Upcoming Seminars & Events

Subscribe to Seminars & Events
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 - 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 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 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
November 13, 2014
3:00pm - 4:00pm
TBA - Scott
Speaker: Alex Scott , Oxford University
Location:
Fine Hall 224
November 13, 2014
4:30pm - 5:30pm
TBA - Neumann
Speaker: Walter Neumann , Columbia University
Location:
Fine Hall 314
November 13, 2014
4:30pm - 6:00pm
TBA - Germain
Speaker: Pierre Germain , NYU
Location:
Fine Hall 322
November 17, 2014
3:15pm - 4:30pm
TBA - Chen
Speaker: Xuwen Chen , Brown University
Location:
Fine Hall 314
November 17, 2014
4:30pm - 5:30pm
The life of a vortex knot: Linking coiling and twisting across scales

This is a joint talk with PACM/MAE.  Can you take a vortex loop - akin to a smoke ring in air - and tie it into a knot or a link? The possibility of such knottiness in a fluid has fascinated physicists and mathematicians ever since Kelvin’s 'vortex atom' hypothesis, in which the atoms of the periodic table were hypothesized to correspond to closed vortex loops of different knot types.  More recently, the knottiness of a fluid has re-emerged as a  conserved quantity in many idealized situations (such as Euler fluids and ideal plasmas).  I will tell of how to make a vortex knot and link in water, in the wave function of a superfluid (on a computer) and of what happens thence. In particular I will talk about how linking coiling and twisting interplay across scales.

Speaker: William Irvine , University of Chicago
Location:
Fine Hall 214

Pages