Geometry and Topology

Speaker: Anibal Medina-Mardones (Western)

"Homotopy Lie algebras and Gauge Theories"

Time: 15:30

Room: MC 107

In this talk we survey an algebro-homotopical perspective on classical gauge field theories in the perturbative regime. We show how cyclic $L_\infty$-algebras encode their essential structures, among them fields, symmetries, and actions. We illustrate this perspective through three central examples: Maxwell's electromagnetism, Chern-Simons theory, and Yang-Mills theory.

Transformation Groups Seminar

Speaker: Vladimir Gorchakov (Western)

"Equivariant formality and the cohomology of subgroups of Right-Angled Coxeter Groups"

Time: 09:30

Room: MC 107

Let $H$ be a subgroup of $(\mathbb{Z}_2)^m$ acting on a real moment-angle complex. In this talk, I will discuss when the H-action is equivariantly formal and how this follows from similar results on torus actions on moment-angle complexes. As an application, I will discuss the cohomology of subgroups of Right-Angled Coxeter Groups. This talk is based on ongoing joint work with S. Amelotte.

Algebra Seminar

Speaker: Hyun Kim (Western)

"Aspects of etale sheaves"

Time: 14:30

Room: MC 107

I will briefly discuss some of the essential concepts that one speaks of in the theory of sheaves on the small etale sites of schemes, such as the etale fundamental group, locally constant sheaves, ell-adic sheaves, etale cohomology, and ell-adic cohomology. Time permitting, I will also state theorems about ell-adic cohomology such as the Grothendieck-Lefschetz Trace Formula, Poincare duality, and the Weil conjectures.

MathBio Seminar Talk

Speaker: Dr Bo Zhang (Oklahoma State University)

"Movement alters ecological dynamics in heterogeneous environments"

Time: 10:30

Room: MC 204

Understanding mechanisms of coexistence is a central topic in ecology. Mathematical analysis of models of competition between two identical species moving at different rates of symmetric diffusion in heterogeneous environments show that the slower mover excludes the faster one. The models have not been tested empirically and lack inclusions of a component of directed movement toward favorable areas. To address these gaps, we extended previous theory by explicitly including exploitable resource dynamics and directed movement. We tested the mathematical results experimentally using laboratory populations of the nematode worm, Caenorhabditis elegans. Our results not only support the previous theory that the species diffusing at a slower rate prevails in heterogeneous environments but also reveal that moderate levels of a directed movement component on top of the diffusive movement allow species to coexist. Additionally, we have expanded our work to test the outcomes of different movement strategies in a various of fragmented and toxincant environments. For instance, we combine mechanistic mathematical modeling and laboratory experiments to disentangle the impacts of habitat fragmentation and locomotion. Our theoretical and empirical results found that species with a relatively low motility rate maintained a moderate growth rate and high population abundance in fragmentation. Alternatively, fragmentation harmed fast-moving populations through a decrease in the populations’ growth rate by creating mismatch between the population distribution and the resource distribution. Our study will advance our knowledge of understanding habitat fragmentation's impacts and potential mitigations, which is a pressing concern in biodiversity conservation.

Ph.D. Public Lecture

Speaker: Shubhankar (Western)

"Polar convexity and its applications"

Time: 13:30

Room: MC 107

A subset Z of R^n is said to be u-convex if for any two points z1, z2 ∈ Z, the arc of the circle through u, z1 and z2, lying between z1, z2 and not containing u, is contained in Z. We call u a pole of Z and Z a polar convex set if this happens. The notion of polar convexity was developed for the complex plane to study the geometry of univariate complex polynomials. This talk discusses some motivations for the theory and presents the extension of polar convexity to higher dimension Euclidean spaces. The introduction of a pole creates a richer theory full of properties that classical convexity has no analogues for. We study the geometrical properties of polar convex sets and develop analogues of theorems from classical convexity. Finally, we define polar derivatives for multivariate polynomials and demonstrate the use of polar convex sets in studying the roots of multivariate polynomials with several analogues of the Gauss-Lucas theorem.

Symplectic and Complex Geometry

Speaker: Rasul Shafikov (Western)

"Polynomially and Rationally convex domains on $\mathbb C^n$"

Time: 13:30

Room: MC 107

In this talk I will introduce the notion of polynomial and rational convexity and present other relevant material in order to formulate a result of Cieliebak and Eliashberg (Invent. Math. 2015) concerning the topology of smoothly bounded domains with polynomially, resp. rationally, convex closure in complex Euclidean spaces.

