Mang Wu
Department of Mathematics
University of Connecticut
Email: mwu@math.uconn.edu
Phone: (860) 486-9091


I am in my final year of the Ph.D. program in the Department of Mathematics, University of Connecticut. My thesis adviser is professor Maria Gordina. I am looking for post-doctoral positions or visiting assistant professor positions. Here is my curriculum vita.

Research Interests:

My research has been focused on stochastic analysis on infinite dimensional Lie groups. The two groups that I have studied are the group Diff(S^1), the group of orientation preserving diffeomorphisms of the unit circle, and the group Sp(\infty), an infinite dimensional symplectic group. The central extension of the group Diff(S^1) is the famous Virasoro group. Both the group Diff(S^1), the Virasoro group, and the quotient group Diff(S^1)/S^1 arise naturally in mathematical physics and have been extensively studied for a long time. The group Sp(\infty) arises as a certain symplectic representation of the group Diff(S^1). One of the goals of research has been to construct and study the properties of Brownian motions with values in these groups.

In BMSpInf.pdf, Gordina and I studied the relations between the group Diff(S^1) and Sp(\infty). We also constructed a Brownian motion on the group Sp(\infty). In RicciSpInf.pdf, following the methods in Gordina's paper, I calculated the Ricci curvature of the group Sp(\infty). In BMDiffS1.pdf, I constructed a Brownian motion on the group Diff(S^1).

My research area is highly interdisciplinary. To do stochastic analysis on infinite dimensional Lie groups, we necessarily need the tools from stochastic analysis, functional analysis, differential geometry, Lie groups and Lie algebras, representation theory. In doing the research, I also found uses of harmonic analysis and theory of partial differential equations.

Teaching:

I am teaching Math2110Q: Multivariable Calculus in fall 2009.

Computer:

I know Java/C++ pretty well. Now I am learning php. Here is a test page written in php.

Publications:

  1. M. Wu, Brownian motions on the group of diffeomorphisms of the unit circle, submitted
  2. M. Gordina and M. Wu, Diffeomorphisms of the circle and Brownian motions on an infinite dimensional symplectic group, Communication on Stochastic Analysis (published)
  3. M. Wu, The lower bound of the Ricci curvature of the group Sp(\infty), preprint