Geometry and Combinatorics

Speaker: Taylor Brysiewicz (Western)

"Hollow 4x4 orthogonal matrices"

Time: 15:30 - 16:30

Room: MC 108

Western Quantiers

Speaker: Liam Hickey (Western)

"An Introduction to Quantum Error Correction III"

Time: 15:30 - 16:30

Room: MC 107

Quantum Error Correction (QEC) serves as one of the most important fields, opening pathways to harness the true power of quantum computing. While quantum computing holds potential, this potential cannot be realized without ways to guarantee the stability and reliability of qubits, which are inherently prone to errors. To address this challenge, I will begin by exploring the origins of error correction, where early methods ensured reliable data transmission without fear of complete loss. From there, I will discuss the challenges of bridging classical and quantum error correction techniques. Finally, I will introduce stabilizer codes, one of the most promising class of codes in QEC. In future talks, I will build on this foundation to explore more advanced stabilizer codes, including topological codes.

Professional Development Session

Speaker: Taylor Bryseiwicz (Western)

"Mathematical Software"

Time: 16:30 - 17:30

Room: MC 107

I will discuss a portion of the vast landscape of mathematical software.

Coffee

Speaker: Social Committee

"Social Event"

Time: 15:00 - 16:30

Room: Math Lounge

This Thursday, the social committee will be supplying tea, coffee and cookies in the Math lounge at 3pm. This event hopes to give our grad students a chance to get to know Faculty members and each other in an informal setting.

Transformation Groups Seminar

Speaker: Vladimir Gorchakov (Western)

"An introduction to $RO(G)$-graded cohomology theories"

Time: 09:30 - 11:00

Room: MC 108

n this talk, we will give an introduction to $RO(G)$-graded cohomology, which, in a certain sense, extends Bredon cohomology.

Graduate Seminar

Speaker: Siyuan Yu (Western)

"The symplectic embeddings of closed balls into the complex projective plane $\mathbb{C}P^2$"

Time: 15:30 - 16:30

Room: MC 108

In this presentation, we investigate the embeddings of five disjoint closed balls into the complex projective plane $\mathbb{C}P^2$. In 1985, Gromov found a new symplectic invariant called Gromov's invariant by studying the embedding of closed balls into a cylinder. This ground-breaking result opens a new era of the research of symplectic geometry. In this presentation, we explore the relationship between the homotopy type of the space of symplectic embeddings and the configuration space of $\mathbb{C}P^2$, focusing on the case of five balls.

Applied dynamical system seminar

Speaker: Yucen Jin (Western)

"TBA"

Time: 11:30 - 12:30

Room: MC 204

Introduction: Topics of these seminars include differential equations (ODEs, PDEs, DDEs, FDEs, etc.), dynamical systems theory, and their applications (often in mathematical biology). To get the brain gears turning, each session will kick off with a fun trivia!

Geometry and Topology

Speaker: Yidi Wang (Western)

"A geometric approach of solving generalized Fermat equations"

Time: 15:30 - 16:30

Room: MC 107

The primitive solutions of generalized Fermat equations, i.e., Diophantine equations of the form $Ax^2+By^2 = Cz^2$, can be studied as integral points on certain stacky curves. In a paper by Bhargava and Poonen, an explicit example of such a curve of genus 1/2 violating local-global principle for integral points was given. However, a general description of stacky curves failing the local-global principle is unknown. In this talk, I will discuss our work on finding the primitive solutions to equation of the form by studying local-global principles for integral points on stacky curves constructed from such equations. The talk is based on a joint project with Juanita Duque-Rosero, Christopher Keyes, Andrew Kobin, Soumya Sankar and Manami Roy.

Pizza Seminar

Speaker: Yvon Verberne (Western)

"Braids, Knots, and Mapping Class Groups"

Time: 17:30 - 18:30

Room: MC 107

This talk is a friendly introduction to the mathematical study of braids, knots, and mapping class groups. We will start with an introduction to the braid group, learn how to interpret braids through a topological lens, and cover some of the foundational theorems of knot theory. This talk will be accessible to all students enrolled in a mathematics module.

Noncommutative Geometry

Speaker: Ali Fathi (US Bank)

"Deep Stochastic Control for the Schroedinger Bridge"

Time: 17:00 - 18:30

Room: MC 107

The Schroedinger Bridge problem as generative modelling tool has been recently studied. It is known that the solution to the problem can be cast as the optimal control (Foellmer drift) which steers a diffusion with fixed marginals at times t= 0 to t= 1 such that the law of the controlled diffusion has minimal KL-divergence with respect to the Wiener measure. In those note, we review this derivation and then use the deep stochastic optimal control- a hybrid method combining deep learning and trajectory optimization- to estimate the Foellmer drift directly.

