Past Events

For an elliptic curve E defined over Q, the Mordell-Weil group E(Q) is a finitely generated abelian group. We prove that there are infinitely many elliptic curves E over Q for which E(Q) has rank 2. Our elliptic curves will be given by explicit models and their ranks will be found using a 2-…

I will discuss a combinatorial conjecture which states that a "core" (or "stable") solution exists for any instance of an election where each voter presents a set of approved candidates (without ranking). Some of the concepts surrounding this conjecture go back to the work of Thiele on elections…

We study the renormalization group method and its applications in probability theory.

Abstract: In 1900, in the second ICM, Hilbert proposed a list of 23 problems that shaped much of mathematics throughout the past century. The tenth problem asked for an algorithm capable of deciding the solvability over the integer of any polynomial equation, in any number…

A theorem of MacMahon states that the number of partitions of n for which no part appears exactly once equals the number of partitions of n into parts ≡ 1 (mod 6). The key fact behind this identity is that the numerator and denominator of a certain rational function are products of cyclotomic…

A key problem in geometric measure theory is to understand singularities in minimal surfaces when multiplicity occurs in the tangent cone. For questions concerning partial regularity, the primary situation to understand is that of a branch point, namely a (non-immersed) singular point where one…

A refinement of the tropical limit (Section 2.5.8–9 of [IMS09])

Abstract:  A classical technique to upper bound ranks of elliptic curve is descent. The case of 2-descent, when studied for quadratic twist families of elliptic curves has attracted the attention of several authors, Heath-Brown, Friedlander--Iwaniec--Mazur--Rubin, Kane, Smith, among some of…

Abstract: Exotic diffeomorphisms are those diffeomorphisms which are in the same path component as the identity of the homeomorphism group, but are not in the identity component in the diffeomorphism group. Several people have found the boundary Dehn twist is an exotic diffeomorphism…

I will present upcoming work proving a forward energy cascade for quasilinear wave equations on Schwarzschild-AdS black hole exteriors. The cascade is driven by a stably trapped 3-mode interaction that transfers energy from low-to high-frequency modes. Our result is motivated by the question of…