Algebra Seminar

Speaker: Ezra Waxman (Afeka College of Engineering (Israel))

"Artin's primitive root conjecture: classically and over algebraic function fields"

Time: 14:30

Room: MC 107

Fix $g \in \mathbb{N}$ such that $g$ is not a perfect square. Artin's primitive root conjecture (1927) states that there exist infinitely many primes $p \in \mathbb{N}$ such that $g$ generates the finite cyclic group $(\mathbb{Z}/p\mathbb{Z})^{\times}$. Nearly a century later, Artin's conjecture remains wide-open: in fact there is no known specified $g$ for which the conjecture has been resolved.

In this talk, we survey the interesting history of Artin's conjecture and introduce several new variants to the problem. Specifically, we discuss an "Artin Twin Primes Conjecture"; and prove an appropriate analogue of Artin's conjecture for algebraic function fields.

PhD Thesis Defence

Speaker: Mojgan Ezadian (Western)

"TBA"

Time: 09:00

Room: MC 204

Symplectic and Complex Geometry

Speaker: Rasul Shafikov (Western)

"Polynomially and Rationally convex domains, Part II"

Time: 13:30

Room: MC 107

In this talk we continue our investigation of polynomially and rationally convex compacts in complex Euclidean spaces. The emphasis will be on the topology of smoothly bounded domains with polynomially and rationally convex closure

Algebra Seminar

Speaker: Chris Hall (Western)

"Division Fields of Superelliptic Curves"

Time: 14:30

Room: MC 108

We will discuss superelliptic curves, their Jacobians, and a family of associated Galois extensions.

Symplectic and Complex Geometry

Speaker: Rasul Shafikov (Western)

"Polynomially and Rationally convex domains, Part III"

Time: 13:30

Room: MC 108

In this talk we formulate the result of Cieliebak and Eliashberg that gives a topological characterization of polynomially and rationally convex domains, and identify the key ingredients of the proof.

PhD Thesis Defence

Speaker: Ruchita Amin (Western)

"TBA"

Time: 09:00

Room: ZOOM

MathBio Seminar Talk

Speaker: Dr. Iain Moyles (York University)

"Dynamics and Bifurcations in a Mathematical Model of Coupled Fear-Disease Transmission"

Time: 11:30

Room: MC 204

We explore a mathematical model of disease transmission with a fearful compartment. Susceptible individuals become afraid by either interacting with individuals who are already afraid or those who are infected. Individuals who are afraid take protective measures via contact reductions to reduce risk of transmission. Individuals can lose fear naturally over time or because they see people recovering from the disease. We consider two scenarios of the model, one where fear is obtained at a slower rate than disease spread and one where it is comparable. In the former we show that behavioural change cannot impact disease outcome, but in the latter, we observe that sufficient behavioural intervention can reduce disease impact. However, response to recovery can induce a bifurcation where contact reduction cannot mitigate disease spread. We identify this bifurcation and demonstrate its implication on disease dynamics and final size.

Fields Special Presentation

Speaker: Fields (University of Toronto)

"Quantitative Information Security Specialist Program"

Time: 14:30

Room: WSC 240

This training program is specifically designed for graduate students and recent PhDs in mathematics or related fields, who are looking to transition to work in the information security industry after graduation.

Geometry and Combinatorics

Speaker: Daniel Bath (KU Leuven)

"Bernstein-Sato polynomials for hyperplane arrangements of rank 3"

Time: 15:30

Room: MC 108

The Bernstein-Sato polynomial (and its roots) are important invariants of hypersurface singularities. It is a Rosetta Stone: it seems most singularity data lies within, if only one could decode it. Unfortunately, after 50 years actual computations remain scarce. I will give a formula for the roots of Bernstein-Sato polynomials of hyperplane arrangements in three variables. It turns out all but one root is determined by the combinatorics, and the outlier root is determined by simple algebraic data. Time permitting I will connect this non-combinatorial root to the realization space of the underlying matroid.

Symplectic and Complex Geometry

Speaker: Siyuan Yu (Western)

"TBA"

Time: 13:30

Room: MC 107

Colloquium

Speaker: Assaf Bar-Natan (Model six)

"Big Surfaces, Medium Geometry, and Small Triangles"

Time: 15:30

Room: MC 107

For a compact surface S, $MCG(S) = Homeo(S)/Homeo_0(S)$ is a group well-studied and loved by many, but especially by geometric group theorists because it is finitely generated, and hence has a coarse geometry coming from its Cayley graph. When S is big (infinite-type), $MCG(S)$ is Polish and no longer discrete, but following the work of Rosendal and Mann-Rafi, we can still define a coarse geometry and a Cayley graph. In ongoing work with Schaffer-Cohen—Verberne and Qing—Rafi, we can show that for some surfaces, $MCG(S)$ is non-elementary $\delta$-hyperbolic, and some have infinite coarse rank. If you like surfaces, geometry, topology, and Polish groups, come by!

Algebra Seminar

Speaker: Mac Martin (Western)

"TBA"

Time: 14:30

Room: MC 108

TBA