From matthew.burke1 at ucalgary.ca Mon Jan 7 20:16:31 2019 From: matthew.burke1 at ucalgary.ca (Matthew Burke) Date: Mon Jan 7 20:16:36 2019 Subject: [Alta-Logic] Peripatetic seminar Message-ID: Speaker: JS Lemay Date and time: Wednesday, January 9th, 2019 at 14:00 Location: MS 337 (subject to booking tomorrow morning) Title: Differential Algebras in Codifferential Categories Abstract: Differential categories have lead to abstract formulations of several notions of differentiation such as, to list a few, the directional derivative, Kahler differentials, differential forms, smooth manifolds , and De Rham cohomology. Therefore, if the theory of differential categories wishes to champion itself as the axiomatization of the fundamentals of differentiation: differential algebras should fit naturally in this story. In this talk, I?ll talk about differential algebras and how they fit in the theory of differential categories. Preprint: https://arxiv.org/pdf/1803.02304.pdf http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ From matthew.burke1 at ucalgary.ca Mon Jan 14 12:14:55 2019 From: matthew.burke1 at ucalgary.ca (Matthew Burke) Date: Mon Jan 14 12:14:58 2019 Subject: [Alta-Logic] Peripatetic seminar Message-ID: <4EACCA4A-10B7-4758-81F1-3DFE6284C1FB@ucalgary.ca> Speaker: Ben MacAdam Date and time: Tuesday, January 15th, 2019 at 12:15 Location: MS 337 Title: Abstract Symplectic Geometry Abstract: In recent years, symplectic geometry has used increasingly sophisticated categorical and homotopical machinery. We will consider how tangent categories may simplify some of these constructions. http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ From jdgall84 at gmail.com Thu Jan 17 17:24:14 2019 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Thu Jan 17 17:24:57 2019 Subject: [Alta-Logic] stack seminar tomorrow! Message-ID: Hello everyone, Dragnet version: Stacks seminar tomorrow, January 18. Location: *MS 522 @ 1-2:30 pm. * Tomorrow we kick of the differential stacks seminar again. Since many of you weren't here for the final seminars we are going to give a quick review of how we introduced (split) stacks. Location: *MS 522 at 1 pm* Title: Differential (split) stacks in under one hour Abstract: In this talk we will review some of the highlights from last semester and then give a perspective on differential stacks that comes from Abstract Differential Geometry and tangent categories. Also, we are pleased to announce a contest, more details tomorrow. -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20190117/a4da1470/attachment.html From matthew.burke1 at ucalgary.ca Mon Jan 21 08:41:46 2019 From: matthew.burke1 at ucalgary.ca (Matthew Burke) Date: Mon Jan 21 08:41:50 2019 Subject: [Alta-Logic] Peripatetic seminar Message-ID: <246AB601-234F-4192-9D52-613632A27DEF@ucalgary.ca> Speaker: Cole Comfort Date and time: Tuesday, January 22nd, 2019 at 12:15 Location: MS 337 Title: Extending CNOT to real stabilizer quantum mechanics Abstract: The stabilizer formalism for quantum mechanics is an important tool for implementing fault tolerant quantum circuits. In this talk we first give a brief overview of the stabilizer formalism. We also will discuss the angle-free fragment of the ZX calculus, which is complete for the real fragment of stabilizer quantum mechanics. We use this fact to extend the category CNOT to be complete for this fragment of quantum mechanics. http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ From benmacadam at gmail.com Thu Jan 24 18:59:39 2019 From: benmacadam at gmail.com (Ben MacAdam) Date: Thu Jan 24 19:00:02 2019 Subject: [Alta-Logic] Stacks seminar postponed Message-ID: Hi Everyone, The stacks seminar is postponed this weak, we instead invite everyone to have a discussion session tomorrow (Friday) at 1:45 in MS 522. Cheers, Ben From matthew.burke1 at ucalgary.ca Mon Jan 28 09:06:19 2019 From: matthew.burke1 at ucalgary.ca (Matthew Burke) Date: Mon Jan 28 09:06:22 2019 Subject: [Alta-Logic] Peripatetic seminar Message-ID: Speaker: Daniel Satanove Date and time: Tuesday, January 29th, 2019 at 12:15 Location: MS 337 Title: Presentations of Theories Abstract: Every algebraic theory T with set of sorts S has a notion of free functor from the category Set^S which is constructed uniformly by Kan extension of models along the canonical interpretation, a functor between classifying categories, Cl(S) -> Cl(T) (where S is considered as a theory with no operations). This can be seen as a uniform way of constructing syntax for algebraic theories - the free functor sends a set of generators to the set of words formed by the operations of the theory on those generators. Furthermore, every object M in the categories of models Mod(T) is isomorphic to a presentation by free objects. In the case of groups, this is the familiar notion of a presentation by generators and relations < X | R >. Parts of this picture extend to essentially algebraic theories via sketches and Gabriel-Ulmer duality. I look at ways of getting a more complete picture and apply it to classifying categories for algebraic and essentially algebraic theories, so that the process of generating classifying categories can be seen as the same sort of syntax generation as for free groups and free algebras of algebraic theories. http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ From benmacadam at gmail.com Thu Jan 31 16:15:46 2019 From: benmacadam at gmail.com (Ben MacAdam) Date: Thu Jan 31 16:15:53 2019 Subject: [Alta-Logic] Stacks Seminar Message-ID: Hi everyone, There will be a stacks seminar tomorrow. Speaker: Ben MacAdam Time and Location: 1:30 PM, Friday January 31, MS537 Title: Enriched Categories and the