Flower Hour

Speaker: (Western)

"Mathematical Biology Seminar"

Time: 11:00

Room: WSC 187

Geometry and Combinatorics

Speaker: Graham Denham (Western)

"Resolving configuration hypersurfaces"

Time: 15:30

Room: MC 108

The hypersurface given by the Kirchhoff polynomial is a singular projective variety with relevance to physics, and also a geometric construction from a matroid realization. I will describe a resolution of singularities for such hypersurfaces using the geometry of matroids. This is based on joint work with Dan Bath, Mathias Schulze, and Uli Walther.

Transformation Groups Seminar

Speaker: Kumar Shukla (Western)

"Syzygies in equivariant cohomology of toric varieties with respect to subtori II"

Time: 09:30

Room: MC 108

Syzygies interpolate between torsion-freeness and freeness. In this talk, we will introduce the concept of syzygies and review criteria for a module to attain a certain syzygy order. Then we will discuss a result of Franz which relates the syzygy order of equivariant cohomology of a toric variety to the combinatorics of the underlying fan. Finally, by restricting the torus action on toric varieties to subtori, we will investigate the resulting changes in the syzygy order of their equivariant cohomology.

This is the second part of this talk.

Ph.D. Candidacy Exam Lecture

Speaker: Harshith Alagandala (Western)

"Local polynomial convexity at hyperbolic CR-singularity in $M^n \subset \mathbb{C}^n$"

Time: 14:30

Room: MC 204

Let $M^n$ be a real $n$-dimensional manifold embedded in $\mathbb{C}^n$. The tangent space of $T_pM$ is totally real at most points $p \in M$. Hence, $M$ is locally polynomially convex at $p$. We may have obstruction to local polynomial convexity at a CR-singularity of $M$. A CR-singularity of order one can be broadly classified as an elliptic or a hyperbolic point. Bishop has shown that $M$ is not locally polynomially convex at an elliptic point $p\in M$. Forstneri\v c and Stout have shown local polynomial convexity of $M$ at $p$ at a hyperbolic point $p\in M^2 \subset \mathbb{C}^2$. We will look at a hyperbolic point $p \in M^n \subset \mathbb{C}^n$ and show local polynomial convexity of $M$ at $p$ under certain condition on the defining functions of $M$.

Professional Development

Speaker: Taylor Brysiewicz and Chris Kapulkin (Western)

"Collaboration Workshop"

Time: 16:30

Room: MC 107

Department Meeting

Speaker:

"Math Comprehensive Exams"

Time: 15:30

Room: MC 107