Video Lectures

Turbulence in Planet Formation

February 17, 2015

Phil Armitage

A combination of sub-mm observations and numerical simulations have the potential to yield direct constraints on the environment of planet formation. After a review of recent observational surprises, I will discuss the implications of our first...

video lecture

The log-concavity conjecture and the tropical Laplacian

February 17, 2015

June Huh

The log-concavity conjecture predicts that the coefficients of the chromatic (characteristic) polynomial of a matroid form a log-concave sequence. The known proof for realizable matroids uses algebraic geometry in an essential way, and the...

video lecture

Symplectic homology via Gromov-Witten theory

February 13, 2015

Luis Diogo

Symplectic homology is a very useful tool in symplectic topology, but it can be hard to compute explicitly. We will describe a procedure for computing symplectic homology using counts of pseudo-holomorphic spheres. These counts can sometimes be...

video lecture

Modern Cosmology and the Origin of the Universe

February 11, 2015

Matias Zaldarriaga

The last decades have seen great advances in our understanding of the history of our universe. I will summarize our current knowledge, describe some of the puzzles that still remain and speculate about future developments in cosmology. Matias...

video lecture

Algebraic curves, tropical geometry, and moduli

February 11, 2015

Sam Payne

Tropical geometry gives a new approach to understanding old questions about algebraic curves and their moduli spaces, synthesizing techniques that range from Berkovich spaces to elementary combinatorics. I will discuss an outline of this method...

video lecture

A Decade of Asteroseismology in Action

February 10, 2015

Conny Aerts

After a basic introduction on how asteroseismology works in practice, we illustrate its application to various kinds of stars of different mass and evolutionary stage. We show how detected oscillation modes allow us to understand details of the...

video lecture

Extending the Prym map

February 10, 2015

Samuel Grushevsky

The Torelli map associates to a genus g curve its Jacobian - a $g$-dimensional principally polarized abelian variety. It turns out, by the works of Mumford and Namikawa in the 1970s (resp. Alexeev and Brunyate in 2010s), that the Torelli map extends...

video lecture

How to round subspaces: a new spectral clustering algorithm

February 10, 2015

Ali Kemal Sinop

Given a $k$-dimensional linear subspace, consider the problem of approximating it (with respect to the spectral norm) in terms of another subspace spanned by the indicators of a $k$-partition of the coordinates. This is known as the spectral...

video lecture

Twisted matrix factorizations and loop groups

February 09, 2015

Daniel Freed

The data of a compact Lie group $G$ and a degree 4 cohomology class on its classifying space leads to invariants in low-dimensional topology as well as important representations of the infinite dimensional group of loops in $G$. Previous work with...

video lecture

Quantum computing with noninteracting particles

February 09, 2015

Alex Arkhipov

We introduce an abstract model of computation corresponding to an experiment in which identical, non-interacting bosons are sent through a non-adaptive linear circuit before being measured. We show that despite the very limited nature of the model...