From robin at ucalgary.ca Fri Jan 7 14:55:42 2011 From: robin at ucalgary.ca (Robin Cockett) Date: Fri Jan 7 14:56:29 2011 Subject: [Alta-Logic] Peripatetic seminars Message-ID: <4D278BDE.1030000@ucalgary.ca> I am hoping to get going with the peripatetic seminars for this semester: (a) SCHEDULING: I am proposing to run them again on Wed. morning 11:00am -- 12:00pm ... the first one on the 20th. Please let me know if you have a conflict so we can jiggle things ... (b) TALKS: I am looking for volunteers! Pavel Hrubes has volunteered some talks so we may kick off with him. I have some things on my mind too. If you have something on your mind you want to talk about please give me heads up and we will start to fit together a schedule. -robin From rzach at ucalgary.ca Wed Jan 12 13:15:41 2011 From: rzach at ucalgary.ca (Richard Zach) Date: Wed Jan 12 13:16:23 2011 Subject: [Alta-Logic] Talk/Dinner with Allen Hazen Message-ID: <1294863341.12579.18.camel@delia> Dear All, Allen Hazen, distinguished logician formerly of the University of Melbourne, and now at the UofA, will give talk in the Philosophy Colloquium series on Friday at 4pm. Please let me know if you're interested in joining Allen for dinner after his talk. -R Allen Hazen - "The Variable: A Metaphysical Inchnofossil" 4pm in SS 1253 Once upon a time there was a metaphysical or semantic debate about the nature of variables: a debate largely forgotten by contemporary philosophers. It left traces, though: fossilized footprints, as it were, in the formation of mathematical logic. Key words: Quine, Russell, Fitch, Cauman. The talk will be ABOUT technical matters, but will not itself BE technical (no theorems proved!). From bauerk at ucalgary.ca Wed Jan 12 14:13:23 2011 From: bauerk at ucalgary.ca (Kristine Bauer) Date: Wed Jan 12 14:22:03 2011 Subject: [Alta-Logic] FW: PIMS Distinguished Lecturer - Dr. Noam Elkies - Jan 14 and 17 In-Reply-To: <5F4CD1C6-DFE3-4AFE-A801-6B7C3B3BC273@math.ucalgary.ca> References: <17195003E80B434CBFA1EA49E54CFD3F26386D114A@EXMB01.admin.ad.ucalgary.ca>, <5F4CD1C6-DFE3-4AFE-A801-6B7C3B3BC273@math.ucalgary.ca> Message-ID: <17195003E80B434CBFA1EA49E54CFD3F26383FF637@EXMB01.admin.ad.ucalgary.ca> Richard's recent advertisement made me remember that some of the Peripatetic seminar participants might be interested in these two talks as well. See abstracts below. Cheers, Kristine PIMS Number Theory CRG Distinguished Lecture January 17, 2011 15:00 ICT 114 On the areas of rational triangles Dr. Dr. Noam Elkies, Harvard University Abstract: By a "rational triangle" we mean a plane triangle whose sides are rational numbers. By Heron's formula, there exists such a triangle of area sqrt(a) if and only if a > 0 and x y z (x + y + z) = a for some rationals x, y, z. In a 1749 letter to Goldbach, Euler constructed infinitely many such (x, y, z) for any rational $a$ (positive or not), remarking that it cost him much effort, but not explaining his method. We suggest one approach, using only tools available to Euler, that he might have taken, and use this approach to construct several other infinite families of solutions. We then reconsider the problem as a question in arithmetic geometry: xyz(x+y+z) = a gives a K3 surface, and each family of solutions is a singular rational curve on that surface defined over Q. The structure of the Neron-Severi group of that K3 surface explains why the problem is unusually hard. Along the way we also encounter the Niemeier lattices (the even unimodular lattices in R^24) and the non-Hamiltonian Petersen graph. Previously advertised?.. January 14, 2011 15:00 ICT 114 How many points can a curve have? Dr. Noam Elkies, Harvard University Abstract: Diophantine equations, one of the oldest topics of mathematical research, remain the object of intense and fruitful study. A rational solution to a system of algebraic equations is tantamount to a point with rational coordinates (briefly, a "rational point") on the corresponding algebraic variety V. Already for V of dimension 1 (an "algebraic curve"), many natural theoretical and computational questions remain open, especially when the genus g of V exceeds 1. (The genus is a natural measure of the complexity of V; for example, if P is a nonconstant polynomial without repeated roots then the equation y^2 = P(x) gives a curve of genus g iff P has degree 2g+1 or 2g+2.) Faltings famously proved that if g>1 then the set of rational points is finite (Mordell's conjecture), but left open the question of how its size