Video Lectures

The symplectic displacement energy

February 20, 2015

Peter Spaeth

To begin we will recall Banyaga's Hofer-like metric on the group of symplectic diffeomorphisms, and explain its conjugation invariance up to a factor. From there we will prove the positivity of the symplectic displacement energy of open subsets in...

video lecture

Eigencurve over the boundary of the weight space

February 19, 2015

Liang Xiao

Eigencurve was introduced by Coleman and Mazur to parametrize modular forms varying $p$-adically. It is a rigid analytic curve such that each point corresponds to an overconvegent eigenform. In this talk, we discuss a conjecture on the geometry of...

video lecture

The cohomology groups of Hilbert schemes and compactified Jacobians of planar curves

February 18, 2015

Luca Migliorini

I will first discuss a relation between the cohomology groups (with rational coefficients) of the compactified Jacobian and those of the Hilbert schemes of a projective irreducible curve $C$ with planar singularities, which extends the classical...

video lecture

Proper base change for zero cycles

February 17, 2015

Moritz Kerz

We study the restriction map to the closed fiber for the Chow group of zero-cycles over a complete discrete valuation ring. It turns out that, for proper families of varieties and for certain finite coefficients, the restriction map is an...

video lecture

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...