March 31 
NO SEMINAR 
April 7 
Preston Wake (UCLA) Drinfeld level structures are a key concept in the arithmetic study of the moduli of elliptic curves. They also play an important role in the moduli of 1 dimensional pdivisible groups, and related Shimura varieties studied by Harris and Taylor. I'll explain why Drinfeld level structures (and the related "full set of sections" defined by Katz and Mazur) are not adequate for studying more general Shimura varieties. I'll discuss two examples of a satisfying theory of level structure outside the Drinfeld case: i) full level structures on the group \mu_p x \mu_p; ii) Gamma_1(p^r)type level structures on an arbitrary pdivisible group (joint work with R. Kottwitz). 
April 14 
Gilbert Moss (Oklahoma State University) In 2012 it was conjectured by Emerton and Helm that the local Langlands correspondence for GL(n) of a padic field should interpolate in \elladic families, where \ell is a prime different from p. Recently, Helm showed that the conjecture follows from the existence of an appropriate map from the integral Bernstein center to a Galois deformation ring. In this talk we will present recent work (joint with David Helm) showing the existence of such a map and describing its image. 
April 21 
NO SEMINAR 
April 28 
NO SEMINAR 
May 5 
Francesc Castella (UCLA) In 2013, Kobayashi proved an analogue of PerrinRiou's padic GrossZagier formula for supersingular primes. In this talk, we will explain an extension of Kobayashi's result to the Lambdaadic setting. The main formula is in terms of plus/minus Heegner points up the anticyclotomic tower, and its proof, rather than on calculations inspired by the original work of GrossZagier, is via Iwasawa theory, based on the connection between Heegner points, BeilinsonFlach elements, and different padic Lfunctions. (Joint work in progress with Xin Wan.) 
May 12 
NO SEMINAR 
May 19 
Samuele Anni (University of Warwick) The inverse Galois problem is one of the greatest open problems in group theory and also one of the easiest to state: is every finite group a Galois group? Hilbert was the first to study it in earnest: Hilbert's irreducibility theorem established a connection between Galois groups over Q and Galois groups over Q[x], and this led him to show that symmetric and alternating groups are Galois realizable over Q. My interest around this problem is connected to the realization of linear groups as Galois groups over Q and over number fields. In this talk I will describe uniform realizations of linear groups using elliptic curves and genus 2 curves. After this introduction, I will describe a joint work with Pedro Lemos and Samir Siksek, concerning the realization of GSp_{6} (F_{ℓ}) as a Galois group for infinitely many odd primes l. I will also present some generalizations which are work in progress with Vladimir Dokchitser. 
May 26

Zev Klagsbrun (Center for Communications Research) We show that the $\phi$Selmer ranks of twists of an elliptic curve $E$ with a point of order two are distributed like the ranks of random groups in a manner consistent with the philosophy underlying the CohenLenstra heuristics. If $E$ has a point of order two, then the distribution of $dim_{\mathbb{F}_2} \Sel_\phi(E^d/\QQ)  dim_{\mathbb{F}_2} Sel_{\hat\phi}(E^{\prime d}/\QQ)$ tends to the discrete normal distribution $\mathcal{N}(0,\frac{1}{2} \log \log X)$ as $X \rightarrow \infty$. We consider the distribution of $dim_{\mathbb{F}_2} \Sel_\phi(E^d/\QQ)  dim_{\mathbb{F}_2} Sel_{\hat\phi}(E^{\prime d}/\QQ)$ has a fixed value $u$. We show that for every $r$, the limiting probability that $dim_{\mathbb{F}_2} \Sel_\phi(E^d/\QQ)= r$ is given by an explicit constant $\alpha_{r,u}$ introduced in Cohen and Lenstra's original work on the distribution of class groups. 
June 2 
Robert Lemke Oliver (Stanford) While the sequence of primes is very well distributed in the reduced residue classes (mod q), the distribution of pairs of consecutive primes among the permissible pairs of reduced residue classes (mod q) is surprisingly erratic. We propose a conjectural explanation for this phenomenon, based on the HardyLittlewood conjectures, which fits the observed data very well. We also study the distribution of the terms predicted by the conjecture, which proves to be surprisingly subtle. This is joint work with Kannan Soundararajan. 