Mathematics Faculty Member Earns Prestigious $35,000 Grant for Research/Travel
Guenther's research centers on geometric evolution equations, with a recent focus on the second-order renormalization group flow. There are three collaborative projects which she plans to pursue with this funding: in the first, she will plan to investigate the use of the Ricci flow to approximate the full renormalization group flow by comparing the asymptotic behavior of the Ricci flow with the second-order truncation of the full flow (the RG-2 flow) on compact three-dimensional homogeneous spaces. In the second, she will apply techniques developed for the Ricci flow to prove stability of the RG-2 flow at flat and hyperbolic fixed points. In the third, she will develop a fundamental solution for manifolds with time-dependent metrics and use it to derive a Li-Yau-Hamilton type Harnack inequality for positive solutions of a generalized heat equation.
About the Simons Foundation
The goal of the Collaboration Grants for Mathematicians program at the Simons Foundation is to support the “mathematical marketplace” by substantially increasing collaborative contacts in the community of mathematicians working in the United States. The foundation will make a large number of grants to accomplished, active researchers who do not otherwise have access to substantial research funding that supports travel and visitors.