We review results about random walks on groups, discussing
results and conjectures relating critical constant for
recurrence/transience, growth and Poisson boundary.
Much less is known about behavior of random walks on Schreier
graphs. Since any...
For each central charge c∈(0,1], we construct a conformally
invariant field which is a measurable function of the local time
field L of the Brownian loop soup with intensity c and i.i.d. signs
given to each cluster. This field is canonically...
In this talk, we start by reviewing recent results on the
dynamics of Reeb vector fields defined by contact forms on
three-dimensional manifolds, and then introduce Reeb fields defined
by stable Hamiltonian structures. These are more general and...
The behavior of quadratic twists of modular L-functions is at
the critical point is related both to coefficients of half integer
weight modular forms and data on elliptic curves. Here we
describe a proof of an asymptotic for the second moment of...
I will talk about three interesting ingredients that goes into
the results on H\"{o}rmander type operators I presented at
Princeton (joint with Shaoming Guo and Hong Wang). They are all
related to algebraic or geometric properties of multivariate...
The ruled hypersurfaces are distinguished by being comprised of
lines. When this characteristic exists as a consequence of
vanishing principal curvatures, it yields possibilities for
comparison with cylinders extending over lower-dimensional...
A conjecture of Erdős states that for every large enough prime
q, every reduced residue class modulo q is the product of two
primes less than q. I will discuss my on-going work with Kaisa
Matomäki establishing among other things a ternary variant
of...
The online list labeling problem is a basic primitive in data
structures. The goal is to store a dynamically-changing set of n
items in an array of m slots, while keeping the elements in sorted
order. To do so, some items may need to be moved over...
Let E be an elliptic curve defined over \Q. The \Q¯-points
of E form an abelian group on which the Galois group
G\Q=\Gal(\Q¯/\Q) acts. The usual Galois representation
associated to E captures the action of G\Q on the points of finite
order. ...
The classic algorithm AdaBoost allows to convert a weak learner,
that is an algorithm that produces a hypothesis which is slightly
better than chance, into a strong learner, achieving arbitrarily
high accuracy when given enough training data. We...
