Video Lectures

A new cubulation theorem for hyperbolic groups

October 27, 2015

Daniel Groves

We prove that if a hyperbolic group $G$ acts cocompactly on a CAT(0) cube complexes and the cell stabilizers are quasiconvex and virtually special, then $G$ is virtually special. This generalizes Agol's Theorem (the case when the action is proper)...

video lecture

CAT(0) cube complexes and virtually special groups

October 27, 2015

Daniel Groves

Sageev associated to a codimension 1 subgroup $H$ of a group $G$ a cube complex on which $G$ acts by isometries, and proved this cube complex is always CAT(0). Haglund and Wise developed a theory of special cube complexes, whose fundamental groups...

video lecture

Algorithmic proof of the Lovasz Local Lemma via resampling oracles

October 27, 2015

Jan Vondrák

For a collection of events on a probability space with specified dependencies, the Lovasz Local Lemma ("LLL") gives a sufficient condition for the existence of a point avoiding all the events. Following Moser's discovery of an efficient algorithm...

video lecture

Quantum Ergodicity for the uninitiated

October 26, 2015

Zeev Rudnick

A key result in spectral theory linking classical and quantum mechanics is the Quantum Ergodicity theorem, which states that in a system in which the classical is ergodic, almost all of the Laplace eigenfunctions become uniformly distributed in...

video lecture

Remembering Patricia Crone (1945–2015)

October 24, 2015

Diana Frank, Thomas Frank, Michael Cook, Judith Herrin, Carol Bakhos, Emma Gannagé, Carmela V. Franklin, Robbert Dijkgraaf, Nicola Di Cosmo

Patricia Crone, Professor Emerita in the School of Historical Studies, helped to establish the Institute as a recognized center for the pursuit of Islamic culture and history. Crone’s insightful work shed important new light on the critical...

video lecture

Dehn twists exact sequences through Lagrangian cobordism

October 23, 2015

Weiwei Wu

In this talk we first introduce a new "singularity-free" approach to the proof of Seidel's long exact sequence, including the fixed-point version. This conveniently generalizes to Dehn twists along Lagrangian submanifolds which are rank one...

video lecture

Concinnitas Exhibit and Discussion

October 21, 2015

Enrico Bombieri, Freeman Dyson, Robbert Dijkgraaf, Dan Rockmore

Concinnitas is a collection of ten aquatints curated by Dan Rockmore and produced from the contributions of ten mathematicians and physicists in response to the prompt to transcribe their “most beautiful mathematical expression.” In this video from 2015, Robbert Dijkgraaf, Director and Leon Levy Professor, moderates a talk and Q&A with two contributors to Concinnitas, Enrico Bombieri and Freeman Dyson, as well as the portfolio curator, Dan Rockmore.

video lecture

Non-orientable knot genus and the Jones polynomial

October 20, 2015

Efstratia Kalfagianni

The non-orientable genus (a.k.a crosscap number) of a knot is the smallest genus over all non-orientable surfaces spanned by the knot. In this talk, I’ll describe joint work with Christine Lee, in which we obtain two-sided linear bound of the...

video lecture

Geometric techniques in knot theory

October 20, 2015

Jessica S. Purcell

We will discuss methods of decomposing knot and link complements into polyhedra. Using hyperbolic geometry, angled structures, and normal surface theory, we analyze geometric and topological properties of knots and links.

video lecture

Lonely Galaxies: The Baryon Content of Isolated Dwarf Galaxies

October 20, 2015

Marla Geha

Environment plays a major in role in the evolution of galaxies. This is particularly true of low mass dwarf galaxies where more massive galaxies dramatically affect the local gravitational potential. Isolated galaxies offer a unique test bed for...