Weak Yoneda lemma Abstract: We take the first step in defining enriched sheaves. We will introduce enriched categories and prove the weak version of the enriched Yoneda lemma. From matthew.burke1 at ucalgary.ca Mon Feb 4 14:32:25 2019 From: matthew.burke1 at ucalgary.ca (Matthew Burke) Date: Mon Feb 4 14:32:29 2019 Subject: [Alta-Logic] Peripatetic seminar Message-ID: <27800447-1579-4322-A334-04C78C3DB7DE@ucalgary.ca> Speaker: Rachel Hardeman Date and time: Tuesday, February 5th, 2019 at 12:15 Location: MS 337 Title: Cubical Sets and A-Homotopy Theory Abstract: In this talk, I will describe the cubical category and cubical sets. Then I will show how A-homotopy theory, a discrete homotopy theory for graphs, gives us an example of a cubical set. Time permitting, I will discuss how this cubical set might lead us to a chain complex. http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ From benmacadam at gmail.com Thu Feb 7 18:52:32 2019 From: benmacadam at gmail.com (Ben MacAdam) Date: Thu Feb 7 18:52:45 2019 Subject: [Alta-Logic] Stacks seminar Message-ID: <19E9C691-D7E5-4DF9-A380-7AB0DB85F696@gmail.com> Hi everyone, We are postponing the stacks seminar to next week, when we will cover the enriched Yoneda lemma. -Ben From matthew.burke1 at ucalgary.ca Mon Feb 11 12:59:38 2019 From: matthew.burke1 at ucalgary.ca (Matthew Burke) Date: Mon Feb 11 12:59:41 2019 Subject: [Alta-Logic] Peripatetic seminar Message-ID: <5271E116-A710-4559-8E52-B2EB1EEAD2C9@ucalgary.ca> Speaker: Geoff Vooys Date and time: Tuesday, February 12th, 2019 at 12:15 Location: MS 337 Title: A Topology on Categories of Locally Ringed Space and Applications to Arithmetic Geometry Abstract: In this talk we present some relevant background on locally ringed spaces and consider a problem that appears in arithmetic geometry. We then use this problem to motivate a class of functors that arise in arithmetic geometry, provide examples of these functors, and show how these functors can induce a Grothendieck topology on their codomains. We then use this topology and its topos of sheaves to make progress towards our motivating problem. http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ From bauerk at ucalgary.ca Thu Feb 14 15:18:15 2019 From: bauerk at ucalgary.ca (Kristine Bauer) Date: Thu Feb 14 15:18:18 2019 Subject: [Alta-Logic] next week's Peripatetic Message-ID: We are planning to have a seminar next week at the same time as usual (12:15 on Tuesday) - Priyaa Srinivasan plans to speak. If you are unable to attend due to the reading week but would otherwise like to go, would you please reply to this message. If many people can?t attend, we can consider postponing. Cheers, Kristine (with Matthew looking over my shoulder!) From benmacadam at gmail.com Thu Feb 14 23:22:41 2019 From: benmacadam at gmail.com (Ben MacAdam) Date: Thu Feb 14 23:22:49 2019 Subject: [Alta-Logic] Stacks seminar Message-ID: <9983D883-4F49-4618-8A26-6BB92E5A6409@gmail.com> Hi Everyone, The stacks seminar continues tomorrow as we get closer to the enriched Yoneda lemma. Title: Enriched ends Speaker: Ben MacAdam Time and location: Friday, February 15 at 1:30 in MS522 Abstract: We introduce the notion of an end in enriched category theory and prove the Fubini theorem. From matthew.burke1 at ucalgary.ca Mon Feb 18 10:16:25 2019 From: matthew.burke1 at ucalgary.ca (Matthew Burke) Date: Mon Feb 18 10:16:28 2019 Subject: [Alta-Logic] Peripatetic seminar Message-ID: <87C42707-D2F6-47ED-AEB3-42B6F5609DF5@ucalgary.ca> Speaker: Priyaa Srinivasan Date and time: Tuesday, February 19th, 2019 at 12:15 Location: MS 337 Title: Dagger linear logic for categorical quantum mechanics Abstract: Categorical quantum mechanics is largely based on dagger compact closed categories. A well-known limitation of this approach is that, while it supports finite dimensional processes, it does not generalize well to infinite dimensional processes. A natural categorical generalization of compact closed categories, in which to seek a description of categorical quantum mechanics without this limitation, is in ?-autonomous categories or, more generally, linearly distributive categories (LDCs). Last winter, Robin, Cole and myself started development of this direction of generalization. An important first step is to establish the behavior of the dagger in this more general setting. Thus, we simultaneously developed the categorical semantics of dagger linear logic. The goal of my talk is to give the definition of Mixed Unitary Categories [1] which is a key structure in the development of the quantum mechanics in the setting of LDCs. I will also show a running example of this category during my talk. Reference: [1] Robin Cockett, Cole Comfort, and Priyaa Srinivasan "Dagger linear logic for categorical quantum mechanics", arXiv:1809.00275 [math.CT], Sep. 2018. http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ From matthew.burke1 at ucalgary.ca Mon Feb 25 14:30:56 2019 From: matthew.burke1 at ucalgary.ca (Matthew Burke) Date: Mon Feb 25 14:30:59 2019 Subject: [Alta-Logic] Peripatetic seminar Message-ID: <95A05A05-9459-4A98-86D8-E8BFF3DC3A0D@ucalgary.ca> Speaker: Priyaa Srinivasan Date and time: Tuesday, February 26th, 2019 at 12:15 Location: MS 337 Title: Dagger linear logic for categorical quantum mechanics Abstract: Categorical quantum mechanics is largely based on dagger compact closed categories. A well-known limitation of this approach is that, while it supports finite dimensional processes, it does not generalize well to infinite dimensional processes. A natural categorical generalization of compact closed categories, in which to seek a description of categorical quantum mechanics without this limitation, is in ?