can vary with V, even for fixed g. Even for g=2 there are curves with literally hundreds of points; is the number unbounded? We briefly review the structure of rational points on curves of genus 0 and 1, and then report on relevant work since Faltings on points on curves of given genus g>1. Mathematics and Statistics Department PIMS - University of Calgary Site Office Mathematical Sciences Building MS 476 2500 University Drive NW University of Calgary AB T2N 1N4 p: 403.220.3951, f: 403.282.5150, w: www.pims.math.ca From robin at ucalgary.ca Fri Jan 14 22:43:29 2011 From: robin at ucalgary.ca (Robin Cockett) Date: Fri Jan 14 22:43:41 2011 Subject: [Alta-Logic] Peripatetic seminar jiggled! Message-ID: <4D313401.7070900@ucalgary.ca> Time: Wed. 19th Jan. 2011 3:30-4:30pm Place: ICT616 Speaker: Pavel Hrubes Title: On twin non-computable functions Abstract: Assume that we have a set X and a total recursive function f such that for every n, X differs from the n-th r.e. set W_n in the point f(n). Then X is strong enough to compute the Halting problem 0'. A similar observation applies when we replace "n-th r.e. set" by "n-th arithmetical set" and 0' by 0^{\omega}. We investigate what happens, if instead of being given a single point where X and W_n differ, we are given a finite list of candidates to choose from. ================================== Still discussing time ... Still looking for volunteers ... See you there ... -robin From robin at ucalgary.ca Tue Jan 25 14:31:57 2011 From: robin at ucalgary.ca (Robin Cockett) Date: Tue Jan 25 14:32:21 2011 Subject: [Alta-Logic] Peripatetic seminar Wed 26th Message-ID: <4D3F414D.2040704@ucalgary.ca> Speaker: Pavel Hrubes Place: ICT 616 Time: Wed. 26th Jan 2011, 3:30pm Title: On twin non-computable functions (continued) Abstract: Assume that we have a set X and a total recursive function f such that for every n, X differs from the n-th r.e. set W_n in the point f(n). Then X is strong enough to compute the Halting problem 0'. A similar observation applies when we replace "n-th r.e. set" by "n-th arithmetical set" and 0' by 0^{\omega}. We investigate what happens, if instead of being given a single point where X and W_n differ, we are given a finite list of candidates to choose from. From robin at ucalgary.ca Tue Feb 1 15:08:19 2011 From: robin at ucalgary.ca (Robin Cockett) Date: Tue Feb 1 15:08:37 2011 Subject: [Alta-Logic] Peripatetic seminar 2nd Feb Message-ID: <4D488453.3080503@ucalgary.ca> Apologies for lateness of announcement ... Speaker: Robin Cockett (me) Time: 3:30pm Wed. 2nd Feb 2011 Place: ICT 616 Title: Categorical semantics for lower complexity Abstract: How does one obtain a categorical semantics for PTIME and PSPACE and other lower complexity settings? It turns out that "polarized" settings and "polarized initial algebras" have a crucial role. These ideas can be used to provide systems in which programs which "type check" are of guaranteed low complexity -- so called "implicit" complexity settings. This is the idea behind the Pola programming language. The talk, however, will focus on the categorical side and develop the key ideas of these settings and give some models .... Next week: Gillman Payette From ggpayett at ucalgary.ca Sun Feb 6 18:08:04 2011 From: ggpayett at ucalgary.ca (Gillman Payette) Date: Sun Feb 6 18:08:17 2011 Subject: [Alta-logic] Peripatetic Seminar Feb 9th. Message-ID: Speaker: Gillman Payette and Masashi Kasaki Time: 3:30pm Wed. Feb 9, 2011 Place: ICT 616 Title: The many dimensions of contextualism in epistemology Abstract: Keith DeRose proposes a counterfactual account of knowledge and combines it with a contextualist semantics. In this paper, first, we give a formal model for DeRose's contextualist counterfactual account of knowledge, by taking it as a variation or augmentation of David Lewis's formal semantics for counterfactuals. Second, we extend our model by assigning two different functions to contexts: to determine the relevant epistemic standard and to specify the relevant similarity measure for ordering possible worlds. As a result, our model can deal with an objection to DeRose's contextualism that it fails to handle the genuine threat of skepticism. -- Gillman Payette Department of Philosophy University of Calgary 2500 University Drive NW Calgary, AB T2N 1N4, Canada Ph 403.220.6463 Fax 403.289.5698 From ggpayett at ucalgary.ca Sun Feb 13 12:58:17 2011 From: ggpayett at ucalgary.ca (Gillman Payette) Date: Sun Feb 13 12:58:29 2011 Subject: [Alta-Logic] Talk