Time: 11:00
Room: WSC 187
Speaker: (Western)
Title: Mathematical Biology Seminar

Time: 15:30
Room: MC 108
Speaker: Graham Denham (Western)
Title: Resolving configuration hypersurfaces

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.

Time: 09:30
Room: MC 108
Speaker: Kumar Shukla (Western)
Title: Syzygies in equivariant cohomology of toric varieties with respect to subtori II

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.

Time: 14:30
Room: MC 204
Speaker: Harshith Alagandala (Western)
Title: Local polynomial convexity at hyperbolic CR-singularity in $M^n \subset \mathbb{C}^n$

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 $M$.

Time: 16:30
Room: MC 106
Speaker: Taylor Brysiewicz, Yvon Verberne, and Lindi Wahl (Western)
Title: Collaboration Workshop

Collaborative work has come to dominate mathematics. The average number of authors of a math paper has increased from 1.3 in 1970 to over 3 in 2020, and the trend is expected to continue. To be a successful academic, you need to be able to navigate the intricacies of collaborations, and this is exactly what our event is about.

The first part of the event will be a panel discussion on the do's and don'ts of collaboration and will be in MC 106. Afterwards, we will move to MC 107 for an introduction to Git, a version control system (i.e., something that manages files on your computer) for collaborative work.

The panelists will be three professors from our department: Taylor Brysiewicz, Yvon Verberne, and Lindi Wahl, covering a broad range of mathematical areas. The discussion will take roughly 45 minutes.

At around 5:15, Taylor Brysiewicz will give a tutorial on how to use Git in MC 107. You're welcome to attend either part of the event without attending the other.

Time: 10:00
Room: MC 204
Speaker: Cortland Griswold (University of Guelph)
Title: Ancestral graph theory of ecological communities and the theoretical population genetics of polyploid cross-over interference

In this talk I will give an overview of ancestral graph theory (the coalescent; ancestral recombination and selection graphs), and present work from my group in which we have applied the theory to understand evolution in microbial communities using metagenomic sampling, as well as the evolution of pangenomes. This will be followed by work on modeling cross-over interference in autotetraploids. The talk will finish with summaries of student-focused research, including plasmid, epigenetic and eco-evolutionary genetic theory.

Time: 15:30
Room: MC 107
Speaker:
Title: Math Comprehensive Exams

Time: 15:30
Room: MC 107
Speaker: Anif Shikder (Western)
Title: An Operator Approach to All-Pairs Shortest Path For Random Graphs

We introduce an analytical model for Erdős–Rényi graphs called GRE and derive expressions approximating its adjacency matrix. We then find expressions approximating its l-path matrix. After formulating key graph measures such as the clustering coefficient, the distance matrix, and the average shortest distance in terms of the l-path matrix, we deduce analytical expressions approximating them. Our expressions do not contain any free parameters and show fast convergence valid non-asymptomatically over the entire probability space. The proposed approach is generalizable to other random graphs and can be used to approximate algebraically well-defined graph measures to investigate finite-sized real-world networks.