The interchange process \sigma_T is a random permutation valued
process on a graph evolving in time by transpositions on its edges
at rate 1. On Z^d, when T is small all the cycles of the
permutation \sigma_T are finite almost surely. In dimension
d...
As has been known since the 90s, there is an integrable
structure underlying two-dimensional gravity theories. Recently,
two-dimensional gravity theories have regained an enormous amount
of attention, but now in relation with quantum chaos -...
Fast radio bursts (FRBs) are the brightest radio transients in
the universe. Since the unexpected discovery in the 21st century,
their extreme nature is one of the biggest mysteries of
astrophysics. FRBs are also unique probes of the universe...
The Cohen-Lenstra heuristics give predictions for the
distribution of the class groups of a random quadratic number
field. Cohen and Martinet generalized them to predict the
distribution of the class groups of random extensions of a fixed
base field...
Lower scalar curvature bounds on spin Riemannian manifolds
exhibit remarkable rigidity properties determined by spectral
properties of Dirac operators. For instance, a fundamental result
of Llarull states that there is no smooth Riemannian metric
on...
This will be a survey talk about recent progress on pointwise
convergence problems for multiple ergodic averages along polynomial
orbits and their relations with the Furstenberg-Bergelson-Leibman
conjecture.
Expander graphs are fundamental objects in theoretical computer
science and mathematics. They have numerous applications in diverse
fields such as algorithm design, complexity theory, coding theory,
pseudorandomness, group theory, etc.
I will discuss the potential importance of a dark-sector phase
transition in the early universe in setting the measured relic
abundance, for a simple scenario with strongly interacting dark
matter. Enhancement of the dark matter density within...
The notion of Schmidt rank/strength for a collection of m
polynomials plays an important role in additive combinatorics,
number theory and commutative algebra; high rank collections of
polynomials are “psuedorandom”. An arbitrary collection
of...
