The SAGE research workshops are preceded by events designed to help graduate students benefit from workshop participation.
This year, graduate students working on topics closely related to the topics of the workshop met weekly with the PI during the preceding semester. One of these, Mike Williams, prepared a presentation for a broad audience of graduate students. This took place as part of UT’s Junior Geometry seminar:
Mike Williams: Nilpotent Lie groups and Ricci solitons (3:30 PM, Thursday, March 24, 2009 in RLM 10.176)
Abstract: What is the “best” possible metric for a given manifold? Einstein metrics are generally regarded as such, being critical points of the Einstein-Hilbert action and fixed points of Ricci flow, but they are rare. In the context of homogeneous nilmanifolds (or nilpotent Lie groups, where Einstein metrics often do not exist), I will discuss a generalization of the Einstein condition and how it relates to Ricci solitons (generalized fixed points of the Ricci flow). Some tools involved include Lie algebra cohomology and the calculus of variations.