The Fourier uniformity conjecture seeks to understand what
multiplicative functions can have large Fourier coefficients on
many short intervals. We will discuss recent progress on this
problem and explain its connection with the distribution of...
The problem of control of large multi-agent systems, such as
vehicular traffic, poses many challenges both for the development
of mathematical models and their analysis and the application to
real systems. First, we discuss how conservation laws can...
I will discuss a result with Bonatti and Crovisier from 2009
showing that the C1 generic diffeomorphism f of a closed manifold
has trivial centralizer; i.e. fg = gf implies that g is a power of
f. I’ll discuss features of the C1 topology that enable...
Let G be an infinite discrete group. Finite dimensional unitary
representations of G are usually quite hard to understand. However,
there are interesting notions of convergence of such
representations as the dimension tends to infinity. One notion
—...
Translational tiling is a covering of a space (such as Euclidean
space) using translated copies of one building block, called a
"translational tile'', without any positive measure
overlaps.
Can we determine whether a given set is a translational...
The Higgs mechanism is a part of the Standard Model of quantum
mechanics that allows certain kinds of particles to have nonzero
mass. In spite of its great importance, there is no rigorous proof
that the Higgs mechanism can indeed generate mass in...
The theory of matroids provides a unified abstract treatment of
the concept of dependence in linear algebra and graph theory. In
this talk we explain Bergman fans of matroids, and we investigate
isomorphisms of Bergman fans for different fan...
The finite field Kakeya problem asks about the size of the
smallest set in (F_q)^n containing a line in every direction.
Raised by Wolff in 1999 as a ‘toy’ version of the Euclidean Kakeya
conjecture, this problem is now completely resolved using...
Motivated by a discovery by Radchenko and Viazovska and by a
work by Ramos and Sousa, we find conditions sufficient for a pair
of discrete subsets of the real axis to be a uniqueness or a
non-uniqueness pair for the Fourier transform. These...
