# Video Lectures

The theory of graph quasirandomness studies sequences of graphs that "look like" samples of the Erdős--Rényi random graph. The upshot of the theory is that several ways of comparing a sequence with the random graph turn out to be equivalent. For...

Given several real numbers α1,...,αk, how well can you simultaneously approximate all of them by rationals which each have the same square number as a denominator? Schmidt gave a clever iterative argument which showed that this can be done...

Many algorithms and heuristics that work well in practice have poor performance under the worst-case analysis, due to delicate pathological instances that one may never encounter. To bridge this theory-practice gap, Spielman and Teng introduced the...

This talk reviews the use of radial quantization to compute Chern-Simons partition functions on handlebodies of arbitrary genus. The partition function is given by a particular transition amplitude between two states which are defined on the Riemann...

We introduce new invariants to the existence of Lagrangian

cobordisms in R^4. These are obtained by studying holomorphic disks

with corners on Lagrangian tangles, which are Lagrangian cobordisms

with flat, immersed boundaries.

We...

Consider the family of automorphic representations on some unitary group with fixed (possibly non-tempered) cohomological representation π0 at infinity and level dividing some finite upper bound. We compute statistics of this family as the level...

Misaligned disks in binaries were commonly thought to evolve to
a coplanar

state. However, recent theory and observations have surprisingly
shown that disks around

eccentric orbit binaries can evolve to a polar state in which the
disk is...

Let G be a simply-connected complex semisimple algebraic group and let C be a smooth projective curve of any genus. Then, the moduli space of semistable G-bundles on C admits so called determinant line bundles. E. Verlinde conjectured a remarkable...

There is a celebrated connection between minimal (or constant mean curvature) hypersurfaces and Ricci curvature in Riemannian Geometry, often boiling down to the presence of a Ricci term in the second variation formula for the area. The first goal...

For the first time, the entire visible sky is being surveyed for the violent, variable, and transient events that shape our universe by the All-Sky Automated Survey for Supernovae (ASAS-SN). Combined, ASAS-SN, Asteroid Terrestrial-impact Last Alert...