Abstracts
11/9 Mang Wu
Title: A Brownian motion on the group of diffeomorphisms of the circle
Abstract: The group Diff(S1) of diffeomorphisms of the circle arises in
many places in mathematical physics. It is an infinite dimensional
Frechet Lie group. Since it is not locally compact, we cannot expect a
Haar measure on it. But by constructing a Brownian motion on it, we can
induce a family of measure on it. In part I of the talk, I will review
basics of the group Diff(S1) and Brownian motions. In part II of the
talk, I will construct a Brownian motion on Diff(S1) by solving a
stochastic differential equation (SDE).
11/23 Dominick
Scaletta
Title: Operator Methods in Quantum Theory and Uncertainty Relations
Abstract:
I will develop the mathematical formalism of quantum mechanics by
precisely defining states and observables. With these tools I will
discuss expectation values, which are what give us physical
predictions. I will then define the commutation relation of
operators
and their physical implications. I will finish by proving
Heisenberg’s uncertainty principle, and if time allows, the
time-energy uncertainty relation. I will not assume prior
knowledge
of quantum mechanics.