on Wednesday Message-ID: <7db9673d5c3ef5a8f5322439f54936b4.squirrel@webmail.ucalgary.ca> Title: The many dimensions of contextualism in epistemology II Start: 02/16/2011 - 15:30 End: 02/16/2011 - 16:30 Speaker: Gillman Payette and Masashi Kasaki Place: ICT 616 Abstract: Keith DeRose proposes a counterfactual account of knowledge and combines it with a contextualist semantics. In this paper, first, we give a formal model for DeRose's contextualist counterfactual account of knowledge, by taking it as a variation or augmentation of David Lewis's formal semantics for counterfactuals. Second, we extend our model by assigning two different functions to contexts: to determine the relevant epistemic standard and to specify the relevant similarity measure for ordering possible worlds. As a result, our model can deal with an objection to DeRose's contextualism that it fails to handle the genuine threat of skepticism. In the last talk we introduced skepticism, contextualism and Lewis's sphere semantics for counterfactuals. In this talk we will briefly review these notions and then present our semantics for contextualism that allows skepticism to remain a genuine threat. -- Gillman Payette Department of Philosophy University of Calgary 2500 University Drive NW Calgary, AB T2N 1N4, Canada Ph 403.220.6463 Fax 403.289.5698 From robin at ucalgary.ca Tue Mar 8 11:52:55 2011 From: robin at ucalgary.ca (Robin Cockett) Date: Tue Mar 8 11:53:23 2011 Subject: [Alta-Logic] Peripatetic seminar Message-ID: <4D767B07.3050100@ucalgary.ca> When/where: Wed 9th March, 3:30pm, ICT616 Title: Understanding Topological Homology theories for commutative rings Who: Kristine Bauer Abstract: There is a very nice relationship between topological (co) homology theories and algebraic (co) homology theories. Often, an algebraic theory (like Hochschild homology, Andre-Quillen homology or K-theory) has a topological analogue. A good example is given by Andre-Quillen homology: topologists understand this homology theory as a kind of linearization of a certain forgetful functor. There's a catch, though --- the linearization relies on the fact that this particular forgetful functor preserves initial and terminal objects. I will explain how to linearize functors from categories which don't have a terminal object. Furthermore, I'll explain how to compute the linear approximations as well as higher degree approximations. The computation is surprisingly discrete in nature, and relies on cosimplicial-simplicial sets. In fact, all such approximations come from a functor of cosimplicial-simplicial sets which strives to approximate the empty set in a very systematic way!! This talk is joint work with Rosona Eldred, Brenda Johnson and Randy McCarthy. The results in this talk are applications of the results I spoke about in last week's math department colloquium, but no familliarity with my previous talk will be assumed!! From rzach at ucalgary.ca Fri Mar 11 12:30:13 2011 From: rzach at ucalgary.ca (Richard Zach) Date: Fri Mar 11 12:30:25 2011 Subject: [Alta-Logic] Summer Research Opportunity for Logic Students Message-ID: <1299871813.3468.227.camel@delia> If you know of any smart and capable undergraduates interested in logic, please forward this to them! Re: Summer Research Opportunity in Logic Hi! I've just been allocated an NSERC Undergraduate Student Research Award for this summer, which means I get to hire an undergraduate student registered in a science or engineering discipline for independent research. Eligibility criteria are here: http://www.nserc-crsng.gc.ca/Students-Etudiants/UG-PC/USRA-BRPC_eng.asp It pays $4,500 for a full 16-week period. You'd work on an independent research project related to logic, under my supervision. If you're interested (and eligible!) please contact me asap at rzach@ucalgary.ca and set up an appointment to discuss the details. (I generally have time Tuesday and Thursday 12:30-2 and after 3:30, but other days are possible.) It would be useful if you could tell me what background you have in logic (courses taken, grades). Your research could be on applications of logic in computer science or mathematics (knowledge representation, database theory, automated theorem proving), or advanced topics in mathematical logic itself (esp. proof theory, non-classical logics). -Richard http://www.ucalgary.ca/~rzach/ From robin at ucalgary.ca Tue Mar 15 15:15:10 2011 From: robin at ucalgary.ca (Robin Cockett) Date: Tue Mar 15 15:15:55 2011 Subject: [Alta-Logic] Peripatetic