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College of Arts and Sciences

2014-2015 Seminars and Colloquia

department of mathematics

BC-MIT Number Theory Seminar

Organizers: Ben Howard and David Geraghty at BC, and Bjorn Poonen at MIT.

September 16, 2014 at BC  McGuinn 334

3:00-4:00 p.m.

Liang Xiao (University of Connecticut, Storrs)

Title: Slopes of modular forms

Abstract: An interesting computation of Buzzard and Kilford suggested that the slope distribution of the Up operators on the space of overconvergent modular forms tends to form an arithmetic progression, when the Nybentypus character is highly divisible by p. Unfortunately, this was only verified for very small prime p and small tame level. I will explain a joint work with Daqing Wan and Jun Zhang, in which we work with overconvergent automorphic forms for a definite quaternion algebra instead. We prove certain weak version of this expectation for general p and general tame level structure.

4:30-5:30 p.m.

Kiran Kedlaya (University of California, San Diego)

Title: Cohomology of local systems on rigid analytic spaces

Abstract: Let K be a finite extension of Q_p. The notion of the etale fundamental group of a rigid analytic space has been introduced by de Jong. It is highly noncompact; consider for example Tate's uniformization of elliptic curves.

Let X be a smooth proper connected rigid analytic space over K. One then has a Riemann-Hilbert-style identification of continuous representations of the etale fundamental group of X on finite-dimensional Q_p-vector spaces with locally constant sheaves of finite-dimensional Q_p-vector spaces with respect to Scholze's pro-etale topology; these are what we call "etale Q_p-local systems" on X. We prove that the cohomology groups of such a sheaf are finite-dimensional Q_p-vector spaces.

The proof uses an extension of p-adic Hodge theory, especially the theory of (phi, Gamma)-modules, to the setting of etale fundamental groups, in order to transform the problem into something resembling the finiteness of cohomology of coherent sheaves on X (proved by Kiehl).

Joint work with Ruochuan Liu (Beijing).


October 14, 2014 at MIT Room 4-163
3:00-4:00 p.m.

Wei Zhang (Columbia U.)

Title: ATC, special parahorics and exotic good reduction

Abstract: I will report a joint work with M. Rapoport and B. Smithling, on an
"arithmetic transfer conjecture" (ATC). Similar to the arithmetic fundamental lemma conjecture (for unramified unitary groups), the transfer conjecture connects the derivative of a relative orbital integral to an intersection number on a formal moduli space of $p$-divisible groups associated to a special parahoric of a ramified unitary group. Miraculously, this formal moduli space has good reduction.

4:30-5:30 p.m.

Martin Olsson (University of California, Berkeley)

Title: Motivic invariants of l-adic sheaves

Abstract: I will give an overview of a project aimed at understanding the motivic nature of l-adic sheaves. I will survey motivating questions about independence of l and past results of Lafforgue, Drinfeld, and others. I will then discuss how to incorporate correspondences into the theory, recent results, and open questions.


November 18, 2014 at BC McGuinn 521

3:00-4:00 p.m.

Laurent Fargues (Directeur de Recherche CNRS, Institut de Mathématiques de Jussieu)

Title: G-bundles on the curve

Abstract: In my joint work with Fontaine, we have defined and studied a "curve" linked to p-adic Hodge theory. We moreover classified vector bundles on this curve. In this talk I will recall the structure of this curve. Then, given a reductive group G over the p-adic numbers, I will explain how one can classify G-bundles on this curve and link this to Kottwitz set B(G) of sigma conjugacy classes in G.

4:30-5:30 p.m.

Joseph H. Silverman (Brown University)

Title: Canonical heights and nef divisors on abelian varieties, with an application to arithmetic dynamics

Abstract: Let A/K be an abelian variety defined over a number field, and let D be a divisor on A. The Neron-Tate height q_D(P) = lim h_D(nP)/n^2 is a quadratic form q_D : A(K) --> R, and if D is ample, then q_D is positive definite on A(K) modulo torsion. I will discuss an extension of this theorem to the case that D is only assumed to be a nef divisor and will give, as an application, a proof for abelian varieties of the following conjecture in arithmetic dynamics: Let f : X --> X be a dominant rational self-map of a smooth projective variety, all defined over a number field. Let P be an algebraic point of X whose forward orbit by iterates of f is well-defined and Zariski dense in X. Then the f-orbit of P has maximal arithmetic complexity. (Joint work with Shu Kawaguchi)

BC Math Society/Mathematics Department Undergraduate Lectures

Wednesday, March 19, 2014 - Stokes S209

Title: The Framingham Heart Study and the Development of Cardiovascular Disease Risk Prediction Functions

Abstract: The Framingham Heart Study (FHS) began in 1948, under the direction of National Heart Institute (now the National Heart Lung and Blood Institute), with the objective of assessing risk factors that contribute to cardiovascular disease (CVD) by examining and following a large cohort of participants from Framingham, MA (n=5,209) who did not have CVD or overt symptoms of CVD. The participants have been periodically examined and followed through death, with approximately 100 of these original cohort participants still alive today. Since 1971, the original cohort’s adult children and their spouses, and since 2002, the grandchildren of the original cohort, have been examined and followed. Also, since 1994, participants reflecting a more diverse Framingham community have been examined and followed. Overall, FHS involves approximately 15,000 participants. The abundance of risk factor and follow-up data collected over the years has allowed FHS to be among the leaders in CVD risk prediction, both clinically and methodologically. Here, we will provide a brief history of FHS, discuss clinical and methodological development of CVD risk prediction, provide examples of how FHS risk prediction models are used by physicians today, and briefly discuss current research.


BC Geometry/Topology Seminar

Meets Thursdays at 4:00 pm in Carney 309


BC Colloquium Series

To be determined.


Boston Area Links

The Mathematical Gazette is published weekly by the Worcester Polytechnic Institute Mathematical Sciences Department. It provides a list of mathematical seminars and colloquia in the Massachusetts area.

BC Number Theory/Algebraic Geometry Seminar

BC Number Theory and Algebraic-Geometry Seminar

Meets Thursdays at 3:00 p.m. in Carney 309

BC Math Society Undergraduate Lecture Series

September 24, 2014, 3:00 p.m., Prof. Bill Keane (BC)
Title: Eureka! The Life and (Some of the) Work of Archimedes.