-autonomous categories or, more generally, linearly distributive categories (LDCs). Last winter, Robin, Cole and myself started development of this direction of generalization. An important first step is to establish the behavior of the dagger in this more general setting. Thus, we simultaneously developed the categorical semantics of dagger linear logic. The goal of my talk is to give the definition of Mixed Unitary Categories [1] which is a key structure in the development of the quantum mechanics in the setting of LDCs. I will also show a running example of this category during my talk. Reference: [1] Robin Cockett, Cole Comfort, and Priyaa Srinivasan "Dagger linear logic for categorical quantum mechanics", arXiv:1809.00275 [math.CT], Sep. 2018. This week we:- - recap the definition of dagger-LDC, dagger mix and dagger isomix categories - define unitary structure for dagger isomix categories - show that compact LDCs are linearly equivalent to monoidal categories - define a mixed unitary category - (If time permits) Finiteness spaces, an example of a Mixed Unitary Category http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ From matthew.burke1 at ucalgary.ca Tue Feb 26 16:28:59 2019 From: matthew.burke1 at ucalgary.ca (Matthew Burke) Date: Tue Feb 26 16:29:01 2019 Subject: [Alta-Logic] Dinner tomorrow evening Message-ID: <42BB9EEC-ACEE-40B1-8575-6EEA03A20224@ucalgary.ca> Hi all, On Saturday Jonathan will be leaving our group to take up a postdoc in Halifax and we are having a dinner out in his honour tomorrow night. Day and time: 7pm Wednesday 27th February Venue: Alforno Cafe, 222 7th Street Southwest, Calgary, AB I suggest those wanting to travel together meet downstairs outside the ICT cafe at 6.15 pm to head over. If you would like to attend please email me directly to confirm. (I?m already assuming those who I have already spoken to are coming.) All the best, Matthew From benmacadam at gmail.com Thu Feb 28 14:35:49 2019 From: benmacadam at gmail.com (Ben MacAdam) Date: Thu Feb 28 14:35:56 2019 Subject: [Alta-Logic] Peripatetic Seminar: Series on Differentiable Stacks Message-ID: <27F3BAC2-14D3-465C-BF5E-561F0CDC2BF0@gmail.com> Hi everyone, Tomorrow is the last talk on enriched category theory! Speaker: Ben MacAdam Time and Location: 1:30PM, Friday March 1, at MS522 Title: The Strong Yoneda lemma Abstract: We will consider the strong Yoneda lemma and an application to metric spaces. From benmacadam at gmail.com Thu Feb 28 19:40:56 2019 From: benmacadam at gmail.com (Ben MacAdam) Date: Thu Feb 28 19:41:05 2019 Subject: [Alta-Logic] Peripatetic Seminar Message-ID: Hello everyone, Due to unforeseen circumstances, tomorrow?s talk is canceled. Sorry about that, Ben From matthew.burke1 at ucalgary.ca Mon Mar 4 10:43:36 2019 From: matthew.burke1 at ucalgary.ca (Matthew Burke) Date: Mon Mar 4 10:43:54 2019 Subject: [Alta-Logic] Peripatetic seminar Message-ID: <73BB1305-E18D-4340-A0F6-EE2A18076EBC@ucalgary.ca> Speaker: Matthew Burke Date and time: Tuesday, March 5th, 2019 at 12:15 Location: MS 337 Title: Involution algebroids and their homotopy theory Abstract: We define involution algebroids which generalise Lie algebroids to the abstract setting of tangent categories. We first sketch the relationship between our new definition and the classical one. Then as an illustrative example of how to work with the new definition we develop some of the homotopy theory of involution algebroids. This is joint work with Ben MacAdam. http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ From matthew.burke1 at ucalgary.ca Mon Mar 11 12:55:55 2019 From: matthew.burke1 at ucalgary.ca (Matthew Burke) Date: Mon Mar 11 12:55:59 2019 Subject: [Alta-Logic] Peripatetic seminar Message-ID: <2EB9BE01-D351-4FBB-A318-6BC9326A69DA@ucalgary.ca> Speaker: Matthew Burke Date and time: Tuesday, March 12th, 2019 at 12:15 Location: MS 337 Title: Involution algebroids and their homotopy theory II Abstract: We define involution algebroids which generalise Lie algebroids to the abstract setting of tangent categories. We first sketch the relationship between our new definition and the classical one. Then as an illustrative example of how to work with the new definition we develop some of the homotopy theory of involution algebroids. This is joint work with Ben MacAdam. http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ From benmacadam at gmail.com Thu Mar 14 09:44:16 2019 From: benmacadam at gmail.com (Ben MacAdam) Date: Thu Mar 14 09:44:28 2019 Subject: [Alta-Logic] Peripatetic Seminar: Series on Differentiable Stacks Message-ID: Hi everyone, We?ll have another seminar on differentiable stacks tomorrow. Speaker: Geoff Vooys Time and Location: MS522, 2-3 PM, Friday, March 15, 2019 Title: An Introduction to the Classical Perspective on Stacks I: Strongly Cartesian Morphisms and (Grothendieck) Fibrations Abstract: In this talk we will begin our descent into (classical) stack theory a la SGA 1 by learning about Grothendieck Fibrations, which essentially allow us to talk about spaces which have categories of fibres above them instead of simply having spaces or sets of fibres. We will go about this by beginning with a study of Strongly Cartesian morphisms, which ``categorify'' what it means for an arrow in a category to be a fibre over an arrow in its base in a reasonable way. This leads us to provide two distinct perspectives on Strongly Cartesian morphisms, and then introduce fibred categories (also called fibrations). From here we will describe some basic properties of the category of fibred categories over a fixed base and describe how to go about a change of base for fibred categories. After