Video Lectures

Symplectic Dynamics Seminar: Symplectic Structures and Dynamics on Vortex Membranes

January 25, 2012

We present a Hamiltonian framework for higher-dimensional vortex filaments (or membranes) and vortex sheets as singular 2-forms with support of codimensions 2 and 1, respectively, i.e. singular elements of the dual to the Lie algebra of divergence...

video lecture

Symplectic Dynamics Seminar: On Conjugacy of Convex Billiards

January 25, 2012

Vadim Kaloshin

There are indications that in the 80s Guillemin posed a question: If billiard maps are conjugate, can we say that domains are the same up to isometry? On one side, we show that conjugacy of different domains can't be C^1 near the boundary. In...

video lecture

CSDM: A Tutorial on the Likely Worst-Case Complexities of NP-Complete Problems

January 24, 2012

Russell Impagliazzo

Abstract The P vs. NP problem has sometimes been unofficially paraphrased as asking whether it is possible to improve on exhaustive search for such problems as Satisfiability, Clique, Graph Coloring, etc. However, known algorithms for each of these...

video lecture

Members Seminar: The Role of Symmetry in Phase Transitions

January 23, 2012

Tom Spencer

This talk will review some theorems and conjectures about phase transitions of interacting spin systems in statistical mechanics. A phase transition may be thought of as a change in a typical spin configuration from ordered state at low temperature...

video lecture

An Optimal Lower Bound for File Maintenance

January 23, 2012

Michael Saks

In the file maintenance problem, n integer items from the set {1,....,r} are to be stored in an array of size m>=n . The items are presented sequentially in an arbitrary order and must be stored in the array in sorted order (but not necessarily in...

video lecture

Can the Continuum Problem be Solved?

December 06, 2011

Menachem Magidor

This is a survey talk about different attempts to deal with the very troubling phenomena of independence in Set Theory.

video lecture

Entropy-Based Bounds on Dimension Reduction in L_1

November 28, 2011

Oded Regev

https://www.ias.edu/math/files/seminars/OdedRegev.pdf

video lecture

An Isoperimetric Inequality for the Hamming Cube and Integrality Gaps in Bounded-Degree Graphs

November 21, 2011

Siavosh Benabbas

In 1970s Paul Erdos asked the following question: Consider all the boolean strings of length n. Assume that one has chosen a subset S of the strings such that no two chosen strings are different in precisely n/4 (or its closest even integer)...

video lecture

Orientability and Open Gromov-Witten Invariants

November 11, 2011

Penka Georgieva

I will first discuss the orientability of the moduli spaces of J-holomorphic maps with Lagrangian boundary conditions. It is known that these spaces are not always orientable and I will explain what the obstruction depends on. Then, in the presence...

video lecture

Bilinearized Legendrian Contact Homology

November 11, 2011

Frederic Bourgeois

Legendrian contact homology (LCH) is a powerful holomorphic curves invariant for Legendrian submanifolds in contact manifolds. It is defined via a differential graded algebra (DGA), but the computation of its homology is often too difficult...