The Mathematical and Computational Sciences at Western are represented by four separate departments: Applied Mathematics, Computer Science, Mathematics, and Statistical & Actuarial Sciences. The Department of Mathematics has established research groups in several areas of contemporary mathematics including algebra, analysis and analytic geometry, homotopy theory, and noncommutative geometry.

Each week the Department of Mathematics hosts a wide variety of seminars and events. For a comprehensive list of events, please consult our departmental calendar.

In this talk we will introduce the notions of join, slice, (co)limits in the context of âˆž-categories. We will also discuss some basic properties relevant to these constructions.

This talk is based on my joint paper with Masoud Khalkhali and Ali Moatadelro (arXiv:1610.04740).
First I will recall GilkeyÃ¢â‚¬â„¢s theorem on asymptotic expansion of heat kernels for the special case of Laplacians. I will also introduce the noncommutatvie 3-torus (NCT3) and then I will conformally perturb the standard volume form on it. Then the corresponding perturbed Laplacian will be discussed, and using ConnesÃ¢â‚¬â„¢ pseudodifferential calculus, I will define the scalar curvature of NCT3. Finally, introducing a rearrangement lemma I will compute an explicit formula for the scalar curvature of the curved noncommutative 3-torus.

The study of instantons on the infinite cylinder $\mathbb{R} \times \mathbb{T}^3$ is facilitated by the Nahm transform, a sort of non-linear Fourier transform for connections. Proving that the Nahm transform does what one believes it should do is a task requiring input from geometric analysis and algebraic geometry. This talk focuses on the geometric analysis aspects. This is joint work with Jacques Hurtubise.
Speaker's web page: http://www.math.uwaterloo.ca/~bcharbon/