College of Arts and Sciences

2011-2012 Seminars and Colloquia

department of mathematics

BC-MIT Number Theory Seminar

Organizers: Sol Friedberg and Ben Howard at BC, and Ben Brubaker and Bjorn Poonen at MIT.

September 20, 2011
at BC - 9 Lake Street, Room 035
Directions
3:00–4:00 p.m.
Marie-France Vigneras (Jussieu)
Title: From $p$-adic Galois representations to $G$-equivariant sheaves on the flag variety $G/P$

4:30–5:30 p.m.
Kristin Lauter (Microsoft Research)
Title: Arithmetic Intersection Theory on the Siegel Moduli Space
October 18, 2011
at MIT, Room 2-132
3:00–4:00 p.m.
Fernando Rodriguez Villegas (University of Texas at Austin)
Title: Hypergeometric motives: the case of Artin L-functions

4:00–4:30 p.m.
Xinyi Yuan (Princeton University)
Title: On the height of the Gross-Schoen cycle
November 15, 2011
at BC, McGuinn 521
Brian Conrey (AIM)
Title: A reciprocity formula for a cotangent sum

Steven D. Miller (Rutgers)

Title: Fourier Coefficients of Automorphic Forms on Exceptional Groups
February 14, 2012
at MIT, Room 3-333
Dihua Jiang (Minnesota)
Title: Constructions of Cuspidal Automorphic Forms for Classical Groups

Wenzhi Luo (Ohio State)
Title: Asymptotic Variance for the Linnik Distribution
March 20, 2012
at BC, McGuinn 521
3:00 - 4:00 p.m.
Kannan Soundararajan (Stanford)
Title: Moments and the distribution of values of L-functions

4:30 - 5:30 p.m.
Samit Dasgupta (UC Santa Cruz)
Title: On the p-adic L-functions of totally real fields.
April 3, 2012
at MIT, Room 3-333
Wen-Ching Winnie Li (Penn State)
Title: Recent progress on noncongruence modular forms

Alex Kontorovich (Yale)
Title: On Zaremba's Conjecture

BC Distinguished Lecturer in Mathematics series

April 18, 2012
3:00–4:00 p.m.
McGuinn 121
Robert Grist, University of Pennsylvania
Talk 1 (general audience)
Title: The Mathematics of Holes
Abstract: Mathematics merely begins with the study of numbers; it advances to motions and machines; computations and colorings; the strings and arrows of life. A singular expression of the beauty and power of Mathematics is revealed in its ability to quantify and qualify that which is not there—the holes. This talk introduces `topology'—the mathematical study of holes—and uses a century's worth of its innovations to explain why your cell phone drops calls, how to survive without GPS, and why you can't find good, cheap, healthy fast-food.
April 19, 2012
4:00–5:00 p.m.
Cushing 209
Talk 2 (colloquial)
Title: Euler Calculus
Abstract: This colloquium surveys a surprisingly beautiful integral calculus based on Euler characteristic, with a focus on computations and applications to problems of network data aggregation.
April 20, 2012
4:00–5:00 p.m.
Fulton 145
Talk 3 (specialized)
Title: Sheaves and Data
Abstract: Algebraic topology invented sheaves as a tool for integrating local data into a global structure. This talk will give an introduction to constructible sheaves; their (co)homology; and, most importantly, their recent applications to problems in optimization, networks, and sensing.

BC Math Society/Mathematics Department Undergraduate Lectures

September 26
4:00–5:00 p.m.
Carney 102

Dr. Paul Garvey, Chief Scientist, MITRE Corporation

Title: "Evaluating Risky Prospects, with a little Calculus"

October 12
Noon
Carney 309
Math for America Info Session
November 17
4:30–5:30 p.m.
Carney 102
Frank Sullivan (Boston College Alumnus)
Title: "On the role of mathematics in my career"
February 16
4:30 p.m.
Devlin 227
Speaker: Puneet Batra
Title: "The Science Behind Big Data"
Abstract: Thousands of organizations now have the means to collect extreme amounts of data per year, from petabyes to exabytes. This explosion of 'Big Data' has led to a number of new insights, from Facebook's 'People You May Know' to algorithms that optimize drug choice for new cancer patients. The Big Data revolution has been driven by analyses on consumer behavior, web traffic, machine logs, cell-phone traffic and healthcare data. In this talk, I'll discuss some of the mathematical and statistical tools that data scientists use to derive meaningful results from 'Big Data' using some concrete examples from services that we've all used, including netflix and facebook.
March 29
5:45 p.m. 
McGuinn 521
Speaker: Steven J. Miller
Title: "Pythagoras at the Bat: An Introduction to Statistics and Modeling"
Abstract: Let RS (resp., RA) denote the average number of runs scored (resp., allowed) in a baseball game by a team. It was numerically observed years ago that a good predictor of a team's won-loss percentage is RS^2 / (RS^2 + RA^2), though no one knew WHY the formula worked. We review elementary concepts of probability and statistics, and discuss how one can build and solve a model for this problem. We'll discuss how to attack problems like this in general (what are the features of a good model, how to solve it, and so on). The only pre-requisite is simple calculus (no baseball knowledge is required, though Red Sox knowledge is always a plus).

 

BC Geometry/Topology Seminar

Schedule for the BC Geometry/Topology Seminar

 

BC Number Theory/Algebraic Geometry Seminar

Schedule for the BC Number Theory/Algebraic Geometry Seminar

Organizers: Avner Ash, Dubi Kelmer, Rob Gross

 

BC Colloquium Series

October 13

2:30 – 3:30 p.m.