this we will describe cleavages of fibred categories, pullback functors between categories of fibres, and leave with a question of how far away from a functor into the category of categories we get if we do a ``category of fibres'' construction from a fixed fibred category with cleavage. From matthew.burke1 at ucalgary.ca Fri Mar 22 20:24:18 2019 From: matthew.burke1 at ucalgary.ca (Matthew Burke) Date: Fri Mar 22 20:24:28 2019 Subject: [Alta-Logic] Peripatetic seminar Message-ID: <572B7EF2-5DE7-49D0-870D-C672AFB2E125@ucalgary.ca> Speaker: Ben MacAdam Date and time: Tuesday, March 26th, 2019 at 12:15 Location: MS 337 Title: Kock-Lawvere Modules in a Tangent Category Abstract: In the category of smooth manifolds, vector spaces have the property that T(V) is isomorphic VxV. When moving to abstract settings for differential geometry, such as synthetic differential geometry, this need not be the case, especially tangent categories without any sort of ring object. Cockett and Cruttwell introduced the notion of a differential object to axiomatize this structure in tangent categories. In this talk we will introduce tangent categories with a scalar object - a differential object satisfying a universal property - and develop the theory of Kock-Lawvere R-modules, or KL modules. This will lead to the presentation of differential objects as models of an enriched sketch. This is joint work with Jonathan Gallagher and Rory Lucyshyn-Wright. http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ From benmacadam at gmail.com Thu Mar 28 21:36:16 2019 From: benmacadam at gmail.com (Ben MacAdam) Date: Thu Mar 28 21:39:07 2019 Subject: [Alta-Logic] Peripatetic Seminar: Series on Differentiable Stacks Message-ID: Hi everyone, Speaker: Geoff Vooys Time and Location: MS522, 2-3 PM, Friday, March 29, 2019 Title: An Introduction to the Classical Perspective on Stacks 2: Strongly Cartesian Morphisms and (Grothendieck) Fibrations Abstract: In this talk we will begin our descent into (classical) stack theory a la SGA 1 by learning about Grothendieck Fibrations, which essentially allow us to talk about spaces which have categories of fibres above them instead of simply having spaces or sets of fibres. We will go about this by beginning with a study of Strongly Cartesian morphisms, which ``categorify'' what it means for an arrow in a category to be a fibre over an arrow in its base in a reasonable way. This leads us to provide two distinct perspectives on Strongly Cartesian morphisms, and then introduce fibred categories (also called fibrations). From here we will describe some basic properties of the category of fibred categories over a fixed base and describe how to go about a change of base for fibred categories. After this we will describe cleavages of fibred categories, pullback functors between categories of fibres, and leave with a question of how far away from a functor into the category of categories we get if we do a ``category of fibres'' construction from a fixed fibred category with cleavage. From benmacadam at gmail.com Fri Apr 5 09:01:00 2019 From: benmacadam at gmail.com (Ben MacAdam) Date: Fri Apr 5 09:01:07 2019 Subject: [Alta-Logic] Stacks seminar Message-ID: Hi everyone, We?ll have another seminar on differentiable stacks today. Speaker: Geoff Vooys Time and Location: MS522, 1:30-2:30 PM, Friday, April 5, 2019 Title: An Introduction to the Classical Perspective on Stacks Abstract: In this talk we will begin our descent into (classical) stack theory a la SGA 1 by learning about Grothendieck Fibrations, which essentially allow us to talk about spaces which have categories of fibres above them instead of simply having spaces or sets of fibres. We will go about this by beginning with a study of Strongly Cartesian morphisms, which ``categorify'' what it means for an arrow in a category to be a fibre over an arrow in its base in a reasonable way. This leads us to provide two distinct perspectives on Strongly Cartesian morphisms, and then introduce fibred categories (also called fibrations). From here we will describe some basic properties of the category of fibred categories over a fixed base and describe how to go about a change of base for fibred categories. After this we will describe cleavages of fibred categories, pullback functors between categories of fibres, and leave with a question of how far away from a functor into the category of categories we get if we do a ``category of fibres'' construction from a fixed fibred category with cleavage. From matthew.burke1 at ucalgary.ca Mon Apr 8 19:32:37 2019 From: matthew.burke1 at ucalgary.ca (Matthew Burke) Date: Mon Apr 8 19:32:39 2019 Subject: [Alta-Logic] Peripatetic seminar Message-ID: <9245A228-8CD0-48A8-9E16-5070A13A6253@ucalgary.ca> Speaker: Daniel Satanove Date and time: Tuesday, April 9th, 2019 at 12:15 Location: MS 337 Title: Generalized sketches with monad sorts Abstract: I give a generalization of sketches which captures the theories of group presentations and certain notions of generalized multicategories. I conjecture that the categories of models of these sorts of sketches are locally finitely presentable, so that therefore this generalization stays within the realm of essentially algebraic theories. http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ From matthew.burke1 at ucalgary.ca Mon Apr 15 09:38:21 2019 From: matthew.burke1 at ucalgary.ca (Matthew Burke) Date: Mon Apr 15 09:38:24 2019 Subject: [Alta-Logic] Peripatetic seminar Message-ID: <6BBC9093-8A76-48E7-91B5-1FA08542FC8A@ucalgary.ca> Speaker: Benjamin Macadam Date and time: Tuesday, April 16th, 2019 at 12:15 Location: MS 337 Title: Bertram?s Lie Calculus Abstract: We will