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Barbara Csima, Department of Pure Mathematics, University of Waterloo

"Degrees of Categoricity"

A degree of categoricity is a Turing degree that exactly captures the complexity of computing isomorphisms between computable copies of some computable structure. In this talk I will start by giving some easy examples of degrees of categoricity. I will then give a review of what is known about degrees of categoricity, culminating in new results (joint work with Dino Rossegger).

Christopher Lang, Department of Pure Mathematics, University of Waterloo

"Hyperbolic Monopoles with Continuous Symmetries"

We examine hyperbolic monopoles with continuous symmetries and develop a structure theorem which generates spherically symmetric hyperbolic monopoles. To do this, we modify the steps laid out in a collaborative paper of mine wherein we proved a similar structure theorem for Euclidean monopoles. We discuss how these steps may be applied to other gauge theoretic objects.

Ty Ghaswala, CEMC, University of Waterloo

"Boundary Dehn twists are excellent!"

Changho Han, Department of Pure Mathematics, University of Waterloo

"Divisors and line bundles on horospherical varieties"

Using the presentation of horospherical varieties as coloured fans, I will present how to describe Borel-invariant Weil and Cartier divisors combinatorically. Then I will give a description of the Picard group of horospherical varieties and detect geometric properties of them.

This seminar will be held jointly online and in person:

Rahim Moosa, Department of Pure Mathematics, University of Waterloo

"When any two solutions are independent"

Jérémy Champagne, Department of Pure Mathematics, University of Waterloo

"Interesting results in equidistribution theory"

An infinite sequence is equidistributed in an interval if the "proportion" of its points lying in any given sub-interval corresponds roughly to the length of the sub-interval. In a sense, this can be regarded as an "almost randomness" property, and sometimes shows up naturally in analytic number theory.

Kieran Mastel, Department of Pure Mathematics, University of Waterloo

"Surreal Numbers and Games"

Yunhai Xiang, Department of Pure Mathematics, University of Waterloo

"Introduction to derived categories"

Jiasheng Teh, McMaster University

"On moduli spaces of Ricci-flat 4-manifolds"

Spiro Karigiannis, Department of Mathematics, University of Waterloo

"Cohomologies on almost complex manifolds and their applications"