Video Lectures

Graphlets: A Spectral Perspective for Graph Limits

February 06, 2012

Fan Chung

To examine the limiting behavior of graph sequences, many discrete methods meet their continuous counterparts, leading to numerous theoretical and applicable advancements. For dense graph sequences, the graph limits have recently been well developed...

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Primes and Equations

February 01, 2012

Richard Taylor

One of the oldest subjects in mathematics is the study of Diophantine equations, i.e., the study of whole number (or fractional) solutions to polynomial equations. It remains one of the most active areas of mathematics today. Perhaps the most basic...

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CSDM: A Survey of Lower Bounds for the Resolution Proof System

January 31, 2012

Avi Wigderson

The Resolution proof system is among the most basic and popular for proving propositional tautologies, and underlies many of the automated theorem proving systems in use today. I'll start by defining the Resolution system, and its place in the proof...

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Joint IAS-PU Symplectic Geometry Seminar: Symplectic Inverse Spectral Theory in the Semiclassical Regime for Toric Systems . . . and Beyond

January 27, 2012

San Vu Ngoc

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Symplectic Dynamics Seminar: Symplectic Structures and Dynamics on Vortex Membranes

January 25, 2012

Boris Khesin

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...

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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...

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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...

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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...

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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...

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Writers Talk - A Conversation with Will Eno

January 20, 2012

Will Eno

American playwright Will Eno talks about his work in a conversation with Derek Bermel, the Institute’s Artist-in-Residence. Eno is the author of Tragedy: a tragedy; The Flu Season; King: a problem play; Oh, the Humanity and other good intentions...