Video Lectures

Non-orientable knot genus and the Jones polynomial

October 20, 2015

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...

video lecture

Adjoint Selmer groups for polarized automorphic Galois representations

October 15, 2015

Patrick Allen

Given the $p$-adic Galois representation associated to a regular algebraic polarized cuspidal automorphic representation, one naturally obtains a pure weight zero representation called its adjoint representation. Because it has weight zero, a...

video lecture

100 Years of General Relativity

October 14, 2015

Robbert Dijkgraaf

The general theory of relativity, which Albert Einstein formulated 100 years ago, is one of the great pillars of modern physics. It is based on profound and elegant principles that connect the physics of motion and mass to the geometry of space and...

video lecture

The four-color theorem and an instanton invariant for spatial graphs II

October 13, 2015

Tomasz Mrowka

Given a trivalent graph embedded in 3-space, we associate to it an instanton homology group, which is a finite-dimensional $\mathbf{Z}/2$ vector space. The main result about the instanton homology is a non-vanishing theorem, proved using techniques...

video lecture

The four-color theorem and an instanton invariant for spatial graphs I

October 13, 2015

Peter Kronheimer

video lecture

Non-constructive combinatorics

October 13, 2015

Noga Alon

I will describe several old and new applications of topological and algebraic methods in the derivation of combinatorial results. In all of them the proofs provide no efficient solutions for the corresponding algorithmic problems. Finding such...

video lecture

The Macrophysics and Microphysics of Cosmic Rays

October 13, 2015

Ellen Zweibel

Cosmic rays comprise only about one billionth of interstellar particles in the Milky Way, but have as much energy as the thermal gas. Low energy cosmic rays affect the chemistry and thermodynamics of interstellar through collisional processes...

video lecture

3-manifold groups

October 12, 2015

Ian Agol

I'll review recent progress on properties of 3-manifold groups, especially following from geometric properties. Then I'll discuss some open questions regarding 3-manifold groups, including their profinite completions, torsion in covers, orderability...