Members’ Colloquium

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 the...

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...

Let p be a prime number. Roughly speaking, rigid analytic geometry is a counterpart of complex analysis where one replaces the field C

of complex numbers by the field Qp of p-adic rational numbers (or some extension thereof).

In this talk, I'll try...

The Zimmer program asks how lattices in higher rank semisimple Lie groups may act smoothly on compact manifolds. Below a certain critical dimension, the recent proof of the Zimmer conjecture by Brown-Fisher-Hurtado asserts that, for SL(n,R) with n...

How do we describe the topology of the space of all nonconstant holomorphic (respectively, algebraic) maps F: X--- greater than Y  from one complex manifold (respectively, variety) to another? What is, for example, its cohomology? Such problems are...

Zeros of L-functions have been extensively studied, due to their close connection to arithmetic problems. Despite several precise conjectures about their behavior, our unconditional understanding of them remains limited. In this talk we will discuss...

The rigorous study of spin systems such as the Ising model is currently one of the most active research areas in probability theory. In this talk, I will introduce one particular class of such models, known as lattice gauge theories (LGTs), and go...