Video Lectures

Microlensing Takes Off: Toward the Galactic Distribution of Planets

February 24, 2015

After 50 years of dreaming about it, space-based microlensing observations are now underway. A 2014 100-hr Spitzer Pilot Program generated "microlens parallaxes" for dozens of lenses, opening the prospect of measuring the Galactic distribution of...

video lecture

Computing inverses

February 24, 2015

Louis Rowen

We compare methods of computing inverses of matrices over division rings. The most direct way is via Cohn's theory of full matrices, which was improved by Malcolmson, Schofield, and Westreich. But it is simpler to work with finite dimensional...

video lecture

Arthur's trace formula and distribution of Hecke eigenvalues for $\mathrm{GL}(n)$

February 23, 2015

Jasmin Matz

A classical problem in the theory of automorphic forms is to count the number of Laplace eigenfunctions on the quotient of the upper half plane by a lattice $L$. For $L$ a congruence subgroup in $\mathrm{SL}(2,\mathbb Z)$ the Weyl law was proven by...

video lecture

Lower bounds for clique vs. independent set

February 23, 2015

Mika Göös

We prove an $\omega(\log n)$ lower bound on the conondeterministic communication complexity of the Clique vs. Independent Set problem introduced by Yannakakis (STOC 1988, JCSS 1991). As a corollary, this implies superpolynomial lower bounds for the...

video lecture

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...