Colloquium

Speaker: Stefan Gille (U Alberta)

"Rost nilpotence and direct sums CANCELLED"

Time: 15:30 - 16:30

Room: MC 107

In the first part of my talk I will recall Rost nilpotence and why this is an important property of varieties. Then I will discuss the following question: Given two smooth projective varieties $X$ and $Y$ satisfying Rost nilpotence, does this property holds for their disjoint union, i.e. the direct sum of their Chow motives? Beside its implications for blow-ups of varieties it turns out that this question has connections to Koethe's conjecture (in ring theory) and the theory of PI-algebras.

Colloquium

Speaker: Dr Terry Moschandreou (TVDSB London ON)

"Using the LambertW function in numerical solutions of the Navier Stokes equations"

Time: 15:30 - 16:30

Room: MC 108

The talk discusses a general model using specific periodic special functions, that is degenerate elliptic Weierstrass P functions composed with the LambertW function, whose presence in the governing equations through the forcing terms simplify the periodic Navier Stokes equations (PNS). The properties of the LambertW function is discussed in context with numerical solutions of the Navier Stokes equations. Results in the literature can provide a systematic approach to study both large space and time behaviour for singular solutions to the Navier Stokes equations. The main part of the discussion will be to show that singular forcing can be used with the Duhamel principle to show numerical results occur and the existence of dipoles and vortices occur. How can we use singularities to show that numerical results with no singularities occur by shifting processes?

Applied dynamical system seminar

Speaker: Rujing Zhao (Western)

"TBA"

Time: 11:30 - 12:30

Room: MC 204

Introduction: Topics of these seminars include differential equations (ODEs, PDEs, DDEs, FDEs, etc.), dynamical systems theory, and their applications (often in mathematical biology). To get the brain gears turning, each session will kick off with a fun trivia!

Western Quantiers

Speaker: Asghar Gorbanpour (Western)

"Mathematical Principles of Stabilizer Codes"

Time: 15:30 - 16:30

Room: MC 107

Stabilizer codes offer a robust and efficient framework for encoding quantum information and detecting errors. This family includes a large class of codes such as CSS codes, surface codes and Toric codes. In this talk, we will focus on the fundamental mathematical principles of stabilizer codes. Using the aspects of subgroups of Pauli groups, this family of the codes offers a unified scheme for detecting and correcting errors in quantum world. This unification simplifies both error detection and error correction for these family of codes.

Colloquium

Speaker: David Jeffrey (Western)

"Computer Algebra and Special Functions"

Time: 15:30 - 16:30

Room: MC 107

The basic notion of this talk is the interplay between mathematics done by computer algebra systems and mathematics done by humans. It will be partly based on first-hand experiences with Maple. One of the unlikely successes of Maple software is the current popularity of the Lambert W special function. The role of Western in this success will be described.

This is part of our "Basic Notions" series.

Transformation Groups Seminar

Speaker: Tao Gong (Western)

"Contractibility of quotients of real toric varieties from Weyl groups"

Time: 09:30 - 11:00

Room: MC 108

Given a reduced crystallographic root system $R$ with the associated Weyl group $W$, the Weyl chambers from a fan and then give out a complex toric variety and its real part $X_R$. We will see that the underlying topological space $X_R/W$ is contractible.

Graduate Seminar

Speaker: Maximilian Petrowitsch (Western)

"Elementary Higher Toposes"

Time: 15:30 - 16:30

Room: MC 108

Elementary toposes are categories that share many properties of the category of sets. Every elementary topos has an internal language which is a version of typed intuitionistic higher-order logic obtained from the lattices of subobjects. It thus makes sense to speak of an elementary topos as a local set theory. The notion of elementary infinity-topos generalises this concept to infinity-categories. It is conjectured that the internal language of an elementary infinity-topos is a version of Homotopy Type Theory. Thus, it makes sense to speak of elementary infinity toposes as univalent dependent type theories, where instead of the lattice of subobjects we have a universal infinity-groupoid of all (small) objects. In the talk, I will introduce and motivate the notion of elementary infinity-topos, focussing on the concept of object classifiers and I will sketch the progress that has been made so far towards proving the conjecture. I will not assume any prior knowledge about toposes, logic or type theory.