The Weizmann Institute of Science Faculty of Mathematics and Computer Science Algebraic Geometry and Representation Theory Seminar Lecture Hall, Room 1, Ziskind Building on Thursday, January 3, 2013 at 13:30 Note the unusual day, time and location Avraham Aizenbud MIT will speak on Representation count, rational singularities of deformation varieties, and pushforward of smooth measures Abstract: 1. The number of n-dimensional irreducible representations of the pro-finite group $SL(d,Z_p)$ is bounded by a polynomial on n whose degree does not depend on d and p (our current bound for the degree is 22). 2. Let $\phi : X \rightarrow Y$ be a flat map of smooth algebraic varieties over a local field $F$ of characteristic 0 and assume that all the fibers of $\phi$ are of rational singularities. Then, the push-forward of any smooth compactly supported measure on $X$ has continuous density. 3. Let $X=Hom(\pi_1(S),SL_d)$ where $S$ is a surface of high enough genus (our current bound for the genus is 12). Then $X$ is of rational singularities. We will also discuss the surprising relation between those results which allowed us to prove them. --------------------------------------------------------- Technion Math Net-2 (TECHMATH2) Editor: Michael Cwikel <techm@math.technion.ac.il> Announcement from: Yaeli Malka <yaeli.malka@weizmann.ac.il>