Algebra and Number Theory Seminar  On the KudlaRapoport conjecture 
4:15pm 
LOM 205

Abstract: The KudlaRapoport conjecture predicts a precise identity between the arithmetic intersection numbers of special cycles on unitary RapoportZink spaces and the derivatives of local representation densities of hermitian forms. It is a key local ingredient to establish the arithmetic SiegelWeil formula, relating the height of generating series of special cycles on Shimura varieties to the derivative of Eisenstein series. We discuss a proof of this conjecture and global applications. This is joint work with Wei Zhang. 
Group Actions and Dynamics  Finiteness of small eigenvalues of geometrically finite manifolds 
4:15pm 
DL413

Let M be a geometrically finite real rank one locally symmetric manifolds. We will take about the spectrum of the Laplace operator on M. By using the LaxPhilips inequality of the energy form, we will prove that the spectrum is finite in a critical interval which is given by the volume entropy. 