Geometry and Combinatorics

Speaker: Mieke Fink (University of Bonn)

"Valuative invariants for matroids"

Time: 08:30

Room: zoom

Contact the organiser for the link!

Transformation Groups Seminar

Speaker: Vladimir Gorchakov (Western)

"Cohomology of Free Loop Spaces II"

Time: 09:30

Room: MC 108

In this talk, we will discuss the cohomology groups of the free loop space of a topological space X, which is the space of all continuous maps from S^1 to X. Using the Eilenberg–Moore spectral sequence, we will connect these cohomology groups and Hochschild homology and compute them in specific cases. We will mostly follow the article "On the Characteristic Zero Cohomology of the Free Loop Space" by L. Smith.

Geometry and Topology

Speaker: Nathan Kershaw (Western)

"Efficient computations of discrete cubical homology"

Time: 15:30

Room: MC 107

We will present the fastest known algorithm for computing discrete cubical homology, a valuable graph invariant with a wide range of applications, including matroid theory, hyperplane arrangements, and topological data analysis. This invariant is capable of detecting certain types of "holes" within a graph, providing insight into its structure.

We will begin by defining discrete cubical homology and outlining the standard approach to its computation. We will then present an algorithm designed to improve efficiency by using techniques such as faster generation of singular cubes, reducing chain complex dimensions through quotients over automorphisms, and preprocessing graphs using results from discrete homotopy theory. These advancements aim to make the invariant more accessible computationally for applications. We are now able to compute examples that were previously considered out of reach by experts. Part of the motivation for this work was a joint project with the research group of R. Laubenbacher (Dept. of Medicine, University of Florida) on analyzing gene regulatory networks.

This talk is based on the paper: Kapulkin, Kershaw, Efficient computations of discrete cubical homology, arXiv:2410.09939.

Pizza Seminar

Speaker: Masoud Khalkhali (Western)

"POSTPONED"

Time: 17:30

Room: MC 107

This talk has been postponed to a later date.

Imagine you don't have perfect knowledge of the entries of a matrix (which is a what happens usually in applications of matrices). What can be said about the eigenvalues of such a matrix?  Is there a pattern to the eigenvalues at all? Can we say anything about them? In this talk I shall start with very simple examples and gradually  examine the question, using some computer calculations and some basic undergraduate mathematics.

Graduate Seminar

Speaker: Diego Tenoch Morales Lopez (Western)

"Mathematics applied to evolution: bridging the gaps between pure mathematics, biology and numerical analysis"

Time: 15:30

Room: MC 107

From the perspective of a pure mathematician, the application of mathematics to concrete problems (like evolution of the species) is not of primary importance. However, that does not imply that applied mathematics deals with problems that are trivial mathematically speaking, or that there is nothing to learn from applications. In this talk, I will showcase different ways in which mathematics are being used in the study of Evolution, ranging from systems of ODEs and PDEs to "simple" stochastic models, with some sprinkles of numerical analysis. My goal is to spark the interest of the pure math audience not only in applying math to biology, but also in further analyzing the mathematics that arise from biological problems for mathematics' sake.

Flower Hour

Speaker: (Western)

"Mathematical Biology Seminar"

Time: 11:00

Room: WSC 187

Transformation Groups Seminar

Speaker: Geoffroy Horel (Paris 13)

"E2 formality via obstruction theory"

Time: 09:30

Room: Zoom ID: 990 6584 3212

I will explain how to approach the question of E2-formality of differential graded algebras over a prime field via obstruction theory. In particular, E2-algebras whose cohomology ring is a polynomial algebra on even degree classes are intrinsically formal. As a consequence we can prove E2-formality of the classifying space of some compact Lie group or of Davis-Januszkiewicz spaces.

Geometry and Topology

Speaker: Nikolay Bogachev (University of Toronto)

"Arithmeticity and commensurability classes of hyperbolic reflection groups"

Time: 15:30

Room: MC 107

Hyperbolic reflection groups appear in various fields of mathematics such as algebraic geometry, discrete subgroups of Lie groups, geometric group theory, geometric topology, and number theory. Cofinite and cocompact hyperbolic reflection groups have the following feature: their fundamental domains are Coxeter polyhedra having simple geometric and combinatorial properties. Based on these properties, Vinberg initiated the theory of hyperbolic reflection groups and proved several fundamental and remarkable theorems related to their arithmeticity and commensurability classes. I will give a survey of this field, and will mention a few recent results in this direction. This talk is partially based on my work with S. Douba and J. Raimbault.

Professional Development

Speaker: Kelvin Chan (Western)

"LaTeX Workshop"

Time: 16:30

Room: MC 107

LaTeX is a document preparation system widely used in mathematics. Every mathematician is expected to know how to use LaTeX. It is used not only for typesetting papers and theses but also for graphics, presentations and CVs. At its core, LaTeX is a mark-up language (similar to markdown or HTML) where plain text special commands produce well-formatted math and other document constructs. Computer programs (such as pdflatex or lualatex) compile LaTeX source files to create beautiful PDFs.

