The University of Toronto Number Theory/Representation Theory Seminar 
2005-06: Wednesday 2:10pm-3:00pm, Bahen Centre 6183 , University of Toronto  

This seminar is organized by Jim Arthur. If you would like to speak at the seminar, please email Jim (arthur at math dot toronto dot edu).
For inquiries regarding this web page, please email Jonathan (jkorman at math dot toronto dot edu).

Last Term's Schedule

Fall 2005 Term Schedule

DATE and TIME  SPEAKER  TITLE 
Sep. 21,  Wednesday
2:10--3:00PM 		 H. Kim    
University of Toronto 		 Functoriality of twisted exterior square
Sep. 28,  Wednesday
2:10--3:00PM 		 E. Knafo    
University of Toronto 		 Variance of distribution of almost primes in arithmetic progressions
Sep. 30,  Friday
2:10--3:00PM  		 Gergely Harcos    
Univ. of Austin, Texas  		 The subconvexity problem for Rankin-Selberg L-functions
and equidistribution of Heegner points  
Oct. 5,  Wednesday
2:10--3:00PM 		 W. Hoffmann    
Universitaet Bielefeld 		 On explicit Fourier transforms of weighted orbital integrals  
Oct. 12,  Wednesday
2:10--3:00PM 		 J. Friedlander    
University of Toronto  		 The problem with prime numbers  
Oct. 19,  Wednesday
2:10--3:00PM 		 J. Gordon    
University of Toronto  		 Are characters of p-adic groups computable?  
Oct. 26,  Wednesday
2:10--3:00PM 		    
 		 ------------No Seminar----------- 
Nov. 2,  Wednesday
2:10--3:00PM 		 J. Korman    
University of Toronto  		 The local character expansion near a tame, semisimple element 
Nov. 9,  Wednesday
2:10--3:00PM 		 A. Douglas    
University of Toronto  		 A classification of the finite dimensional indecomposable representations
of the Euclidean algebra $\mathfrak{e}(2)$ having two generators.  
Nov. 16,  Wednesday
2:10--3:00PM 		 L. Spice    
University of Michigan 		 Characters of tame division algebras over a p-adic field  
Nov. 23,  Wednesday
2:10--3:00PM 		 E. Lawes    
Univ. of Toronto 		 An Introduction to Galois-fixed points of Buildings  
Nov. 30,  Wednesday
2:10--3:00PM 		 G.-V. Nguyen-Chu  
Univ. of Toronto 		 Satake transform of some compact characters 


Summary

October 19
Title: Are characters of p-adic groups computable?
Speaker: Julia Gordon (U of T)
Abstract: It is known that in general, it is impossible to have a formula for characters of representations of p-adic groups, because there are examples of the character values that depend on a number of points of elliptic or hyperelliptic curves over finite fields. However, one can ask if the equations for varieties that are responsible for character values can be found explicitly (and if such varieties exist in general). This talk will address these questions (under certain circumstances both answers are positive). We will use the group SL2(Qp) as a source of explicit examples for "motivic "calculations. This is joint work with Clifton Cunningham.

November 2
Title: The local character expansion near a tame, semisimple element.
Speaker: Jonathan Korman (U of T)
Abstract: Consider the character of an irreducible admissible representation of a p-adic reductive group. The Harish-Chandra-Howe local expansion expresses this character near a semisimple element as a linear combination of Fourier transforms of nilpotent orbital integrals. Under mild hypotheses, we describe an explicit region on which the local character expansion is valid. This is joint work with Jeff Adler.

November 9
Title: A classification of the finite dimensional indecomposable representations of the Euclidean algebra $\mathfrak{e}(2)$ having two generators.
Speaker: Andrew Douglas (U of T)
Abstract: The Euclidean algebra $\mathfrak{e}(2)$ is the Lie algebra of the group E(2) of Euclidean transformations of the plane. This thesis examines the finite dimensional representations of $\mathfrak{e}(2)$ having two generators. Given a representation with a fixed pair of generators we associate a graph: the graph is dependent on the choice of generators and for each isomorphism class of representations there are infinitely many possible graphs. In term of graphs, we give a criterion for the indecomposability of such representations and describe an invariant for the indecomposable representations. Next, we classify the finite dimensional, indecomposable representations of $\mathfrak{e}(2)$ having two generators. We describe a procedure that enables us to select a single graph for each isomorphism class. This graph uniquely identifies the class.

November 16
Title: Characters of tame division algebras over a p-adic field.
Speaker: Loren Spice (Univ. of Michigan)
Abstract: Yu generalised a construction of Corwin and Howe for division algebras to produce many supercuspidal representations of tame p-adic groups. In this talk, we will describe how to use the Harish-Chandra integral formula to compute the characters of these representations in some cases. In particular, all characters can be computed for tame division algebras.

November 23
Title: An Introduction to Galois-fixed points of Buildings.
Speaker: Elliot Lawes (Univ. of Toronto)
Abstract: We'll start gently by defining some basics of Buildings. We'll then discuss what is known about the Galois fixed-points of these. Finally we'll explore the differences in behaviour between the (known) case when the Galois extension is tame, and the (less well understood) case when it is wild.

November 30
Title: Satake transform of some compact characters.
Speaker: Gia-Vuong Nguyen-Chu (U of T)
Abstract: We construct explicitly some irreducible representations of $GL(n, F)$ (where $F$ is a local non archimedean field) which are stable by the involution $\theta$, rougly defined by $\theta(g) = {}^{t}g^{-1}$. We show that the Satake transforms of the twisted, compact characters of such representations are rational functions in $[\frac{n}{2}]$ (the entire part of $\frac{n}{2})$ variables. When $n$ is odd we expect that these functions generate the space of $Satake$ transforms of stable unipotent distributions on $Sp(n-1, F)$.