Speaker: Jeff Egger Time: Friday Sept. 30th, 1-2pm Place: FTX 137 Title: Categorical models of effect calculi and linear logic Abstract: Effect calculi, though motivated independently, prove to be (equivalent to) ``fragments'' of linear logic---in the weak sense that a model of linear logic is also a model of the enriched effect calculus (EEC), and therefore also of the basic effect calculus (EC) which is syntactically equivalent to Levy's call-by-push-value (CBPV). =============================================================== TITLE: Toposes of toric quasicoherent sheaves SPEAKER: James Dolan (N/A) DATE: Monday, October 17, 2011 TIME: 1:00 am ROOM: KED B015 ABSTRACT: Analogous to the abelian category of quasicoherent sheaves over an ordinary variety, there's a topos of toric quasicoherent sheaves over a toric variety. (This talk will be a more detailed version of the one at Octoberfest.) ================================================================ Speaker: Alex Hoffnung (UofO) Room: FTX 137 Time: Friday Oct. 21, 1pm Title: Higher categories: what are all those diagrams? Abstract: The need for higher categories in modern mathematics has become quite clear. Unfortunately, the development of these structures has been less so. There are very technical reasons for this. Putting aside technical issues, as we progress to higher categories, we come to another hurdle -- the overwhelming amount of data found in the coherence laws. This data turns out to be important surprisingly often. In this talk, I hope to convey a sense of simplicity of the structure and coherence for low-dimensional higher categories. If time permits, I may talk about some particular examples. ============================================================ Speaker: Pieter Hofstra Time: Friday Oct. 4th, 1pm Place: KEDB015 Title: The free bicompletion of a fibration Abstract: I will explain how Joyal's construction of the free bicomplete category can be generalized to fibrations by exhibiting a pseudo-monad which freely adds both left- and right adjoints to substitution functors (without invoking any distributive law). While the monad in question can abstractly be described as the coproduct of the monad which adds existential quantification and the monad which adds universal quantification, part of the interest lies in finding a concrete presentation. Among other things, this makes use of a construction by Lack which exhibits a correspondence between pseudo-monads and suitable functors out of a generalization of the simplex category. ================================================= Speaker: Eduardo J. Dubuc Title: The intimate relationship between the McNaughton and the Chinese Theorems Time: Friday, Nov. 11, 2:30 pm Room: B015, 585 King Edward Abstract: (Joint work with Yuri Poveda). We will show the intimate relationship between McNaughton Theorem and the Chinese Theorem for MV-algebras. We develop a very short and simple proof of McNaughton Theorem. The arguing is elementary and right out of the definitions. We exhibit the theorem as just an instance of the Chinese theorem. Since the variety of MV-algebras is arithmetic, the Chinese theorem holds for MV-algebras. However, to stress how elementary is our proof of McNaughton, we will also show a simple proof of the Chinese Theorem for MV-algebras. We will not assume any prior knowledge of MV-algebras by the audience. =================================================== Speaker: Rory Lucyshyn-Wright (York) Time: Friday Nov 18th, 1pm Place: FTX361 Title: Algebraic theory of vector-valued integration Abstract: We define a monad M on a category of measurable bornological sets, and we show how this monad gives rise to a theory of vector-valued integration that is related to the notion of Pettis integral. We show that an algebra X of this monad is a bornological locally convex vector space endowed with operations which associate vectors \int f dm in X to incoming maps f:T --> X and measures m on T. We prove that a Banach space is an M-algebra as soon as it has a Pettis integral for each incoming bounded weakly-measurable function. It follows that all separable Banach spaces, and all reflexive Banach spaces, are M-algebras. ==================================================== Speaker: Geoff Cruttwell (UofO) Time: Friday Nov. 25th, 1pm Place: KEDB004 Title: Reconsidering Cartesian differential categories Abstract: Cartesian differential categories were invented to abstractly describe categories where each map has a "derivative". Over time, however, several small problems (philosophical, theoretical, and practical) have arisen with the definition. We'll look at the definition, investigate the problems, and propose a generalized definition of Cartesian differential categories that will solve the problems while providing many new examples.