Title: Gaussian measures on infinite dimensional spaces and applications
Speaker: Nathan Totz, University of Massachusetts Amherst
Abstract: We review the classical extension of the Gaussian probability measure from finite dimensional spaces to infinite dimensional spaces. Such Gaussian measures (along with their weighted relatives) play an important role as invariants of flows defined on infinite dimensional spaces. As an application of this idea, we employ Gaussian measures to address the question of the long time existence of a flow corresponding to a family of modified surface quasigeostrophic equations, regarded as a flow on a space of Fourier coefficients. We present recent results (joint with Andrea Nahmod, Natasha Pavlovic, and Gigliola Staffilani) showing that such flows are global in time on a subset of a rough Sobolev space of full measure.