Motivated by a formal similarity between the Hard Lefschetz
theorem and the geometric Satake equivalence we study vector spaces
that are graded by a weight lattice and are endowed with linear
operators in simple root directions. We allow field...
In his seminal paper from 1973, Garland introduced a machinery
for proving vanishing of group cohomology for groups acting on
Bruhat-Tits buildings. This machinery, known today as “Garland’s
method”, had several applications as a tool for proving...
Expander graphs in general, and Ramanujan graphs in particular,
have played an important role in computer science and pure
mathematics in the last four decades. In recent years the area of
high dimensional expanders (i.e. simplical complexes with...
A recent line of work has focused on the following question: Can
one prove strong unconditional lower bounds on the number of
samples needed for learning under memory constraints? We study an
extractor-based approach to proving such bounds for a...
We will discuss recent developments of the theory of
a-contraction with shifts to study the stability of discontinuous
solutions of systems of equations modeling inviscid compressible
flows, like the compressible Euler equation.
Low-dimensional topology and geometry have many problems with an
easy formulation, but a hard solution. Despite our intuitive
feeling that these problems are "hard", lower or upper bounds on
algorithmic complexity are known only for some of them...
I'll talk about two related projects, with two different groups,
both aiming to see three-dimensional manifolds "from the inside".
That is, we generate images assuming that light travels along
geodesics in the geometry of the manifold. The first...
Let GG be a reductive group over a number
field FF and HH a subgroup. Automorphic periods
study the integrals of cuspidal automorphic forms
on GG over H(F)∖H(AF)H(F)∖H(AF). They are often
related to special values of certain L functions. One of the...
Before the "geometric Satake equivalence" there was a
decategorified version of it which however contained most of its
essential features. In my talk I will talk about some of the ideas
which have led to this theory. In particular I will explain
the...
Several well-known open questions (such as: are all groups
sofic/hyperlinear?) have a common form: can all groups be
approximated by asymptotic homomorphisms into the symmetric
groups Sym(n)Sym(n) (in the sofic case) or the finite
dimensional...