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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.)

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)

4:30-5:30 p.m.

Joseph H. Silverman (Brown University)

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

September 26, 2013

    Yulan Quin (Tufts)
    Title: Boundaries of CAT(0) spaces with Right Angles

October 3, 2013

    Ailsa Keating (MIT)
    Title: Tori in four-dimensional Milnor fibres

October 10, 2013

    Peter Lambert-Cole (LSU)

October 17, 2013

    Corrin Clarkson (Columbia)
    Title: 3-Manifold Mutations Detected by Geegaard Floer Homology

October 24, 2013

    Lukas Lewark (Durham)

October 31, 2013

    Jessica Banks (UQAM)

November 7, 2013

    Gabor Lippner (Harvard)

November 21, 2013

    Liam Watson (Glasgow)


BC Number Theory/Algebraic Geometry Seminar

To be determined.


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.