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Sean Monahan, Department of Pure Mathematics, University of Waterloo

"Introduction to horospherical varieties"

We will begin the seminar with an introduction to horospherical varieties. In this talk we will define horospherical varieties, and we will (at least start to) discuss their “colours”.

This seminar will be held jointly online and in person:

Xingchi Ruan, Department of Pure Mathematics, University of Waterloo

"On the Solubility of Diophantine Systems"

Andy Zucker, Department of Pure Mathematics, University of Waterloo

"Polish partition principles and the Halpern-Lauchli theorem"

Kevin Hare, Department of Pure Mathematics, University of Waterloo

"Matrix based number system"

Most number systems are of the form $a_k d^k + a_{k-1} d^{k-1} + … + a_0$ where the $a_i$ are taken from a finite set of digits, and $d$ is the base of the number system.

In this talk we will discuss what happens if $d$ is taken to be a $n \times n$ Jordan block and $a_i$ are taken to be vectors.

Claude LeBrun, Stony Brook University

"Four-Manifolds, Conformal Curvature, and Differential Topology"

Sang-Gyun Youn, Seoul National University

"Information-theoretic analysis of covariant quantum channels"

Catherine St-Pierre, University of Waterloo

"Borel fixed Ideals (in Krull dimension 0)"

Talk #1 (9:30am-10:45am): Paul Mcauley, Department of Pure Mathematics, University of Waterloo

"Vertical and Horizontal Spaces"

For a given Riemannian manifold (M,g), a vector bundle E over M, we can define the vertical space VE which is a submanifold of TE. Given a connection on E we can then define the horizontal space HE which is a submanifold of TE. These spaces give us a fibre metric on TE and then we can look at the Levi-Civita connection in terms of these vertical and horizontal spaces.

Jeremy Usatine, Brown University

"Gromov-Witten theory and invariants of matroids"

Sean Monahan, Department of Pure Mathematics, University of Waterloo

"A GIT construction for horospherical varieties"

David Cox developed a way of writing a given toric variety as a good quotient of a quasiaffine toric variety by a diagonalizable group. This construction has a very nice interpretation using the combinatorics of the toric varieties, i.e. their fans. I will give an outline of this construction through an example, and we will see how it can be generalized to horospherical varieties.