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.
For an algebraic group G over an arbitrary field F, the geometry of projective homogeneous G-varieties has yet to be fully classified. A effective tool used towards such a classification is the cohomological invariant given by the set of Tits algebras of G. A result of Panin provides a connection from the Tits algebras of G to the Grothendieck group of G, and in particular to its associated gamma-filtration. In this talk, we use the Tits algebras of G to construct a torsion element in the gamma-filtration of a flag variety twisted by means of a PGO-torsor. This generalizes a construction in the HSpin case previously obtained by Zainoulline.
I will explain the construction of Kontsevich-Vishik canonical trace on non-integer order classical pseudodifferential operators.
This construction has it roots in the old methods of extracting a finite part from a divergent sum or integral (infra-red and ultra-violet divergence),
used by mathematicians and physicists.
If time permits I will explain some of the results on generalizations of this construction to noncommutative setting.
We will outline a certain program for Nakajima quiver varieties, in the cyclic quiver example. The picture includes two algebras that act on the K-theory of these varieties: one is the original picture by Nakajima, rephrased in terms of shuffle algebras, and the other one is the Maulik-Okounkov quantum toroidal algebra. The connection between the two is provided by the action of certain operators in the so-called "stable basis", and we will present formulas for this action. These formulas can be perceived as a generalization of Lascoux-Leclerc-Thibon ribbon tableau Pieri rules.