Upcoming Seminars & Events

Subscribe to Seminars & Events
October 23, 2014
12:30pm - 1:30pm
Braid Groups and Categorification

Braid groups are fundamental objects in mathematics and categorification is the process of replacing set-theoretic theorems by category-theoretic analogues. We will connect the two by discussing a categorification of the Temperley-Lieb Algebra which results in a braid group action. We will conclude by discussing how a braid group action leads to a homology theory of links - triply graded link homology recently discovered by Mikhail Khovanov. 

Speaker: Amitesh Datta , Princeton University
Location:
Fine Hall 314
October 23, 2014
2:00pm - 3:30pm
Burgers equation with random forcing

The Burgers equation is one of the basic nonlinear evolutionary PDEs. The study of ergodic properties of the Burgers equation with random forcing began in 1990's. The natural approach is based on the analysis of optimal paths in the random landscape generated by the random force potential. For a long time only compact cases of the Burgers dynamics on a circle or bounded interval were understood well. In this talk I will discuss the Burgers dynamics on the entire real line with no compactness or periodicity assumption on the random forcing. The main result is the description of the ergodic components and existence of a global attracting random solution in each component. The proof is based on ideas from the theory of first or last passage percolation. My new work on kicked forcing is an extension of joint work with Eric Cator and Kostya Khanin on Poissonian forcing. 

Speaker: Yuri Bakhtin , Courant Institute of Mathematical Sciences, New York University
Location:
Fine Hall 601
October 23, 2014
3:00pm - 4:00pm
Stein's conjecture and other fair representation problems

Stein's conjecture states that if an n x n matrix has entries 1...n, where each symbol appears exactly n times, then there exists a generalized diagonal where all but two symbols appear exactly once. I will talk about this conjecture and other settings in which we look for a small structure proportionally representing the bigger structure from which it is taken. 

Speaker: Eli Berger , Haifa University
Location:
Fine Hall 224
October 23, 2014
3:00pm - 4:00pm
On the topological complexity of 2-torsion lens spaces

The topological complexity of a topological space is the minimum number of rules required to specify how to move between any two points of the space. A ``rule'' must satisfy the requirement that the path varies continuously with the choice of end points. We use connective complex K-theory to obtain new lower bounds for the topological complexity of 2-torsion lens spaces. We follow a program set up by Jesus Gonzalez, and answer a question posed by him.

Speaker: Don Davis , Lehigh University
Location:
Fine Hall 314
October 23, 2014
4:30pm - 5:30pm
An algebro-geometric theory of vector-valued modular forms of half-integral weight

We give a geometric theory of vector-valued modular forms attached to Weil representations of rank 1 lattices. More specifically, we construct vector bundles over the moduli stack of elliptic curves, whose sections over the complex numbers correspond to vector-valued modular forms attached to rank 1 lattices. The key idea is to construct vector bundles of Schrodinger representations and line bundles of half-forms over appropriate `metaplectic stacks' and then show that their tensor products descend to the moduli stack of elliptic curves. We discuss extensions to the cusp at infinity and give an algebraic notion of q-expansions of vector-valued modular forms. We give algebraic notions of holomorphic vector-valued modular forms and cusp forms and compute algebraic dimension formulas for these spaces over any algebraically closed field of characteristic not dividing 2,3, by using the Riemann-Roch theorem for DM stacks. A special case of this theory can be used to give an algebro-geometric theory of modular forms of half-integral weight, as defined in the complex-analytic case by Shimura.

Speaker: Luca Candelori , LSU
Location:
IAS Room S-101
October 24, 2014
11:00am - 12:00pm
Joint Columbia-IAS-Princeton Symplectic Seminar: Symplectic embeddings from concave toric domains into convex ones

This is a Joint Columbia-IAS-Princeton Symplectic Seminar. Embedded contact homology gives a sequence of obstructions to four-dimensional symplectic embeddings, called ECH capacities. These obstructions are known to be sharp in several interesting cases, for example for symplectic embeddings of one ellipsoid into another. We explain why ECH capacities give a sharp obstruction to embedding any "concave toric domain" into a "convex" one. We also explain why the ECH capacities of any concave or convex toric domain are determined by the ECH capacities of a corresponding collection of balls. Some of this is joint work with Keon Choi, David Frenkel, Michael Hutchings, and Vinicius Ramos.

Speaker: Dan Cristofaro-Gardiner , Harvard University
Location:
IAS Room S-101
October 24, 2014
1:30pm - 2:30pm
Joint Columbia-IAS-Princeton Symplectic Seminar: Beyond ECH capacities

This is a Joint Columbia-IAS-Princeton Symplectic Seminar.   ECH (embedded contact homology) capacities give obstructions to symplectically embedding one four-dimensional symplectic manifold with boundary into another. These obstructions are known to be sharp when the domain is a "concave toric domain" and the target is a "convex toric domain” (see previous talk). However ECH capacities often do not give sharp obstructions, for example in many cases when the domain is a polydisk. In this talk we explain how more refined information from ECH gives stronger symplectic embedding obstructions when the domain is a polydisk, or more generally a convex toric domain. We use these new obstructions to reprove a result of Hind-Lisi on symplectic embeddings of a polydisk into a ball, and generalize this to obstruct some symplectic embeddings of a polydisk into an ellipsoid. We also obtain a new obstruction to symplectically embedding one polydisk into another, in particular proving the four-dimensional case of a conjecture of Schlenk.

