Stochastic and geometric analysis of two infinite-dimensional groups

Authors

Mang Wu, University of Connecticut

Date of Completion

January 2010

Keywords

Mathematics

Degree

Ph.D.

Abstract

The two groups I studied in this dissertation are Diff(S ¹), the group of orientation-preserving C ^∞-diffeomorphisms of the circle, and Sp(∞), an infinite-dimensional symplectic group arising from certain symplectic representation of the group Diff(S¹). In Chapter 1, I constructed Brownian motion on Diff(S¹) associated with a very strong metric of the Lie algebra diff(S¹). In Chapter 2, I first studied the relationship between Diff(S ¹) and Sp(∞) and found that they are not isomorphic with each other, then I constructed a Brownian motion on the group Sp(∞). In Chapter 3, I computed the Ricci curvature of the group Sp(∞) associated with a certain inner product on the Lie algebra sp (∞). ^

Recommended Citation

Wu, Mang, "Stochastic and geometric analysis of two infinite-dimensional groups" (2010). Doctoral Dissertations. AAI3420183.
https://digitalcommons.lib.uconn.edu/dissertations/AAI3420183