Video Lectures

Global results related to scalar curvature and isoperimetry

December 04, 2018

I will first survey some recent progress on global problems related to scalar curvature and area/volume, focusing in particular on scale breaking phenomena in such problems. I will then discuss the role of the Hawking mass in the resolution of this...

video lecture

Mean action of periodic orbits of area-preserving annulus diffeomorphisms

December 03, 2018

Morgan Weiler

An area-preserving diffeomorphism of an annulus has an "action function" which measures how the diffeomorphism distorts curves. The average value of the action function over the annulus is known as the Calabi invariant of the diffeomorphism, while...

video lecture

Recent Progress on Zimmer's Conjecture

December 03, 2018

David Fisher

Lattices in higher rank simple Lie groups are known to be extremely rigid. Examples of this are Margulis' superrigidity theorem, which shows they have very few linear represenations, and Margulis' arithmeticity theorem, which shows they are all...

video lecture

Branched conformal structures and the Dyson superprocess

November 30, 2018

Govind Menon

In the early 1920s, Loewner introduced a constructive approach to the Riemann mapping theorem that realized a conformal mapping as the solution to a differential equation. Roughly, the “input” to Loewner’s differential equation is a driving measure...

video lecture

The Lucky Logarithmic Derivative

November 29, 2018

Will Sawin

We study the function field analogue of a classical problem in analytic number theory on the sums of the generalized divisor function in short intervals, in the limit as the degrees of the polynomials go to infinity. As a corollary, we calculate...

video lecture

Bubbling theory for minimal hypersurfaces

November 27, 2018

Ben Sharp

We will discuss the bubbling and neck analysis for degenerating sequences of minimal hypersurfaces which, in particular, lead to qualitative relationships between the variational, topological and geometric properties of these objects. Our aim is to...

video lecture

Kinematics of Circumgalactic Gas

November 27, 2018

Crystal Martin

Most of the baryons associated with galaxy halos reside in the circumgalactic medium. A significant fraction of the mass is at temperatures well below the halo virial temperature. What holds the cool CGM up? I will present new measurements of the...

video lecture

Homotopical effects of k-dilation

November 27, 2018

Larry Guth

Back in the 70s, Gromov started to study the relationship between the Lipschitz constant of a map (also called the dilation) and its topology. The Lipschitz constant describes the local geometric features of the map, and the problem is to...

video lecture

Monotone Circuit Lower Bounds from Resolution

November 27, 2018

Mika Göös

For any unsatisfiable CNF formula F that is hard to refute in the Resolution proof system, we show that a gadget-composed version of F is hard to refute in any proof system whose lines are computed by efficient communication protocols---or...

video lecture

Classical Verification of Quantum Computations

November 26, 2018

Urmila Mahadev

We present the first protocol allowing a classical computer to interactively verify the result of an efficient quantum computation. We achieve this by constructing a measurement protocol, which allows a classical string to serve as a commitment to a...