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!

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.

Movement is fundamental to life as it is what allows us to interact with our environment. Daily tasks from walking to speaking are the result of voluntary muscle control. The brain center that controls voluntary motion is the motor cortex. We can model the motor cortex using Artificial Neural Networks. Although these models are computationally powerful, they are not typically analytically solvable. However, recently it has been shown that there are networks that can perform computations and which can be solved mathematically. In this presentation we explore these networks in the context of modelling the motor cortex, and how they can be used to capture motor trajectories of a six-muscle arm. We will then discuss the mathematical analysis done on a network which can model motor behaviour and which is solvable. This analysis involves concepts from Spectral Analysis and Linear Algebra.

We will discuss the article "Cup-products for the polyhedral product functor" by A. Bahri, M. Bendersky, F. R. Cohen, and S. Gitler.