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3 Graduate Seminar
Graduate Seminar Speaker: Nicholas Meadows (Western) "the Hilbert scheme of Cohen-Macauley curves" Time: 11:20 Room: MC 106 After reviewing very quickly some algebraic geometry, I will define the Hilbert scheme which parameterizes closed subschemes of projective space Pnk and state its basic properties, for k an algebraically closed field of characteristic 0. I will then define various notions of deformations (deformations sheaves, deformations over the dual numbers etc). Finally, I will use obstruction theory for a local ring to prove a lower bound on the dimension of irreducible components of the Hilbert scheme of Cohen-Macauley curves of genus g and degree d in P3k Geometry and Topology
Geometry and Topology Speaker: Chris Kapulkin (Western) "Internal languages for higher categories" Time: 15:30 Room: MC 107 Every category C looks locally like a category of sets, and further structure on C determines what logic one can use to reason about these "sets". For example, if C is a topos, one can use full (higher order) intuitionistic logic.
Similarly, one expects that every higher category looks locally like a higher category of spaces. A natural question then is: what sort of logic can we use to reason about these "spaces"? It has been conjectured that such logics are provided by variants of Homotopy Type Theory, a formal logical system, recently proposed as a foundation of mathematics by Vladimir Voevodsky.
After explaining the necessary background, I will report on the progress towards proving this conjecture. |
4 Analysis Seminar
Analysis Seminar Speaker: Thomas Ransford (U. Laval) "Capacity and coverings" Time: 14:30 Room: MC 107 I shall discuss two elementary inequalities relating capacity to coverings. They provide an approach to determining whether a set has positive capacity and, if so, to estimating the value of the capacity. (Joint work with Quentin Rajon, Jeremie Rostand and Alexis Selezneff). |
5 Homotopy Theory
Homotopy Theory Speaker: Cihan Okay (Western) "Homotopy groups of the circle" Time: 12:00 Room: MC 106 (Note the unusual day, time, and room.)
I will talk about homotopy type theoretic proofs of a well known topological fact that the fundamental group of the circle is the set of integers. There are two closely related proofs. The homotopy-theoretic proof follows a similar reasoning used in the classical proof in topology,
whereas the encode-decode proof is more type theoretic. |
6 Colloquium
Colloquium Speaker: David Riley (Western) "Hopf algebra actions, gradings, and identical relations" Time: 15:30 Room: MC 107 I will begin by discussing how and when the action of a Hopf
algebra H on an algebra A can be viewed as a grading of A. For
example, if G is a finite group and H is the dual of the group algebra
K[G], then A is an H-algebra precisely when A is group-graded by
G. I will then discuss the identical relations of an algebra with a Hopf
algebra action. In particular, I will address the following question: when
does the existence of an H-identity on A imply the existence of an
ordinary polynomial identity on A?
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7 Algebra Seminar
Algebra Seminar Speaker: Martin Frankland (Western) "Locally presentable categories and applications" Time: 14:30 Room: MC 107 We will survey some characterization theorems for locally presentable categories and variants thereof. Then we will discuss some applications of locally presentable categories to homological and homotopical algebra. |
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