Carney 309

Speaker: Izzet Coskun, University of Illinois, Chicago

Title: Pictures and homogeneous spaces

Abstract: Many important problems in representation theory have analogues in geometry. For example, decomposing tensor products of representations of GL(n) into irreducible representations is very closely tied to the geometry of the Grassmannian. Similarly, studying the restriction of a representation of GL(n) to subgroups such as SO(n) or SP(n) has geometric analogues in terms of the geometry of flag varieties. In this talk, I will show you how drawing a few  pictures can make studying such lofty problems a lot of fun. I will specifically concentrate on Littlewood-Richardson rules and geometric branching rules. I intend to make the talk accessible to anyone who is willing to be seduced by pictures.

October 27

4:00 – 5:00 p.m.

Fulton 230

Speaker: Richard Askey, University of Wisconsin

Title: The binomial theorem, beta and gamma functions, and some extensions of each.

Abstract: It is well known that the number of permutations of the set 1,2,...,n is n!. An extension of this where one counts inversions was posed as a problem by M. Stern in 1839. These will be the starting place to build up the binomial theorem, the extension of n! which we now write as the gamma function, the beta integral of John Wallis, Euler's integral representation of the gamma function as an integral, and the connection between these three things. This connection will be looked at in two different settings, the classical one which most of you know reasonable well, and what will be called q-extensions of these classical results into a world which has finally started to come into its own.

November 9, 

4.00 – 5.00 p.m.

Carney 309

Speaker: András Stipsicz (Rényi Institute of Mathematics)

Title:  3-dimensional contact topology

Abstract: After reviewing results about the existence of tight contact structures on closed 3-manifolds, we show how to use Heegaard Floer theory (in particular, the contact Ozsvath-Szabo invariant) to verify tightness of certain contact structures on 3-maniolds given by surgery along specific knots in S^3

November 17, 

2:30 – 3:30 p.m

Carney 309

Speaker: Joseph Harris, (Harvard University)

Title:  Title: The Interpolation Problem

Abstract: See here.

December 7, 

4:15 – 5:15 p.m.

Carney 309

Speaker: Ian Agol, (University of California, Berkeley)

Title: Virtual properties of 3-manifolds

Abstract: In his article "3-Dimensional manifolds, Kleinian groups, and hyperbolic geometry", William Thurston posed 24 problems related to the topology and geometry of Kleinian groups and hyperbolic 3-manifolds. We'll discuss four of the remaining open problems from this list, 15-18, having to do principally with finite-sheeted covers of hyperbolic 3-manifolds. We'll discuss how recent work of Kahn-Markovic and Wise implies that these problems are essentially equivalent, and the prospects for answering these questions combining their results.

March 14, 2012

3:00 – 4:00 pm

Carney 309

Speaker: Martin Moeller (Frankfurt)

Title: Fuchsian differential equations and derivatives of theta functions

Abstract: Usually the power series expansion of solutions to a Fuchsian differential equation with integral coefficients has huge denominators. One instance when the solution is actually integral was discovered by Apery and gave a proof of the irrationality of Zeta(3). We give another instance of such a special Fuchsian differential equation with integral expansion. It is related to derivatives of Hilbert theta functions. The proofs connect (Hilbert) modular forms to the geometry of billard tables.

March 28, 2012

3:00 – 4:00 pm

Carney 309

Speaker: Chen-Yu Chi (Harvard)

Title: On the L^1-norm on the space of quadratic differentials

Abstract: The spaces of quadratic differentials play essential roles in the studies of Riemann surfaces and their moduli spaces. Each of these spaces is equipped with a canonical norm. In 1971, Royden shows that two closed Riemann surfaces of genus greater than 1 are isomorphic if and only if their spaces of quadratic differentials are isometric with respect to their canonical norms. We will first review Royden's proof and then outline a program initiated in a joint-work with Yau which can be regarded as further developments in higher dimensions along the same direction. If time permits, we will also talk about a recent observation due to Stergios Antonakoudis.

April 24, 2012

4:00 – 5:00 pm

Carney 309

Speaker: Peter Kronheimer (Harvard)

Title: Knots, webs and unitary representations

Abstract: A basic invariant of a knot K in 3-space is the fundamental group, Π, of the knot complement; and a basic way to study any group such as Π is to look at its representations in a standard group G, such as a permutation group or a linear group. In the case of knot groups, representations of Π in dihedral groups contain information encoded in the Alexander polynomial of the knot.

Already when we look at the case G=U(2), something emerges from the deep: if K is non-trivial then there always exists at least one non-abelian representation of Π in U(2). The proof of this result involves taking a distinguished set representations of Π in U(2) and assembling them to form an invariant of the knot K -- its instanton Floer homology group -- with surprising connections to both the Alexander polynomial and the Khovanov homology of the knot.

In this talk, we will introduce some of these concepts, and look a little past the group U(2) to the case of U(N). In this case, it is natural to extend our objects of study, from knots to "webs", and to seek connections with the knot homology groups defined by Khovanov and Rozansky.

May 3, 2012

3:00 – 4:00 pm

Carney 309

Speaker: John Etnyre (Georgia Tech)

Title: Curvature and (contact) topology

Abstract: Contact geometry is a beautiful subject that has important interactions with topology in dimension three. In this talk I will give a brief introduction to contact geometry and discuss its interactions with Riemannian geometry. In particular I will discuss a contact geometry analog of the famous sphere theorem and more generally indicate how the curvature of a Riemannian metric can influence properties of a contact structure adapted to it.  This is joint work with Rafal Komendarczyk and Patrick Massot.

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.