There are striking analogies between topology and arithmetic
algebraic geometry, which studies the behavior of solutions to
polynomial equations in arithmetic rings. One expression of these
analogies is through the theory of etale cohomology, which...
Suppose we have a cancellative binary associative operation * on
a finite set X. We say that it is delta-associative if the
proportion of triples x, y, z such that x*(y*z) = (x*y)*z is at
least delta.
DNA rearrangement is observed at developmental and evolutionary
scale. The recombination process can be directly modeled by
4-regular graphs and Gauss codes, also called double occurrence
words. We discuss properties of these graphs, their spatial...
Following Bourgain, Gamburd, and Sarnak, we say that the Markoff
equation x2+y2+z2−3xyz=0 satisfies strong approximation at a prime
p if its integral points surject onto its Fp points. In 2016,
Bourgain, Gamburd, and Sarnak were able to establish...
This is the last talk towards understanding
Bezrukavnikov-Finkelberg's derived geometric Satake equivalence.
With the preparations from previous talks, we will introduce two
filtrations: a topological filtration on the equivariant cohomology
and an...
A countable group G is called sofic if it admits a sofic
approximation: a sequence of asymptotically free almost actions on
finite sets. Given a sofic group G, it is a natural problem to try
to classify all its sofic approximations and, more...
Given a set E of Hausdorff dimension s>d/2 in ℝd , Falconer
conjectured that its distance set Δ(E)={|x−y|:x,y∈E} should have
positive Lebesgue measure. When d is even, we show that
dimHE>d/2+1/4 implies |Δ(E)|>0. This improves upon the work
of Wolff...
(joint work with Assaf Naor) A key problem in metric geometry
asks: given metric spaces X and Y, how well does X embed in Y? In
this talk, we will consider this problem for the case of the
Heisenberg group and explain its connections to geometric...
We prove new lower bounds on the well known Gap-Hamming problem
in communication complexity. Our main technical result is an
anti-concentration bound for the inner product of two independent
random vectors. We show that if A, B are arbitrary subsets...
We will give an explicit construction and description of a
supercuspidal local Langlands correspondence for any p-adic group G
that splits over a tame extension, provided p does not divide the
order of the Weyl group. This construction matches any...