seminar: Wednesday and Friday (double dipping!!) Message-ID: <4D7FD6DE.2000707@ucalgary.ca> Speaker: Robin Cockett Where and when: ICT 616, Wednesday, 16th March, 3:30pm Title: On the Totals of a Turing Category Abstract: A Turing category is an abstract setting for describing computability. I put the following question to Pavel (Hrubes): "Can the polynomial time functions be the totals of a Turing category?" Pavel responded by making some interesting general observation about the totals of a Turing category which have allowed a completely characterization of the (Cartesian) categories which can be the total maps of a Turing category .... and not only are the polynomial time maps included but possibly also classes of even lower complexity. The aim of the talk is to begin to describe these results and, possibly, to discuss some other desirable structural aspects which are really needed in order to bring these observations to bear. (Joint work with Pavel Hrubes) Speaker Geoff Crutwell Where and when: ICT 616, Friday, 18th March, 3:00pm Title: Embeddings of Atlas Categories Abstract: A few months ago, I talked about Marco Grandis' construction of the atlas-completion of a join restriction category. This generalizes the idea of "atlas" so that one can describe atlases in virtually any setting in which one has a well-behaved notion of partial map. However, in many contexts, a "manifold" need not be given by an atlas: instead, it can be seen as a type of "space" which locally looks like one of the modeling spaces. For example, instead of describing schemes as atlases of affine schemes, they can be (and typically are) described as locally ringed spaces which locally look like an affine space. This is not always obviously possible: there is no obvious notion of "space" in which manifolds modeled on infinite dimensional vector spaces (eg., convenient vector spaces, or Frechet spaces) live in. Thus these manifolds are typically described by atlases. In the talk, after reviewing Grandis' generalized atlases, I'll talk a bit about work-in-progress on trying to make the above idea work generally: showing that every atlas can be seen as a kind of space which locally looks like one of the modeling spaces. From robin at ucalgary.ca Tue Mar 22 17:46:14 2011 From: robin at ucalgary.ca (Robin Cockett) Date: Tue Mar 22 17:46:25 2011 Subject: [Alta-Logic] Peripatetic seminar: Wednesday Message-ID: <4D8934C6.4010206@ucalgary.ca> Speaker: Robin Cockett Where and when: ICT 616, Wednesday, 23rd March, 3:30pm Title: On the Totals of a Turing Category (cont.) Abstract: A Turing category is an abstract setting for describing computability. I put the following question to Pavel (Hrubes): "Can the polynomial time functions be the totals of a Turing category?" Pavel responded by making some interesting general observation about the totals of a Turing category which have allowed a completely characterization of the (Cartesian) categories which can be the total maps of a Turing category .... and not only are the polynomial time maps included but possibly also classes of even lower complexity. (Joint work with Pavel Hrubes) The aim of THIS talk is to take a look at some of the proofs. As Pavel is now back from Isreal it allow him to see how I have reorganize his material. ALSO we are looking for speakers! From robin at ucalgary.ca Mon Mar 28 13:21:04 2011 From: robin at ucalgary.ca (Robin Cockett) Date: Mon Mar 28 13:21:27 2011 Subject: [Alta-Logic] Peripatetic seminar talk: Peter Zvengrowski Message-ID: <4D90DFA0.5080703@ucalgary.ca> Where/when: ICT615, 3:30pm, 30th March 20011 Speaker; Peter Zvengrowski Title: Goursat's Lemma About Subobjects of Direct Products Abstract: This talk will be an elementary exposition of Goursat's Lemma, which describes how to find the subgroups of $A\times B$, where $A,B$ are two given groups. In fact this lemma appears as a homework problem in some undergraduate algebra texts. We will start by giving the proof and a couple of examples. Then we describe how some interesting generalizations of the lemma seem to be possible, including a proper categorical setting. From robin at ucalgary.ca Mon Jul 11 11:01:42 2011 From: robin at ucalgary.ca (Robin Cockett) Date: Mon Jul 11 11:02:10 2011 Subject: [Alta-Logic] Talk by Richard Garner: 11:00am, 13th July 2011, ICT616 Message-ID: <4E1B2C76.4080207@ucalgary.ca> Who: Richard Garner When: 11:00am Wed 13th July Where: ICT616 Title: "On the axioms for adhesive and quasiadhesive categories" (joint