April 4 
NO MEETING 
April 11 
Nolan Wallach (UC San Diego) + pretalk 1:201:50 In his monumental book "On the Functional Equations satisfied by Eisenstein Series" Langlands proved that the Kfinite Eisenstein series, initially defined, convergent and holomorphic in appropriate open tube of the parameter space can be meromorphically continued to the entire parameter space. The Kfiniteness was critical to his proof of the theorem. In this lecture I will show how to use Langlands' theorem to prove the meromorphic continuation for smooth Eisenstein series. These results are valid in the full context of Langlands' theorem but I will only talk about arithmetic groups for which the definitions are easier. (Indeed, Langlands' definition of the groups that that would be studied was only completed at the end of the induction in his notorious chapter 7). Note: There will be a pretalk aimed at graduate students and postdocs, 1:201:50. 
April 18 
NO MEETING 
April 25 
Rudy Perkins (Cuyamaca College) TBA 
May 2 
NO MEETING 
May 9 
NO MEETING 
May 16 
Thomas Grubb (UC San Diego)

May 21 (TUESDAY) 
Wayne Raskind (Wayne State University) 45 PM in the Halkin Room (6402); pretalk 3:203:50pm Let k be a global field, that is, a number field of finite degree over Q or the function field of a smooth projective curve C over a finite field F. Let X be a smooth projective variety over k, and let K be the maximal cyclotomic extension of k, obtained by adjoining all roots of unity. If X is an abelian variety, a famous theorem, due to Ribet in the number field case and LangNeron in the function field case when X has trace zero over the constant subfield of K, asserts that the torsion subgroup of the MordellWeil group of X over K is finite. Denoting by k_{sep} a separable closure of k, this result is equivalent to finiteness of the fixed part by G=Gal(k_{sep}/K) of the etale cohomology group H^1(X_{k_{sep}},Q/Z), where we ignore the ppart in positive characteristic p. In a recent paper, RoesslerSzamuely generalize this result to all odd cohomology groups. The trace zero assumption in the function field case is replaced by a "large variation" assumption on the characteristic polynomials of Frobenius acting on the cohomology of the fibres of a morphism f: \cal{X}\to C from a smooth projective variety \cal{X} over a finite field to C with generic fibre X. In this talk, I will discuss the case of even degree, proving some positive results in the number field case and negative results in the function field case. Note: There will be a preparatory talk for graduate students and postdocs 3:203:50pm in the seminar room. 
May 23 
Piper H (University of Hawaii) pretalk 1:201:50pm The shape of a degree $n$ number field is a $n1$variable real quadratic form (up to equivalence and scaling) which keeps track of the lattice shape of its ring of integers relative to $\mathbb{Z}$. For number fields of small degree, in previous joint work with Bhargava, we showed that shapes of $S_n$number fields are equidistributed, when ordered by absolute discriminant. The proof relies heavily on Bhargava's parametrizations which introduces but ultimately ignores the notion of resolvent rings. This talk discusses work in progress, joint with Christelle Vincent, in which we define the joint shape of a ring and its resolvent ring in order to prove equidistribution of joint shapes of quartic fields and their cubic resolvent fields. Note: The speaker will give a preparatory lecture for graduate students and postdocs in the seminar room from 1:201:50pm. 
May 30 
Naser Sardari (University of WisconsinMadison) pretalk 1:201:50pm Fix an integer N and a prime (p,N)=1 where p>3. We show that the number of newforms f (up to a scalar multiple) of level N and even weight k such that T_p(f) = 0 is bounded independently of k, where T_p is the Hecke operator. 
June 6 
Francois Thilmany (UC San Diego) TBA 