A discrete subgroup of PSL(2,C) is called a Kleinian group. I
will present a criterion on when a discrete faithful
representation of a Kleinian group into PSL(2,C) is a conjugation,
or equivalently a criterion on when an equivariant embedding
of...
The goal of this learning seminar is to explain some of the core
model theoretic notions which are behind Tao’s algebraic regularity
lemma about definable graphs in finite fields (Tao 2012).
We will assume minimal knowledge of model theory and...
The celebrated product theorem says if A is a generating subset
of a finite simple group of Lie type G, then |AAA| \gg \min \{
|A|^{1+c}, |G| \}. In this talk, I will show that a similar
phenomenon appears in the continuous setting: If A is a
subset...
The talk will consists of a long historical introduction to
the topic of deviation
of ergodic averages for locally Hamiltonian flows on compact
surafces as well as
some current results obtained in collaboration with Corinna
Ulcigrai and Minsung...
In the study of some dynamical systems, the limsup set of a
sequence of measurable sets is often of interest. The shrinking
targets and recurrence are two of the most commonly studied
problems that concern limsup sets. However, the zero-one laws
for...
A famous conjecture of Littlewood states that the Fourier
transform of every set of N integers has $l^1$ norm at least
log(N), up to a constant multiplicative factor. This was proved
independently by McGehee-Pigno-Smith and Konyagin in the
1980s...
In model theory Fraisse limits are certain highly homogeneous
countable structures -- examples include the rational
numbers as the unique dense linear order without endpoints,
and the Rado graph as the "unique infinite random
graph". I will discuss...
A word on d letters is an element of the free group of rank d,
say, with basis x_1,…,x_d. Given a word w=w(x_1,…,x_d) on d
letters, for every group G, there is a word map w:G^d—> G given
by substituting the x_i’s with elements of G. We say that a...
A number is called y-smooth if all of its prime factors are
bounded above by y. The set of y-smooth numbers below x forms a
sparse subset of the integers below x as soon as x is sufficiently
large in terms of y. If f_1, …, f_r \in Z[x_1,…,x_s] is a...
