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.

Upcoming Events

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.

Homotopy type theory with the univalence axiom of Voevodsky provides both a new
logical foundation for mathematics (Univalent Foundations) and a formal
language usable with computers for checking the proofs mathematicians make
daily. As a foundation, it replaces set theory with a framework where sets are
defined in terms of a more primitive notion called "type". As a formal
language, it encodes the axioms of mathematics and the rules of logic
simultaneously, and promises to make the extraction of algorithms and values
from constructive proofs easy. With a semantic interpretation in homotopy
theory, it offers an alternative world where the proofs of basic theorems of
mathematics can be formalized with minimal verbosity and verified by computer.
As a relative newcomer to the field, I will survey these recent developments
and sketch the basic concepts for a general mathematical audience.

In this talk, we will discuss Noncommutative Poisson Structure which was introduced by Crawley-Boevey and how it fits nicely with Kontsevich-Rosenberg principle.
We will also give some examples.
If time allows, we will also discuss its relation to Van den Bergh's Double Poisson Algebras.

A few years ago I gave a Pizza Seminar talk where I showed how to regularize an infinite sum like \( 1+2+3+4+5+\cdots \) and show that it
is equal to \( \frac{-1}{12} \). In this talk I shall discuss a multiplicative version and show how one can regularize infinite products like \( 1.2.3.4.\cdots \). This topic
is intimately related to Riemann's zeta function and its analytic continuation and special values. Some tools of classical analysis like Euler-Maclaurin
summation formula will be introduced and used extensively in my talk.

Since creation of quantum groups theory numerous
attempts to elaborate an appropriate corresponding differential calculus were undertaken.
Recently, a new type of noncommutative geometry has been obtained this way.
Namely, we have succeeded
in introducing the notions of partial derivatives on the enveloping algebras
U(gl(m)) and constructing the corresponding de Rham complexes.
All objects arising in our approach are deformations of their
classical counterparts. In my talk I plan to introduce some basic notions of the
Quantum Groups theory and to exhibit possible applications of this
type Noncommutative Geometry to quantization of certain dynamical models.