consider Bertram?s Lie Calculus, which develops the foundations of differential calculus and Lie theory concurrently. In particular, we shall consider his presentation of Connes? Tangent Groupoid on the category of smooth manifolds and consider how this could relate to a categorical semantics for identity types. http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ From benmacadam at gmail.com Tue Jun 18 14:02:36 2019 From: benmacadam at gmail.com (Ben MacAdam) Date: Tue Jun 18 14:03:50 2019 Subject: [Alta-Logic] Peripatetic Seminar Message-ID: <508ab479-9cf1-4bdd-91f6-04fe4bbc8d87@Spark> Date: 19 June, Wednesday Time: 11:00am - 1:30pm Venue: MS337 The talk will be presented by Stefano Gogoiso, a post doc working with Bob Coecke at the University of Oxford. Title: A Process-Theoretic Church of the Larger Hilbert Space Abstract: We show how to reconstruct a process theory of local systems starting from a global theory of reversible processes on a single global system, by using the purification principle. In such a process theory, local systems are not given, but rather ?emerge? as the global system is decomposed into subsystems. Local systems thus have specific identities and their composition is naturally limited by structural constraints, a behaviour which we formalise by defining symmetric partially-monoidal categories. We reconstruct quantum theory from the global theories of unitary groups acting on projective Hilbert spaces. https://arxiv.org/abs/1905.13117 This talk will be presented by Nicola Pinzani, a PhD student working with Bob Coecke at the University of Oxford. Title: Categorical Semantics for Time Travel Abstract: We introduce a general categorical framework to reason about quantum theory and other process theories living in spacetimes where Closed Timelike Curves (CTCs) are available, allowing resources to travel back in time and provide computational speedups. Our framework is based on a weakening of the definition of traced symmetric monoidal categories, obtained by dropping the yanking axiom and the requirement that the trace be defined on all morphisms. We show that the two leading models for quantum theory with closed timelike curves?namely the P-CTC model of Lloyd et al. and the D-CTC model of Deutsch?are captured by our framework, and in doing so we provide the first compositional description of the D-CTC model. Our description of the D-CTC model results in a process theory which respects the constraints of relativistic causality: this is in direct contrast to the P-CTC model, where CTCs are implemented by a trace and allow post-selection to be performed deterministically https://arxiv.org/abs/1902.00032 -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20190618/9cb2cca5/attachment.html From benmacadam at gmail.com Tue Jun 18 14:11:39 2019 From: benmacadam at gmail.com (Ben MacAdam) Date: Tue Jun 18 14:11:50 2019 Subject: [Alta-Logic] Two talks In-Reply-To: <6345d087-011b-49b3-b936-5245ed6d9722@Spark> References: <6345d087-011b-49b3-b936-5245ed6d9722@Spark> Message-ID: <8d36e0e5-c318-4b75-9689-ad583b5154dd@Spark> Sorry for the mix-up: Date: 19 June, Wednesday Time: 12:00pm - 1:30pm Venue: MS337 The talk will be presented by Stefano Gogoiso, a post doc working with Bob Coecke at the University of Oxford. Title: A Process-Theoretic Church of the Larger Hilbert Space Abstract: We show how to reconstruct a process theory of local systems starting from a global theory of reversible processes on a single global system, by using the purification principle. In such a process theory, local systems are not given, but rather ?emerge? as the global system is decomposed into subsystems. Local systems thus have specific identities and their composition is naturally limited by structural constraints, a behaviour which we formalise by defining symmetric partially-monoidal categories. We reconstruct quantum theory from the global theories of unitary groups acting on projective Hilbert spaces. https://arxiv.org/abs/1905.13117 Date: 20 June, Thursday Time: 11:00am - 1:30 Venue: MS337 This talk will be presented by Nicola Pinzani, a PhD student working with Bob Coecke at the University of Oxford. Title: Categorical Semantics for Time Travel Abstract: We introduce a general categorical framework to reason about quantum theory and other process theories living in spacetimes where Closed Timelike Curves (CTCs) are available, allowing resources to travel back in time and provide computational speedups. Our framework is based on a weakening of the definition of traced symmetric monoidal categories, obtained by dropping the yanking axiom and the requirement that the trace be defined on all morphisms. We show that the two leading models for quantum theory with closed timelike curves?namely the P-CTC model of Lloyd et al. and the D-CTC model of Deutsch?are captured by our framework, and in doing so we provide the first compositional description of the D-CTC model. Our description of the D-CTC model results in a process theory which respects the constraints of relativistic causality: this is in direct contrast to the P-CTC model, where CTCs are implemented by a trace and allow post-selection to be performed deterministically https://arxiv.org/abs/1902.00032 -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20190618/b84ce3d6/attachment.html From carlomaria.scandolo at ucalgary.ca Wed Jun 19 10:06:37 2019 From: carlomaria.scandolo at ucalgary.ca (Carlo Maria Scandolo) Date: Wed Jun 19 10:06:39 2019 Subject: [Alta-Logic] Fwd: Reminder: IQST seminar by Niel de Beaudrap of University of Oxford In-Reply-To: References: Message-ID: <592bd83e-4c7d-fb77-62c2-072bde4e3277@ucalgary.ca> Dear all, apologies