work with Steve Lack) The notion of adhesive category was introduced by Lack and Sobocinski as a formalisation of the basic structure on a category needed to carry out graph rewriting in it. A category is adhesive if it has finite limits and pushouts along monomorphisms, and these pushouts are suitably well-behaved. Unfortunately, in an adhesive category every monomorphism is necessarily regular, and this means that many of the categories in which graph-rewriters like to work are not actually adhesive. On this account Lack and Sobocinski also introduced the notion of quasi-adhesive category; here one requires only well-behaved pushouts along regular monomorphisms, and this allows an acceptably large class of examples to be captured. Any topos is adhesive and in fact (if we conveniently ignore size issues) a category is adhesive if and only if it admits an embedding into a topos which preserves the adhesive structure. Lack and Sobocinski's intention was that quasi-adhesive categories should stand in the same relationship to quasi-toposes, but unfortunately this is not the case. We shall discuss in this talk how the definition of quasi-adhesiveness can be changed to patch this up. Along the way we will see that the original definitions of adhesive and of quasi-adhesive category---which are slightly fiddly---can be given in a much simplified manner. =============== Richard Garner obtained his PhD from the University of Cambridge in 2006, he is currently a holder of an Australian Research Fellowship and works with the Sydney Category theory seminar at the University of Macquarie. He has worked in higher dimensional category theory, homotopy theory, and type theory. From robin at ucalgary.ca Fri Sep 23 13:29:52 2011 From: robin at ucalgary.ca (Robin Cockett) Date: Fri Sep 23 13:30:03 2011 Subject: [Alta-Logic] Peripatetic seminars this semester .... Message-ID: <4E7CDE30.1080502@ucalgary.ca> I propose to arrange the Peripatetic seminars this semester on Wednesdays (as usual): I am tentatively suggesting a time of 11:00 -12:00am in ICT616. However, at this stage: (a) I am soliciting feedback on everyone's schedules on Wed. as I would like to hold it at a time when people can actually come! (b) I am looking speakers ... what is on your minds! -robin From robin at ucalgary.ca Mon Oct 3 13:01:09 2011 From: robin at ucalgary.ca (Robin Cockett) Date: Mon Oct 3 13:01:21 2011 Subject: [Alta-Logic] Peripatetic talk this Wed. Message-ID: <4E8A0675.1020503@ucalgary.ca> Our first talk of the season. If you never understood division by zero by the end of this talk by Jonathan there will be absolutely no hope! If you volunteered to talk you will are likely to be scheduled when we meet! -robin Place: ICT 616 Time: 11:00am, Wed 5th October 2011 Speaker: Jonathan Gallagher Title: "The weak fraction construction" Abstract: In this talk, the construction of fractions will be revisited: The fractional equivalence $\frac{a}{a} \sim 1$ will be a replaced by a weaker equivalence: $\frac{a}{a2} \sim \frac{1}{a}$. This weaker equivalence has a number of impacts on the operations one expects of fractions, and requires us to use weaker structures than commutative rigs: called weak commutative rigs. This fraction construction will be shown to be a monad on the category of weak commutative rigs. The category of algebras for this monad will also be developed, and from this category of algebras we will build the partial map category with respect to 'localizations' to obtain a very general category of rational functions. A series of adjunctions relates this general category of rational functions to the partial map category of commutative rings with respect to localizations. From robin at ucalgary.ca Tue Oct 11 17:17:52 2011 From: robin at ucalgary.ca (Robin Cockett) Date: Tue Oct 11 17:18:59 2011 Subject: [Alta-Logic] Peripatetic talk Message-ID: <4E94CEA0.5060005@ucalgary.ca> Apologies for the late announcement --- thanksgiving lethargy! Time: 11:00am Wed. 12 Sept. Place: ICT 616 Speaker: Robin Cockett Title: Timed Sets A very simple construction is to associate with a (partial) function in sets a timing in some partially ordered commutative monoid: two maps are then equal if, not only are they the same partial function, but also their timing is the same. From the perspective of complexity one often wants to relax this very strict notion of equality to allow maps in the same "complexity class" to be equal. For example, if we are considering P-time maps we may want two maps