indeed, in BJORT, we established the chain rule by first establishing that the category of abelian categories is a cartesian differential category. This, together with the associated tangent structure, lead to a much simpler proof of the chain rule. Following the program laid out by Arone and Ching, we are now looking for the expected operad structure and classification theorems. In this talk, I will explain the derivative (as opposed to the directional derivative) for abelian functor calculus, and the candidate for our operad. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20171211/bf6473ad/attachment.html From jdgall84 at gmail.com Fri Dec 15 21:04:29 2017 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Fri Dec 15 21:05:19 2017 Subject: [Alta-Logic] two mini-talks on Monday 1pm Message-ID: There will be two mini talks given: Location: ICT 616 Time: Monday, December 18, in ICT 616, at 1pm. Speaker: Jonathan Gallagher Mini-title: Infinitely short paths Abstract: Let X be a space, that is, a type in homotopy type theory. Obtain two points in X that are infinitesimally close. We ask the following question: given a fixed point A, is the set of infinitesimally close points to A a reasonable notion of tangent space? This talk is based on conversations with Felix Wellen. Mini-title: Productive expansion reduction in the differential lambda calculus Abstract: Consider computing the derivative (f(x))'. One may use the chain rule to change this to f(x)'*x'; x' is of course 1, so f(x)' = f(x)'. In rewriting theory, we can consider the chain rule as a kind of expansion rule, and expansions like the above are not productive in the sense that they do not contribute towards a normal form. In this talk, we will introduce productive expansion reduction systems, and show how differentiation gives rise to a system where only 'good' expansions are performed. The notion of expansion reduction was used by Blute, Cockett, Seely, and Trimble in exploring circuits for linearly distributive categories. We had to tweak their definition slightly to get it to work for differentiation, but the idea is theirs. -------------- next part -------------- An HTML attachment was scrubbed... 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