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>