for cross-posting. This is a talk about applications of ZX calculus for quantum computation. Please come if you are interested! Best regards, Carlo Maria Scandolo -------- Messaggio Inoltrato -------- Oggetto: Reminder: IQST seminar by Niel de Beaudrap of University of Oxford Data: Wed, 19 Jun 2019 15:05:26 +0000 Mittente: Nancy Jing Lu A: all-iqst-l@mailman.ucalgary.ca , mail=quantum-l@mailman. ca This is a friendly reminder of our seminar today at 3pm. --------------------- Hi all, We shall have a IQST seminar at 3pm on Wednesday 19 June 2019. ? Wednesday 19th June, 2019 3:00-4:00pm in SA 107 Niel de Beaudrap [University of Oxford] Title: Pauli Fusion: a computational model to realise quantum transformations from ZX terms Abstract: The ZX calculus is an abstract mathematical tool to represent ? and importantly to calculate with ? tensors of a sort that are common in quantum computational theory. We present an abstract model of quantum computation, the Pauli Fusion model, whose primitive operations correspond closely to generators of the ZX calculus (and are also straightforward abstractions of basic operations in some leading proposed quantum technologies). These operations have non-deterministic heralded effects, similarly to measurement-based quantum com- putation. We describe sufficient conditions for Pauli Fusion procedures to be deterministically realisable, so that it performs a given transformation independently of its non-deterministic outcomes. This provides an operational model to realise ZX terms beyond the circuit model. Thanks, Nancy -------------- next part -------------- An HTML attachment was scrubbed... URL: http://mailman.ucalgary.ca/pipermail/alta-logic-l/attachments/20190619/1b6521a3/attachment.html From benmacadam at gmail.com Thu Aug 29 16:00:07 2019 From: benmacadam at gmail.com (Ben MacAdam) Date: Thu, 29 Aug 2019 16:00:07 -0600 Subject: [Alta-Logic] Peripatetic Seminar In-Reply-To: <38815758-231c-4abc-a4f0-6be5ec67dce1@Spark> References: <38815758-231c-4abc-a4f0-6be5ec67dce1@Spark> Message-ID: <5f43b361-6e68-4b7c-bcf6-699223f97b3f@Spark> Date: August 30, Friday Time: 2:00 pm - 3:30 pm Venue: ICT 616 We will be meeting at the LDL at 3:30pm for a late lunch to welcome our new member, anyone interested is welcome. Title: Reverse differentiation Abstract: The reverse derivative is a fundamental operation in machine learning and differential programming.? This talk will give an axiomatization of the reverse derivative.? We will then explore an interesting consequence of the reverse derivative: it forces a dagger structure on the linear maps, and forces the biproducts that exist to be dagger biproducts.? If time permits we will explore how partiality interacts with reverse differentiation. -------------- next part -------------- An HTML attachment was scrubbed... URL: From benjamin.macadam at ucalgary.ca Thu Aug 29 15:43:20 2019 From: benjamin.macadam at ucalgary.ca (Benjamin MacAdam) Date: Thu, 29 Aug 2019 21:43:20 +0000 Subject: [Alta-Logic] Peripatetic Seminar References: <4d3779c7-9e90-49b0-b537-d56fa1c1ff09@Spark> Message-ID: <4084ba49-4d20-4162-a666-ae1f074f047f@Spark> Date: August 30, Friday Time: 2:00 pm - 3:30 pm Venue: ICT 616 We will be meeting at the LDL at 3:30pm for a late lunch to welcome our new member, anyone interested is welcome. Title: Reverse differentiation Abstract: The reverse derivative is a fundamental operation in machine learning and differential programming. This talk will give an axiomatization of the reverse derivative. We will then explore an interesting consequence of the reverse derivative: it forces a dagger structure on the linear maps, and forces the biproducts that exist to be dagger biproducts. If time permits we will explore how partiality interacts with reverse differentiation. -------------- next part -------------- An HTML attachment was scrubbed... URL: From benmacadam at gmail.com Wed Sep 4 11:47:15 2019 From: benmacadam at gmail.com (Ben MacAdam) Date: Wed, 4 Sep 2019 11:47:15 -0600 Subject: [Alta-Logic] Peripatetic Seminar: Scheduling! References: Message-ID: <4fcb0ea3-595b-4418-8cad-fcd275872c4e@Spark> Hi everyone, The semester is beginning and everyone has their schedules, so we should try to book a time for the peripatetic seminar. I?ve spoken to a few people and looked at some schedules and narrowed down the available times for the peripatetic seminar. Please fill out this doodle poll and let me know what times you aren?t available, and what times you?d rather not have the seminar - I?ll try to find some sort of local maximum of convenient times vs available seminar rooms. https://doodle.com/poll/y99zn99vq9eiff83 Ben -------------- next part -------------- An HTML attachment was scrubbed... URL: From benjamin.macadam at ucalgary.ca Fri Sep 6 10:37:00 2019 From: benjamin.macadam at ucalgary.ca (Benjamin MacAdam) Date: Fri, 6 Sep 2019 16:37:00 +0000 Subject: [Alta-Logic] Peripatetic Seminar Message-ID: <92edb606-8c32-4090-b5a0-cd22f8eebf00@Spark> Speaker: Matthew Burke Date and time: Friday, September 6th, 2019 at 15:00 Location: ICT 616 Title: Differential bundles in the category of smooth manifolds Abstract: In this talk we give a sketch of the proof that differential bundles in smooth manifolds are vector bundles. If we have time we describe how the addition map of a differential bundle may be recovered from the rest of the structure. http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ -------------- next part -------------- An HTML attachment was scrubbed... URL: From jdgall84 at gmail.com Fri Sep 6 10:56:58 2019 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Fri, 6 Sep 2019 10:56:58 -0600 Subject: [Alta-Logic] research event in applied category theory next week! Message-ID: Dear Peripatetic Seminar, Next week, there will be a small group gathering at the University of Calgary to pursue some recently discovered applications of category theory to machine learning. We will be holding working sessions in the afternoon in MS 452 and/or 522 Mon,Tues,Thurs,Fri. Please feel free to drop by and say hi and meet our guests who are working with us during the week. Our guests will include: 1. Shin-ya Katsumata: project leader of group 0 of the Erato MMSD project,, Tokyo. 