Speaker: Daniel Wise, McGill University
Time/Date: Wednesday, July 20, 2022, 10 a.m.
Room: HH-3017
Title: Continuously many different residually finite groups.

Abstract:
We describe two neat families of finitely generated residually finite groups. The first family of groups are pairwise non-isomorphic. The second family of groups are pairwise non-quasi-isometric. This is joint work with William Hip Kuen Chong.

 

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Speaker: Tom Baird, Memorial University of Newfoundland
Time/Date: March 18, 2022, 2:00 p.m.
Room: HH-3013
Title: The Kontsevich quantization formula

Abstract: 
In this expository lecture I will present the Kontsevich Quantization formula, which solves the deformation quantization problem for all Poisson manifolds. Along the way I will explain Poisson geometry, geometric quantization and deformation quantization, and a surprising connection between Kontsevich’s formula and the Riemann zeta function. I will try to make the lecture accessible to a general audience.

 

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Speaker: Mitja Mastnk, Saint Mary’s University
Time/Date: November 10, 2021, 1:00pm
Room: HH-3017
Title: Universal measurings and related constructions

Abstract:
If C is a coalgebra and A, B are algebras, then we say that a map f: C ⊗ B → A is a measuring (or that (C, f) measures B to A) if it corresponds to an algebra map from B to the convolution algebra Hom(C, A), i.e., if f(c, xy) = f(c1, x)f(c2, y) and f(c, 1B) = ε(c)1A for c ∈ C and x, y ∈ B. Measurings are needed for constructing smash products and unify the concepts of homomorphism and derivations. As Grunenfelder and Par ́e explained in the 1980’s (about two decades after Sweedler initiated a systematic study of measurings), they can be thought of as C-indexed families of homomorphisms.

Sweedler showed that given algebras B, A there exists the universal measuring coalgebra M(B, A) and the universal measuring θ: M(B, A)⊗ B → A with the property that every other measuring of B to A factors through it. In the presentation we will revisit Sweedler’s universal construction and will also discuss some related constructions for the cases when we assume additional structure on A, B, C.

 

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Speaker: Dr Cameron Ruether, University of Ottawa
Time/Date: September 22, 2021, 1:00pm
Room: HH-3017
Title: Twisting Spin, Half-spin, and Hopf Algebras

Abstract:
It is well known that central simple algebras are twisted forms of matrix algebras. That is, when we consider a central simple algebra A over a field F, if we extend scalars to the separable closure of F we have an isomorphism between Asep and Mn(Fsep) for some n. Conversely, by modifying the natural Galois action on Mn(Fsep) in a process called twisting, we can identify A as a set of fixed points within Mn(Fsep). This procedure readily extends to linear algebraic groups which come from subgroups of Mn(F), such as SLn or SOn, to produce their twisted counterparts, SL(A) or SO(A, t), where t is an orthogonal involution on A. This twisting result applies to all classical linear algebraic groups, in particular we show that we can twist Spinn and HSpinn to produce Spin(A, t) and HSpin(A, t). In addition, and in order to produce the result about HSpin, we discuss how the twisting story for linear algebraic groups is mirrored in their representing Hopf algebras. If H is the Hopf algebra of a group G, and G(A) is the twisted form, we show how to construct a modified Galois action on Hsep whose fixed points are the representing Hopf algebra of G(A).