Analysis Seminar

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Gauge-Invariant Boundary Conditions with Possible Applications to a Millennium Problem

Speaker: Antonella Marini, Yeshiva University

Location: Warren Weaver Hall 1302

Date: Thursday, February 19, 2015, 11 a.m.

Synopsis:

A brief history of elliptic boundary value problems arising in Yang-Mills theory will be given, as well as their application to on-going work in collaboration with Moncrief (Yale) and Maitra (Wenthworth Institute of Technology) on a new method for Euclidean-signature semi-classical Yang-Mills fields, directed at a possible new approach to the mass gap problem.

The review will include the Dirichlet, Neumann, and generalized Neumann boundary conditions for Yang-Mills in dimension 4, as well as the proof of existence of a very rich structure for the space of solutions, including non-minimal solutions, for the Dirichlet problem with small boundary data (joint work with Isobe, Tokyo Institute of Technology).

The difficulties inherent in these natural boundary value problems and their main points of interest will be discussed, as well as the extension to Yang-Mills fields of the modified semi-classical method developed for the analysis of finite dimensional, nonlinear quantum oscillations systems (with Moncrief and Maitra).