Events

Matthew Beckett, Department of Pure Mathematics, University of Waterloo

“The exterior derivative, integration, and Stokes’ Theorem”

We continue our discussion of differentiable manifolds by talking about the exterior derivative and how to integrate n-forms. We will then prove Stokes’ Theorem which is a generalization of the Fundamental Theorem of Calculus.

Raymond Cheng, Department of Pure Mathematics, University of Waterloo

“Hopf algebras, symmetric functions and representation theory”

We introduce the notion of Hopf algebras, from which we will obtain a new perspective on the representation theory introduced thus far. The Hopf algebra of symmetric functions will then be introduced.

Talk 1: Mateusz Olechnowicz - 1:00 pm

Pure Mathematics Department, University of Waterloo

Christopher Dugdale, Department of Pure Mathematics University of Waterloo

“Goldie Theorems”

When can a ring be embedded into a field? Goldie knew the answer, and made it more general! Come to this talk and find out for yourself.

Michael Baker, Department of Pure Mathematics, University of Waterloo

“Schur functors, Young tableaux, and representation theory”

Having now developed adequate preparation, we will discuss Schur-Weyl duality, the monoidal category of Schur functors and its Grothendieck ring (the ring of symmetric functions), and finally Young tableaux and their connections to

Adam Dor On, Department of Pure Mathematics, University of Waterloo

"Monopoly, Drunkards and Markov chains"

Monopoly is a classic game of chance and strategy. It turns out one can model it using Markov chains to deduce useful tactics for systematically obliterating your opponents. The methods used then bring us to consider the seemingly unrelated question of whether or not a drunken man or drunken angel can return home safely from the pub.

Talk 1. Mateusz Olechnowicz, Pure Mathematics Department, University of Waterloo

“Group schemes II”

How is an affine group a scheme? The goal of this talk is to make less tenuous the claimed equivalence between group schemes and affine groups.

Cameron Williams, Department of Pure Mathematics, University of Waterloo

“A further generalization of the Cauchy integral formula: the Cauchy-Pompeiu formula.”

In this talk, we will develop a generalization of the Cauchy integral formula to C1 functions.

Jordan Hamilton, Pure Mathematics, University of Waterloo

"Generalized Complex Structures on Kodaira Surfaces"

In this thesis, we study generalized complex structures on Kodaira surfaces, which are non-Kähler surfaces that admit holomorphic symplectic structures. We show, in particular, that the moduli space of even-type generalized complex structures on a Kodaira surface is smooth of complex dimension four.

Justin Sawon, University of North Carolina, Chapel Hill

“Holomorphic Lagrangian fibrations”

In this talk we survey Lagrangian fibrations on holomorphic symplectic manifolds. We describe examples, existence of Lagrangian fibrations, the structure of singular fibres, the relation between dual fibrations, and finiteness results for Lagrangian fibrations.

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Analysis learning seminar