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29 Geometry and Combinatorics
Geometry and Combinatorics Speaker: Mieke Fink (University of Bonn) "Valuative invariants for matroids" Time: 08:30 - 09:30 Room: zoom Contact the organiser for the link! Transformation Groups Seminar
Transformation Groups Seminar Speaker: Vladimir Gorchakov (Western) "Cohomology of Free Loop Spaces II" Time: 09:30 - 11:00 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. |
30 Geometry and Topology
Geometry and Topology Speaker: Nathan Kershaw (Western) "Efficient computations of discrete cubical homology" Time: 15:30 - 16:30 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
Pizza Seminar Speaker: Masoud Khalkhali (Western) "POSTPONED" Time: 17:30 - 19:00 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. |
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1 Graduate Seminar
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 - 16:30 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. |
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Flower Hour
Flower Hour Speaker: (Western) "Mathematical Biology Seminar" Time: 11:00 - 12:00 Room: WSC 187 Geometry and Combinatorics
Geometry and Combinatorics Speaker: Graham Denham (Western) "Resolving configuration hypersurfaces" Time: 15:30 - 16:30 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
Transformation Groups Seminar Speaker: Geoffroy Horel (Paris 13) "E2 formality via obstruction theory" Time: 09:30 - 11:00 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.
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Geometry and Topology
Geometry and Topology Speaker: Nikolay Bogachev (University of Toronto) "Arithmeticity and commensurability classes of hyperbolic reflection groups" Time: 15:30 - 16:30 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
Professional Development Speaker: Kelvin Chan (Western) "LaTeX Workshop" Time: 16:30 - 17:30 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.
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Graduate Seminar
Graduate Seminar Speaker: Nathan Pagliaroli (Western) "The Free Central Limit Theorem" Time: 15:30 - 16:30 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. |
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Flower Hour
Flower Hour Speaker: (Western) "Mathematical Biology Seminar" Time: 11:00 - 12:00 Room: WSC 187 Geometry and Combinatorics
Geometry and Combinatorics Speaker: (Western) "no talk this week" Time: 15:30 - 16:30 Room: MC 108 Public Lecture
Public Lecture Speaker: Aaron Crighton (Fields Institute) "Fields Quantitative Information Security Specialist Program" Time: 15:30 - 16:30 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. |
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Flower Hour
Flower Hour Speaker: (Western) "Mathematical Biology Seminar" Time: 11:00 - 12:00 Room: WSC 187 Geometry and Combinatorics
Geometry and Combinatorics Speaker: Girtrude Hamm (Western) "TBA" Time: 15:30 - 16:30 Room: MC 108 |
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Flower Hour
Flower Hour Speaker: (Western) "Mathematical Biology Seminar" Time: 11:00 - 12:00 Room: WSC 187 |
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Department Meeting
Department Meeting Speaker: "Math Comprehensive Exams" Time: 15:30 - 16:30 Room: MC 107 |
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