2. David Sprunger: project researcher of group 0 of the Erato MMSD project, Tokyo. 3. Geoff Cruttwell: assistant professor in Math and Computer Science, Mount Allison University. See http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ where respective bios will be posted soon, as well as details about public talks that will be given (also see below). This meeting is made possible due to funding from NSERC, PIMS, AARMS, and the Erato MMSD project. There will be a talk on *Tuesday at 12:30 in ICT 616* *Speaker*: *David Sprunger* *Title*: *Differential Categories, Recurrent Neural Networks, and Machine Learning* *Abstract*: We review recent results using Cartesian differential categories to model backpropagation through time, a training technique from machine learning used with recurrent neural networks. We show that the property of being a Cartesian differential category is preserved by a variant of a stateful construction commonly used in signal flow graphs. Using an abstracted version of backpropagation through time, we lift the lift the differential operator from the starting differential category to the stateful one. *Bio*: David is a project research at the ERATO MMSD project in Tokyo. This project aims to extend formal methods and software verification techniques to cyber-physical systems, with particular emphasis on applications to automotive control and manufacturing. David received a PhD in mathematics at Indiana University in August 2017 as a student of Larry Moss. His academic research interests are primarily in coalgebra, logic, and category theory. Since moving to Tokyo, he has been developing an interest in quantitative refinements of bisimulation and other coalgebraically defined structures. He has also been looking into deep learning and neural networks. There will also be a talk by Geoff Cruttwell on Thursday at 12:30 pm, details to be provided in a separate message. Sincerely, Jonathan -------------- next part -------------- An HTML attachment was scrubbed... URL: From jdgall84 at gmail.com Fri Sep 6 16:40:24 2019 From: jdgall84 at gmail.com (Jonathan Gallagher) Date: Fri, 6 Sep 2019 16:40:24 -0600 Subject: [Alta-Logic] Geoff Cruttwell's Talk on Thursday, next week! Message-ID: Dear Peripatetic Seminar, Details for Geoff Cruttwell's talk next week are below. *Speaker: *Geoff Cruttwell *Location: MS 452*, Thursday, *September 12* @ *12:30--2:30 pm* *Title*: Vector fields and flows, categorically *Abstract*: In this talk we?ll investigate how to define vector fields and their flows in a tangent category, and how to prove a result about commutation of vector fields and flows in this setting. In the first half of the talk, we?ll introduce the notion of a ?curve object? in a tangent category: an object which ?uniquely solves ordinary differential equations in the tangent category?. In the second half of the talk, we?ll see how considering ?vector fields and flows in the tangent categories of vector fields and flows? leads to a new proof of the commutation theorem for vector fields and flows (Proposition 18.5 in Lee?s ?Introduction to Smooth Manifolds?). *Bio*: Geoff is an Associate Professor at Mount Allison University in Sackville, NB. His general interest is category theory. He is currently investigating how to generalize as much of differential geometry as possible to the setting of tangent categories. Geoff received his PhD at Dalhousie University in 2009 under the supervision of Richard Wood, and subsequently did postdoctoral research at the University of Calgary (supervised by Robin Cockett) and the University of Ottawa (supervised by Rick Blute) before taking up his current position at Mount Allison. - Jonathan -------------- next part -------------- An HTML attachment was scrubbed... URL: From benjamin.macadam at ucalgary.ca Tue Sep 17 18:09:03 2019 From: benjamin.macadam at ucalgary.ca (Benjamin MacAdam) Date: Wed, 18 Sep 2019 00:09:03 +0000 Subject: [Alta-Logic] Peripatetic Seminar References: <15a6e9af-349e-4ef0-9970-4e95eebe3dcc@Spark> Message-ID: <2fdbedc5-18e8-4f59-8bbb-0d373be78d71@Spark> Speaker: Ben MacAdam Date and time: Friday, September 20th, 2019 at 15:00 Location: ICT 616 Title: Generalized Algebraic Theories and Differential Objects Abstract: We introduce enriched algebraic theories with generalized arities, and see how this can be applied to tangent categories. In particular, we will show that every tangent category embeds into a so-called linear/nonlinear system between a monoidal differential category and cartesian tangent category. This is part of an ongoing collaboration with Jonathan Gallagher and others. http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ -------------- next part -------------- An HTML attachment was scrubbed... URL: From benjamin.macadam at ucalgary.ca Thu Oct 10 10:59:02 2019 From: benjamin.macadam at ucalgary.ca (Benjamin MacAdam) Date: Thu, 10 Oct 2019 16:59:02 +0000 Subject: [Alta-Logic] Peripatetic Seminar Message-ID: <077a3cb9-9d59-4bf7-b94c-8a938c286f34@Spark> Speaker: Priyaa Srinivasan Date and time: Saturday, October 12th, 2019 at 15:00 Location: ICT 616 Title: