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...
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...
A famous conjecture of Littlewood states that the Fourier
transform of every set of N integers has l^1 norm at least log(N),
up to a constant multiplicative factor. This was proved
independently by McGehee-Pigno-Smith and Konyagin in the 1980s.
This...
Humans have been thinking about polynomial equations over the
integers, or over the rational numbers, for many years. Despite
this, their secrets are tightly locked up and it is hard to know
what to expect, even in simple looking cases. In this talk...
