The polynomial Freiman-Ruzsa conjecture is one of the important
open problems in additive combinatorics. In computer science, it
already has several diverse applications: explicit constructions of
two-source extractors; improved bounds for the log...
My goal in this talk is to survey some of the emerging
applications of polynomial methods in both learning and in
statistics. I will give two examples from my own work in which the
solution to well-studied problems in learning and statistics
can...
In joint work with Paul Valiant, we consider the tasks of
estimating a broad class of statistical properties, which includes
support size, entropy, and various distance metrics between pairs
of distributions. Our estimators are the first proposed...
We explain in this talk how Ramanujan graphs can be used to
devise optimal cycle codes and review how other graph families
related to a construction proposed by Margulis yield interesting
families of quantum codes with logarithmic minimum distance...
The history of digital computing can be divided into an Old
Testament whose prophets, led by Gottfried Wilhelm Leibniz,
supplied the logic, and a New Testament whose prophets, led by John
von Neumann, built the machines. Alan Turing, whose “On...
The families of motives of the title arise from classical
one-variable hypergeometric functions. This talk will focus on the
calculation of their corresponding L-functions both in theory and
in practice. These L-functions provide a fairly wide...
In FT-mollification, one smooths a function while maintaining
good quantitative control on high-order derivatives. This is a
continuation of my talk from last week, and I will continue to
describe this approach and show how it can be used to show...
The braid group on n strands may be viewed as an infinite analog
of the symmetric group on n elements with additional topological
phenomena. It appears in several areas of mathematics, physics and
computer sciences, including knot theory...
A conjecture of Langlands-Rapoport predicts the structure of the
mod p points on a Shimura variety. The conjecture forms part of
Langlands' program to understand the zeta function of a Shimura
variety in terms of automorphic L-functions.