Dagger linear monoids in dagger LDCs Abstract: Categorical quantum mechanics describes quantum observable as dagger Frobenius Algebra with extra properties in the category of finite-dimensional Hilbert Spaces. In this talk, I will generalize the notion of dagger Frobenius Algebras to dagger linearly distributive categories (dagger-LDCs). We call the dagger Frobenius Algebras in this setting as dagger linear monoids. We observe that in the setting symmetric dagger LDCs, a dagger linear dual gives rise to endomorphism monoids (usually referred to as the pants monoid) for which the multiplication is anti-isomorphic to the dagger of the comultiplication. Finally, we examine the conditions under which the anti-isomorphic pants monoid coincides with the usual pants monoid in a unitary category. http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ -------------- next part -------------- An HTML attachment was scrubbed... URL: From benjamin.macadam at ucalgary.ca Thu Oct 10 11:17:23 2019 From: benjamin.macadam at ucalgary.ca (Benjamin MacAdam) Date: Thu, 10 Oct 2019 17:17:23 +0000 Subject: [Alta-Logic] Peripatetic Seminar - Correction References: Message-ID: Sorry for the mix up! Speaker: Priyaa Srinivasan Date and time: Friday, October 11th, 2019 at 03:00 Location: ICT 616 Title: Dagger linear monoids in dagger LDCs Abstract: Categorical quantum mechanics describes quantum observable as dagger Frobenius Algebra with extra properties in the category of finite-dimensional Hilbert Spaces. In this talk, I will generalize the notion of dagger Frobenius Algebras to dagger linearly distributive categories (dagger-LDCs). We call the dagger Frobenius Algebras in this setting as dagger linear monoids. We observe that in the setting symmetric dagger LDCs, a dagger linear dual gives rise to endomorphism monoids (usually referred to as the pants monoid) for which the multiplication is anti-isomorphic to the dagger of the comultiplication. Finally, we examine the conditions under which the anti-isomorphic pants monoid coincides with the usual pants monoid in a unitary category. http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ -------------- next part -------------- An HTML attachment was scrubbed... URL: From benjamin.macadam at ucalgary.ca Tue Oct 22 19:04:30 2019 From: benjamin.macadam at ucalgary.ca (Benjamin MacAdam) Date: Wed, 23 Oct 2019 01:04:30 +0000 Subject: [Alta-Logic] Peripatetic Seminar References: Message-ID: Speaker: Ben MacAdam Date and time: Friday, October 25th, 2019 at 15:00 Location: ICT 616 Title: Graphs and Anchored Bundles Abstract: Lie's second theorem for groupoids states that there is a full and faithful functor from the category of Lie groupoids to Lie algebroids. We will consider a simplification of this theorem by looking at reflexive digraphs rather than groupoids and the corresponding functor to anchored bundles. http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ -------------- next part -------------- An HTML attachment was scrubbed... URL: From benjamin.macadam at ucalgary.ca Tue Oct 29 12:28:41 2019 From: benjamin.macadam at ucalgary.ca (Benjamin MacAdam) Date: Tue, 29 Oct 2019 18:28:41 +0000 Subject: [Alta-Logic] Peripatetic Seminar Message-ID: Speaker: Matthew Burke Date and time: Friday, November 1st, 2019 at 15:07 Location: ICT 616 Title: Lie algebroids are the same as involution algebroids in the category of smooth manifolds. Abstract: Involution algebroids are a generalisation of Lie algebroids that make sense in any tangent category. The aim of this talk is to sketch a proof that the category of Lie algebroids is isomorphic to the category of involution algebroids in the category of smooth manifolds. Our method is to use the structure equations of the Lie algebroid to mediate between the two definitions. The advantage of this approach is that it reveals that the Tulczyjew involution in Lagrangian mechanics satisfies the involution algebroid axioms. This is joint work with Ben MacAdam and is based on an idea of Richard Garner. http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ -------------- next part -------------- An HTML attachment was scrubbed... URL: From benjamin.macadam at ucalgary.ca Sat Dec 14 18:48:06 2019 From: benjamin.macadam at ucalgary.ca (Benjamin MacAdam) Date: Sun, 15 Dec 2019 01:48:06 +0000 Subject: [Alta-Logic] Peripatetic Seminar References: <3c76ef18-0cd4-4212-b312-a42b03c1bd4a@Spark> Message-ID: <8271325a-044e-4cc5-bc70-62b005ab1606@Spark> Speaker: JS Lemay Date and time: Wednesday, December 18th, 2019 at 11:00 Location: ICT 616 Title: Exponential Functions for Cartesian Differential Categories. Abstract: We introduce differential exponential maps in Cartesian differential categories, which generalizes the exponential function from classical differential calculus. In particular, differential exponential maps can be defined without the need for limits, converging power series, multiplication, or unique solutions of certain differential equations -- which most Cartesian differential categories do not necessarily have. Every differential exponential map induces a commutative rig, called a differential exponential rig, and conversely, every differential exponential rig induces a differential exponential map. Examples of differential exponential maps in the Cartesian differential category of real smooth functions include the exponential function, the complex exponential function, and the dual numbers exponential. Preprint: https://arxiv.org/pdf/1911.04790.pdf http://peripatetic-seminar.cpsc.ucalgary.ca/wp/ -------------- next part -------------- An HTML attachment was scrubbed... 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