Bounds on the eigenvalues of Laplace-Beltrami operators and Witten Laplacians on Riemannian manifolds

Series
Math Physics Seminar
Time
Friday, April 19, 2013 - 3:00pm for 1 hour (actually 50 minutes)
Location
Skiles 006
Speaker
Ahmad El Soufi – Université François Rabelais, Tours, France – ahmad.elsoufi@lmpt.univ-tours.fr – http://www.lmpt.univ-tours.fr/~elsoufi/
Organizer
Evans Harrell

Please Note: El Soufi will be visiting Harrell for the week leading up to this seminar

We shall survey some of the classical and recent results giving upper bounds of the eigenvalues of the Laplace-Beltrami operator on a compact Riemannian manifold (Yang-Yau, Korevaar, Grigor'yan-Netrusov-Yau, etc.). Then we discuss extensions of these results to the eigenvalues of Witten Laplacians associated to weighted volume measures and investigate bounds of these eigenvalues in terms of suitable norms of the weights.