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.
There is a result from the 1980's that allows us to describe the equivariant $K$-theory of curves: if $X$ and $Y$ are curves, G is a finite reducible group and $Y = X/G$, then we can write $K_G(X)$ in terms of $K(Y)$ and some representation rings associated to the group. Prof. Dhillon and I have generalized this result to any dimension using the description of the category of coherent sheaves on a root stack given by Borne and Vistolli.
I will report on results obtained in a recent paper with Baran Serajelahi.
I will describe quantization constructions, obtained from Berezin-Toeplitz quantization,
for an n-dimensional compact Kahler manifold regarded as a (2n-1)-plectic manifold,
and for a hyperkahler manifold.
To each differential-graded algebra and element a\in A^1,
we associate a cochain complex, where the map is defined by
the multiplication by a. The degree l resonance variety is
the set of elements a in A^1 such that the l-th cohomology
is not zero. It is shown that The degree l resonance
variety, up to ambient linear isomorphism, is an invariant
of A. The characteristic varieties of a space are the jump loci for homology
of rank 1 local systems. The main motivation for the study of resonance
varieties comes from the tangent cone, which there is a close relation
between the degree-one resonance varieties to the characteristic varieties,
where the tangent cone of W at 1 is the algebraic subset
TC_1(W) of C^n defined by the initial ideal in(J) \subset S.
In this talk we describe the degree-one resonance variety.
We will be particularly interested in the resonance varieties of graphical
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.