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.
I will describe the ball model and the Siegel space model of the n-dimensional complex hyperbolic space H^n_C.
The matrix group SU(n,1) acts on H^n_C. The group of holomorphic isometries of H^n_C is PU(n,1).
Let \Gamma be a discrete subgroup of SU(n,1) which acts freely and properly discontinuously on H^n_C.
I will give the definition of an automorphic form for \Gamma.
I will talk about constructing automorphic forms associated to certain submanifolds of H^n_C / \Gamma .
Levi flat hypersurfaces are characterized by vanishing
of the Levi form on them. Their regular part is foliated by complex
hypersurfaces, this is called the Levi foliation. It is an open question
whether one can extend this foliation to the ambient space. As
example of Brunella shows, near singular points the extension may
exist in general only as a singular holomorphic web. A smooth
holomorphic web is simply the union of several foliations. A singular
web is a more general object which loosely can be thought of as a
foliation with branching. In this talk I will give a detailed background
concerning holomorphic webs, and will discuss some recent progress
on extension of the Levi foliation. This is joint work with A. Sukhov.