The LaTeX workshop is facilitated by Kelvin Chan. Everyone is welcome, even if you already know some LaTeX. The workshop will be tailored to the needs of the audience.

We will gain some hands-on experience with LaTeX. At the end of the workshop, you will

know the basics of LaTeX to typeset a wide range of mathematical entities, have created a basic paper or presentation, have successfully produced PDFs from your skeleton document, know how to manage multi-file projects know some LaTeX technical terms so you know how to ask for help and have references for more LaTeX-related goodies.

Participants should bring a laptop with a local LaTeX installation (see https://tug.org/texlive/) or an Overleaf.com account.

Overleaf is free and suitable for learning LaTeX and typesetting short documents. However, collaboration features require a paid subscription. You can get paid Overleaf features for free with a local installation. Windows users should follow the easy install instructions. The full package includes an editor called TeXworks. Mac users should install MacTeX. It includes an editor called TeXShop. If you can run TeXworks on Windows or TexShop on Mac, your installation is ready. Don't worry if you run into problems. We will help you get a local installation up and running.

Pizza Seminar

Speaker: Masoud Khalkhali (Western)

"What is not random about random matrices?"

Time: 17:30

Room: MC 108

In many applications, matrices are often only partially known or contain elements influenced by randomness. This raises the question: what can we say about the eigenvalues of such matrices? Do they follow any patterns, and can we make meaningful predictions about them? In this talk, I will begin with basic examples of matrices with random independent entries and, with the help of computer calculations and accessible undergraduate mathematics, explore the surprising regularities that emerge. I will conclude by sketching a proof of Wigner's Semicircle Law, which shows that, for random matrices, the bell curve familiar from probability theory is replaced by a semicircular distribution.

Graduate Seminar

Speaker: Nathan Pagliaroli (Western)

"The Free Central Limit Theorem"

Time: 15:30

Room: MC 107

Free Probability is used to study non-commutative random variables and has its roots in Voiculescu’s work on operator algebras in the 1980s. The notion of free independence serves as the non-commutative analogue of independence in classical probability theory. One of the most famous results in probability theory is the central limit theorem and in this talk we will prove the analogous result in free probability theory, known as the free central limit theorem.  The proof is combinatorial in nature and all relevant notions of Free Probability will be introduced beforehand.

Flower Hour

Speaker: (Western)

"Mathematical Biology Seminar"

Time: 11:00

Room: WSC 187

Geometry and Combinatorics

Speaker: (Western)

"no talk this week"

Time: 15:30

Room: MC 108

Public Lecture

Speaker: Aaron Crighton (Fields Institute)

"Fields Quantitative Information Security Specialist Program"

Time: 15:30

Room: MC 107

Representatives from Fields Information Security will present on their Information Security Specialist Program. Email cschul3@uwo.ca for more information and program brochure.

Transformation Groups Seminar

Speaker: Vladimir Gorchakov (Western)

"Cohomology of Free Loop Spaces III"

Time: 09:30

Room: MC 108

Graduate Seminar

Speaker: Theofanis Chatzidiamantis Christoforidis (Western)

"Formalising higher category theory"

Time: 15:30

Room: MC 107

Homotopy type theory (HoTT) is a formal system that allows us to do homotopy-invariant mathematics in a natural way, where types can be seen as representing topological spaces. In HoTT, every type has types of paths (identity types) between its terms, paths between paths, etc., giving types a higher groupoidal structure. Simplicial type theory is an extension of HoTT that adds extra categorical structure to types using constructions similar to those in simplicial sets, making it possible to state a definition of an infinity-category that does not depend on a particular set-theoretic model. Additionally, using type-theoretic foundations makes it easier to formalise parts of the theory of infinity-categories in proof assistants, and in particular the Rzk proof assistant developed specifically for this type theory. We present an introduction to HoTT and simplicial type theory, and discuss possible directions one can consider in synthetic higher category theory.

Flower Hour

Speaker: (Western)

"Mathematical Biology Seminar"

Time: 11:00

Room: WSC 187

Geometry and Combinatorics

Speaker: Girtrude Hamm (Western)

"TBA"

Time: 15:30

Room: MC 108

Transformation Groups Seminar

Speaker: Kumar Shukla (Western)

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

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.

Graduate Seminar

Speaker: Harshith Alagandala (Western)

"Polynomial convexity and approximation by polynomials"

Time: 15:30

Room: MC 107

A compact subset K of C^n is said to be polynomially convex if every point in the complement of K can be separated from K by a polynomial. Oka-Weil theorem tells us that holomorphic functions can be approximated by polynomials on polynomially convex sets. This is a generalization of Runge approximation theorem to higher dimension. We will go through some approximation results in complex analysis, look at examples of polynomially convex sets, and analyze the local polynomial convexity of real n-dimensional manifolds embedded in C^n.

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