A dark matter candidate lighter than about 30 eV exhibits wave
behavior in a typical galactic environment. Examples include the
QCD axion as well as other axion-like-particles. We review the
particle physics motivations, and discuss experimental and...
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...
One of the key objectives of modern astrophysics is to
understand the formation and evolution galaxies. In this regard,
the Milky Way is a critical testing ground for our theories of
galaxy formation. However, dissecting the assembly history of
the...
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...
