We first describe mathematical foundation of DSGRN (Dynamic
Signatures Generated by Regulatory Networks), an approach that
provides a queryable description of global dynamics of a network
over its entire param- eter space. We describe a connection...
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...
A classical result identifies holomorphic modular forms with
highest weight vectors of certain representations of SL2(ℝ). We
study locally analytic vectors of the (p-adically) completed
cohomology of modular curves and prove a p-adic analogue of...
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...