Speaker: Michael Hutchings , UC Berkeley
Location:
IAS Room S-101
October 31, 2014
1:30pm - 2:30pm
On the Gromov width of polygon spaces

After Gromov’s foundational work in 1985, problems of symplectic embeddings lie in the heart of symplectic geometry. The Gromov width of a symplectic manifold \((M, \omega)\) is a symplectic invariant that measures, roughly speaking, the size of the biggest ball we can symplectically embed in \((M, \omega)\). I will discuss tecniques to compute the Gromov width of a special family of symplectic manifolds, the moduli spaces of polygons in \(\mathbb{R}^3\) with edges of lengths \((r_1,\ldots, r_n)\). Under some genericity assumptions on lengths \(r_i\), the polygon space is a symplectic manifold. After introducing this family of manifolds, I will concentrate on the spaces of 5-gons and calculate their Gromov width. This is joint work with Milena Pabiniak, IST Lisbon.

Speaker: Alessia Mandini , University of Pavia
Location:
Fine Hall 322
November 3, 2014
3:15pm - 4:30pm
Decouplings and applications

We describe a new Fourier analytic method for estimating a wide variety of exponential sums. The talk will mainly focus on  the applications to number theory and PDEs. This is joint work  with Jean Bourgain. 

Speaker: Ciprian Demeter , Indiana University
Location:
Fine Hall 314
November 3, 2014
4:30pm - 5:30pm
Set Oriented Numerical Methods for Dynamical Systems and Optimization

Over the last two decades so-called set oriented numerical methods have been developed in the context of the numerical treatment of dynamical systems. The basic idea is to cover the objects of interest - for instance invariant sets or invariant measures - by outer approximations which are created via multilevel subdivision techniques. At the beginning of this century these methods have been modified in such a way that they are also applicable to the numerical treatment of multiobjective optimization problems. Due to the fact that they are set oriented in nature these techniques allow for the direct computation of the entire so-called Pareto set.  In this talk recent developments in the area of set oriented numerics will be presented both for dynamical systems and optimization problems. The reliability of these methods will be demonstrated by several applications such as the approximation of transport processes in ocean dynamics, or the optimization of a cruise control with respect to energy consumption and travel distance. Moreover a new algorithmic idea will be described which allows to compute invariant sets directly by Newton's method.

Speaker: Michael Dellnitz , University of Paderborn, Germany
Location:
Fine Hall 214
November 6, 2014
3:00pm - 4:00pm
TBA - Holm
Speaker: Tara Holm , Cornell and the IAS
Location:
Fine Hall 314
November 6, 2014
4:30pm - 6:00pm
Thin knotted vortex tubes in stationary solutions to the Euler equation

In this talk we will discuss the proof of the existence of thin vortex tubes for stationary solutions to the incompressible Euler equation in R^3. More precisely, given a finite collection of (possibly linked and knotted) disjoint thin tubes in R^3, we will show that they can be transformed using a small diffeomorphism into a set of vortex tubes of a Beltrami field that tends to zero at infinity.

 

Speaker: Alberto Enciso, ICMAT - Madrid
Location:
Fine Hall 322
November 6, 2014
4:30pm - 5:30pm
TBA - Hou
Speaker: Yong Hou, Zanty Electronics
Location:
Fine Hall 314
November 6, 2014
4:30pm - 5:30pm
TBA - Tiep
Speaker: Pham Tiep , Harvard University / University of Arizona
Location:
IAS Room S-101
November 7, 2014
1:30pm - 2:30pm
TBA - Müller
Speaker: Stefan Müller , UIUC
Location:
IAS Room S-101
November 7, 2014
3:00pm - 4:00pm
TBA - Lee
Speaker: John Lee, University of Washington, Seattle
Location:
Fine Hall 314
November 7, 2014
4:15pm - 5:15pm
TBA - Chodosh
Speaker: Ottis Chodosh, Stanford University
Location:
Fine Hall 314
November 10, 2014
3:15pm - 4:30pm
TBA - Nahmod
Speaker: Andrea Nahmod, University of Massachusetts Amherst
Location:
Fine Hall 314
November 10, 2014
4:30pm - 5:30pm
The physical and mathematical structure of images

Images are both maps of continuous physical phenomena and discrete mathematical objects. While Shannon established the fundamental relationship between physical and mathematical images over half a century ago, considerable further progress in understanding this relationship has been achieved in the past quarter century through the development of wavelets and compressive measurement. This talk reviews simple physical models for the physical to mathematical transformation and discusses strategies for coding the physical interface to increase measurement efficiency. We specifically discuss novel sampling strategies for x-ray tomography, diffraction tomography and focal imaging. 

Speaker: David Brady , Duke University - Electrical & Computer Engineering
Location:
Fine Hall 214
November 13, 2014
2:00pm - 3:30pm
TBA - Hooper
Speaker: Pat Hooper , City College of New York, City University of New York
Location:
Fine Hall 601

Pages