Past Events
Part of the Henri Poincaré Distinguished Lecture Series
In 1919, Besicovitch constructed a compact set in the plane with Lebesgue measure 0 that contains a unit line segment pointing in every direction.…
Our work begins with the following question about rainbow triangles, inspired by the joints problem: If G is a graph with m edges, each colored with one of r colors, then what is the maximum number of rainbow triangles G can have (as a function of m)? In 2023, Chao and Yu answered this…
The simplest cipher is just a permutation of the alphabet, which can be easily broken from a (long enough) encrypted piece of text using frequency analysis. Now suppose that I encrypt my text such that each subsequent letter is encrypted using a different permutation, out a list of 10^16 unique…
HPD-stratifications [BO, 4.1-4.4], and crystals [BO, 6.1-6.6]
Machine learning is usually presented as function approximation: in supervised learning, one aims to recover an unknown map from inputs to outputs, and results such as universal approximation theorems and generalization bounds explain why neural networks can, in principle, learn rich function…
A typical Tauberian theorem deduces an asymptotic for the partial sums of a sequence of non-negative real numbers from analytic properties of an associated Dirichlet series. Tauberian theorems appear in a tremendous variety of applications, and are so “classical” that sometimes practitioners…
The Toda lattice is a system of classical mechanics discovered by Toda in 1967, which describes interacting particles on a line. Due to its integrability, the Toda lattice with N particles possesses N independent conserved quantities. In this work, we show that under a certain class of random…
Abstract: Investigating mixtures of bosons and fermions is an extremely active area of research in experimental physics for constructing and understanding novel quantum bound states such as those in superconductors, superfluids, and supersolids. These ultra-cold Bose-Fermi mixtures are…
Equivariant knots are knots equipped with a specified symmetry. Extending this notion, one can define equivariant Seifert surfaces in S^3 and equivariant slice surfaces in D^4. However, even the equivariant Seifert genus is difficult to determine, as there is no analogue of the classical Seifert…
In this talk, I will give a brief overview of the p-adic theory of differential equations and its application to quantum differential equations arising in enumerative geometry. This perspective reveals similarities with mirror symmetry, manifested through p-adic exponential sums. I will…