to be considered equal if, to within "polynomial bounds", their timings are equal. All this can be made good sense of categorically ... what is a little surprising is that this, under certain very naturally conditions, makes timed sets into a restriction category -- in which the total maps are precisely those whose timing are in the complexity class one started with. This allows one to construct categories which not only directly express complexity but also express computability (in the sense of being Turing categories) while having their total maps belonging to a low complexity classes. Joint work with Ximo Boils, Jonathan Gallagher, and Pavel Hubres From rzach at ucalgary.ca Thu Oct 13 13:19:00 2011 From: rzach at ucalgary.ca (Richard Zach) Date: Thu Oct 13 13:20:24 2011 Subject: [Alta-Logic] Terry Horgan talk tomorrow in Philosophy Message-ID: <1318533540.1644.11.camel@debbie> The Sleeping Beauty problem is really neat. Should be a fun talk. http://phil.ucalgary.ca/node/795 http://en.wikipedia.org/wiki/Sleeping_Beauty_problem Friday Oct 14, 4pm, Social Sciences Building, Room 1253 "Generalized Conditionalization and the Sleeping Beauty Problem" About the Paper I will begin with an opinionated overview of philosophical debate about the Sleeping Beauty Problem. I will summarize Adam Elga's arguments for the 1/3 solution, David Lewis's argument (in reply to Elga) for the 1/2 solution, the "double halfer" position that I originally favored (and is defended by Joel Pust), my conversion experience from double halfism to thirdism, my post-conversion argument (different from Elga's arguments) for the 1/3 position, Pust's critique of my argument, my response to Pust, and Pust's subsequent response to me. I will then summarize a new argument for the 1/3 conclusion, presented by Anna Mahtani and me in our paper "Generalized Conditionalization and the Sleeping Beauty Problem" (Erkenntnis, in press). This argument entirely evades Pust's objection to my earlier argument, and also evades another objection that Pust raises against numerous pro-thirder and pro-halfer arguments in the literature. The various arguments and counter-arguments will be presented in a way that maximizes intuitiveness and minimizes technicality. About the Speaker Terry Horgan is Professor of Philosophy at the University of Arizona. He has published numerous articles in the areas of metaphysics, epistemology, mind, and metaethics. His most recent book, Austere Realism: Contextual Semantics Meets Minimal Ontology (with M. Potrc) was published by MIT in 2008. From robin at ucalgary.ca Mon Oct 17 11:30:55 2011 From: robin at ucalgary.ca (Robin Cockett) Date: Mon Oct 17 11:31:32 2011 Subject: [Alta-Logic] Peripatetic talk: Wed. 11:00am, 19th Oct. , ICT 616 Message-ID: <4E9C664F.1020708@ucalgary.ca> Time: 11:00 am Wed. (19th Oct. 2001) Place: ICT 616 Speaker: Peter Zvengrowski Title: Goursat II Abstract: Goursat's Lemma goes back to 1889 and gives a method for determining the subgroups of the direct product AxB of two groups. This past spring a talk about Goursat's Lemma was given by myself in this seminar, and a few interesting further questions were mentioned. Since then, in joint work with Kristine Bauer and Debasis Sen, one of those questions has been solved, namely generalizing the lemma from direct products of two groups to direct products of a finite number of groups (or rings, modules, etc.), and this will be the main subject of the present talk. Some of the history will also be updated, including a strong Canadian connexion. From robin at ucalgary.ca Mon Oct 24 08:25:59 2011 From: robin at ucalgary.ca (robin@ucalgary.ca) Date: Mon Oct 24 08:27:04 2011 Subject: [Alta-Logic] Peripatetic talk Wed 26 Message-ID: <97f947f56c7acbeb0c7f1bd68b338760.squirrel@webmail.ucalgary.ca> Place: ICT 616 Time: 11:00 Wed 26 Oct. 2011 Speaker: Tristan Title: A Simplicial Construction of Homotopy Colimits The homotopy (co)limit of topological spaces is a generalization of ordinary (co)limits in such a way that the result is homotopy invariant. I will present an explicit construction of the homotopy colimit which works by building a certain simplicial space out of a given diagram. The construction I present will allow one to construct the homotopy colimit of an arbitrary diagram, but I will focus primarily on homotopy pushouts as an illustrative example. If time permits, I will also discuss how this construction can be dualized to construct homotopy limits, and I will also mention the classic