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.

A basic problem in complex analysis is to approximate holomorphic maps by algebraic ones. This problem has a natural generalization in complex analytic geometry. Namely, one can ask whether a complex analytic set can be approximated by branches of algebraic sets (so-called Nash sets). In the case when the analytic set has only isolated singularities, this question is closely related to the classical problem of transforming an analytic set onto a Nash set by a biholomorphic map. The situation is quite different when the singular locus is of higher dimension, as there exist analytic set germs which are not biholomorphically equivalent to any Nash set germ. A major progress in this direction was allowed by the use of the so-called Neron desingularization.
In this talk, we will report on the recent developments in Nash approximation of analytic sets and mappings. Particularly, on the problem of relative approximation along arbitrary subsets.
Speaker's homepage: http://www.math.uwo.ca/~jadamus/

On relative Nash approximation of complex analytic sets.
Abstract: A basic problem in complex analysis is to approximate holomorphic maps by algebraic ones. This problem has a natural generalization in complex analytic geometry. Namely, one can ask whether a complex analytic set can be approximated by branches of algebraic sets (so-called Nash sets). In the case when the analytic set has only isolated singularities, this question is closely related to the classical problem of transforming an analytic set onto a Nash set by a biholomorphic map. The situation is quite different when the singular locus is of higher dimension, as there exist analytic set germs which are not biholomorphically equivalent to any Nash set germ. A major progress in this direction was allowed by the use of the so-called Neron desingularization.
In this talk, we will report on the recent developments in Nash approximation of analytic sets and mappings. Particularly, on the problem of relative approximation along arbitrary subsets.
Speaker's homepage: http://www.math.uwo.ca/~jadamus/

Symmetric decreasing rearrangement replaces
a given function f on R^d by a radially decreasing
function f* that is equimeasurable to f. Symmetrization
techniques have been used to determine the sharp constants
in classical functional inequalities such as the Sobolev inequality, and for solving minimization problems in Geometry and Mathematical Physics. Symmetrization also
motivates the definition of rearrangement-invariant
function spaces.
I will describe recent work with A. Ferone
on the extremals of the Polya-Szego inequality.
The inequality says that the p-norms of the
gradient decrease under symmetrization. It is known
that there are non-trivial cases of equality, even
when p>1. We use Ryff's polar factorization to describe
these equality cases.
Speaker's homepage: http://www.math.toronto.edu/almut/