Rankin-Selberg integrals provide factorization of certain period
integrals into local counterparts. Other, more elusive, periods can
be studied in principle by the relative trace formula and other
methods.
In a sequence of extremely fundamental results in the 80's,
Kaltofen showed that any factor of n-variate polynomial with degree
and arithmetic circuit size poly(n) has an arithmetic circuit of
size poly(n). In other words, the complexity class VP is...
We will give an overview of some of the developments in recent
years dealing with the description of asymptotic states of
solutions to semilinear evolution equations ("soliton resolution
conjecture").
I will discuss several results on abstract homomorphisms between
the groups of rational points of algebraic groups. The main focus
will be on a conjecture of Borel and Tits formulated in their
landmark 1973 paper.
I will explain an application of the geometric Satake
correspondence (in its derived form due to
Bezrukavnikov-Finkelberg) to the study of differential operators on
$G$-spaces (for $G$ complex reductive) and its classical version,
the study of...
This talk will be an introduction to the methods used in the
study of spectral properties of Schroedinger operators with a
potential defined via the action of an ergodic transformation. Open
problems relating to Lyapunov exponents over a skew shift...
The Random Fourier Features (RFF) method (Rahimi, Recht, NIPS
2007) is one of the most practically successful techniques for
accelerating computationally expensive nonlinear kernel learning
methods. By quickly computing a low-rank approximation for...
We develop efficient algorithms for estimating low-degree
moments of unknown distributions in the presence of adversarial
outliers. The guarantees of our algorithms improve in many cases
significantly over the best previous ones, obtained in
recent...
Last semester I gave a talk that was a 1-hour condensation of
undergrad machine learning. https://www.ias.edu/video/membsem/2017/1127-SanjeevArora
. This semester's talk will be a 1-hour treatment of some research
directions in theoretical machine...
An error-correcting code is called locally repairable if any
coordinate of a codeword can be recovered by accessing only few
other coordinates. For locally repairable codes over small
alphabets (such as binary), the optimal trade-off between...