Bousfield-Kan construction of homotopy colimits. From robin at ucalgary.ca Tue Oct 25 10:36:08 2011 From: robin at ucalgary.ca (Robin Cockett) Date: Tue Oct 25 10:36:26 2011 Subject: [Alta-Logic] re: Wednesday's talk Message-ID: <4EA6E578.3090704@ucalgary.ca> A reminder ... but also a useful addition/correction: the speaker is Tristan Jugdev! See you ICT 616, 11:00am tomorrow! -robin Speaker: Tristan Jugdev Title: A Simplicial Construction of Homotopy Colimits Abstract: The homotopy (co)limit of topological spaces is a generalization of ordinary (co)limits in such a way that the result is homotopy invariant. I will present an explicit construction of the homotopy colimit which works by building a certain simplicial space out of a given diagram. The construction I present will allow one to construct the homotopy colimit of an arbitrary diagram, but I will focus primarily on homotopy pushouts as an illustrative example. If time permits, I will also discuss how this construction can be dualized to construct homotopy limits, and I will also mention the classic Bousfield-Kan construction of homotopy colimits. From robin at ucalgary.ca Mon Oct 31 12:02:40 2011 From: robin at ucalgary.ca (Robin Cockett) Date: Mon Oct 31 12:02:53 2011 Subject: [Alta-Logic] Peripatetic talk: Wed. 2nd Nov. Message-ID: <4EAEE2C0.50000@ucalgary.ca> Time: 11:00am, November 2nd, 2011 Place: ICT616 Speaker: Kristine Bauer Title: Homotopy (co)limits, II The homotopy colimit (or limit) of a diagram is the universal object which completes a diagram into one which has a terminal (initial) object. Heuristically, it can be thought of as assembling the information in a diagram into some kind of union. In homotopy theory, where one only wants to work with equivalence classes of objects up to weak equivalence, the homotopy (co)limit can be problematic as it does not preserve the equivalence relation. Last week, Tristan Jugdev explained the problems with (co)limits, the idea of a homotopy (co)limit, and the constructions used by topologists to compute homotopy (co)limits. In this talk, I will explain the homotopy (co)limit as a derived functor of the (co)limit. I will explain to what extent a homotopy (co)limit does or does not satisfy a universal property. I will explain how non-topological categories which have a well defined equivalence relation, such as the category of chain complexes, also have homotopy (co)limit constructions. We'll explore some examples of these. From robin at ucalgary.ca Mon Nov 21 18:57:49 2011 From: robin at ucalgary.ca (Robin Cockett) Date: Mon Nov 21 18:58:13 2011 Subject: [Alta-Logic] peripatetic seminar talk: Real rank versus nonnegative rank Message-ID: <4ECB019D.7000903@ucalgary.ca> Title: Real rank versus nonnegative rank Time: 11:00am Wednesday, 23rd Nov., 2011 Place: ICT 616 Speaker: Pavel Hrubes For a nonnegative real matrix M, its nonnegative rank is the smallest k such that M is a sum of k nonnegative rank one matrices. While it is easy to construct examples of matrices whose nonnegative rank is strictly greater than the real rank, it is an open problem to determine how large the gap between rank and nonnegative rank can be. I will discuss this problem and its connection to questions in computational complexity. From robin at ucalgary.ca Tue Nov 29 11:00:28 2011 From: robin at ucalgary.ca (Robin Cockett) Date: Tue Nov 29 11:01:02 2011 Subject: [Alta-Logic] Peripatetic talk Message-ID: <4ED51DBC.1070809@ucalgary.ca> Time: 11:0am Wednesday, 30th November Place: ICT 616 Speaker: Berndt Bremken Title: Partial isometries Abstract: A partial isometry on a Hilbert space is an isometry defined on a closed subspace and mapping the orthogonal complement to zero. Over the past century these basic operators have played a fundamental role in the study of operators, and of algebras of operators, through, for example, the polar decomposition of an operator, the classification of projections and von Neumann algebras, and the K-theory of operator algebras. There has been recent interest in graph C*-algebras which are generated by families of partial isometries with relations determined by the directed edges of a graph. The universal algebra generated by a single partial isometry has not been considered, although special cases are well understood, so algebras generated by a unitary operator, or an isometry. In joint work with Z. Niu we establish a close connection between partial isometries and contractions to examine the algebra generated by a partial isometry.