Applied dynamical system seminar

Speaker: Rujing Zhao (Western)

"TBA"

Time: 11:30

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

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

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

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

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.

Applied dynamical system seminar

Speaker: Xiangyuan Liang (Western)

"TBA"

Time: 11:30

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 Ghorbanpour (Western)

"Mathematical Principles of Stabilizer Codes-II"

Time: 15:30

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.

Department Meeting

Speaker: (Western)

"N/A"

Time: 15:30

Room:

Transformation Groups Seminar

Speaker: Tao Gong (Western)

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

Time: 09:30

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 $X_{\mathbb{R}}$. We will see that the underlying topological space $X_{\mathbb{R}}/W$ is contractible.

This is a continuation of last week's talk.

Graduate Seminar

Speaker: Nathan Kershaw (Western)

"Efficient computations of discrete cubical homology"

Time: 15:30

Room: MC 108

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.

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

Applied dynamical system seminar

Speaker: Ruchita Amin (Western)

"TBA"

Time: 11:30

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!

Final Presentation

Speaker: David Johnson (Western)

"Finding configurations of 9 points lying on circles"

Time: 11:30

Room: MC 107

We will discuss the problem of finding the maximum number of 4-point circles given 9 points, where a 4-point circle is a circle on which lie exactly 4 of the 9 given points. This problem is solved for points in $\mathbb{R}^2$, we present a generalization to $\mathbb{C}^2$. Our approach uses techniques from polyhedral geometry and group theory. In particular, we will construct a polytope whose lattice points represent candidate point-circle incidences of 9-point configurations. This method works until the number of circles is greater than 4, at which point solving for the lattice points becomes computationally infeasible. We present then another method which instead recursively constructs these configurations. We reduce computations by leveraging symmetries of $S_9$. Finally, we discuss the original motivation for this work, coming from an interpolation problem in mechanical engineering involving four-bar linkages.

This is a final presentation for the course AM 4999Z.

Geometry and Topology

Speaker: Dan Isaksen (Wayne State University)

"Unstable homotopy groups of spheres"

Time: 15:30

Room: MC 107

Colloquium

Speaker: Kasra Rafi (Toronto)

"TBA"

Time: 15:30

Room: MC 107

Pizza Seminar

Speaker: Geoff Wild (Western)

"TBA"

Time: 17:30

Room: MC 107

TBA

Applied dynamical system seminar

Speaker: Haifeng Wang (Western)

"TBA"

Time: 11:30

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!

Colloquium

Speaker: (Basic Notions) Taylor Brysiewicz (Western)

"Sparse Polynomial Systems"

Time: 15:30

Room: MC 107

As implied by Bezout's theorem, n generic polynomials of degrees d1,...,dn in C^n have exactly d1*d2*...*dk common roots. Here, the degrees of each polynomial are specified, but they are otherwise generic. Adding constraints, one may impose which *monomials* are involved in each polynomial, resulting in a 'sparse polynomial system'. The analogue of Bezout for sparse systems is the celebrated Bernstein-Kouchnirenko-Khovanskii (BKK) theorem.

The BKK theorem relates a solution count to the polyhedral geometry of the monomial support of a sparse system. Relating other algebro-geometric features to combinatorial data of sparse systems is an active area of research. I will give a survey of what is known about some of these connections, how the associated theorems are used in practice, and what has yet to be discovered.

Applied dynamical system seminar

Speaker: Dr. Terry Moschandreou (TVDSB)

"TBA"

Time: 11:30

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: Diego Manco Berrio (Western)

"TBA"

Time: 15:30

Room: MC 107

Applied dynamical system seminar

Speaker: Qian Qin (Western)

"TBA"

Time: 11:30

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 Combinatorics

Speaker: Leo Jiang (University of Toronto)

"Topology of real matroid Schubert varieties"

Time: 15:30

Room: MC 108

Every linear representation of a matroid determines a matroid Schubert variety whose geometry encodes combinatorics of the matroid. When the representation is over the real numbers, we study the topology of the real points of the variety. Our main tool is an explicit cell decomposition, which depends only on the oriented matroid structure and can be extended to define a combinatorially interesting topological space for any oriented matroid. This is joint work with Yu Li.

Department Meeting

Speaker: (Western)

"N/A"

Time: 15:30

Room: