EVENT DETAILS AND ABSTRACT

Title: Stochastic parallel transport and Yang-Mills equations
Speaker: Professor Robert Bauer
Speaker Info: Georgia Tech
Brief Description:
Special Note:
Abstract:

We first describe the notion of Yang-Mills field and the notion of diffusion on a manifold. We then give a new stochastic approach to Yang-Mills fields in vector bundles by studying the derivative of the stochastic parallel transport in the vector bundle under a variation of connection. We establsh the martingale criteria for variations induced by the flow of vector fields of gradient type on the base manifold. In dimension four we link the local Yang-Mills action to the quadratic variation of the derivative process by scalings of the driving Brownian motion in a coordinate chart.