Upcoming Events
In this interactive talk you will be introduced to pencil puzzles, which are types of logic puzzles that can be described and solved on paper. (The most famous examples being sudoku and slitherlink.) We will explore multiple different genres of puzzles, introduce some key logical ideas…
Abstract: A Besicovitch set is a compact subset of R^n that contains a unit line segment pointing in every direction. The Kakeya set conjecture asserts that every Besicovitch set in R^n has Minkowski and Hausdorff dimension n. I will discuss some recent progress on this conjecture, leading to…
We study the renormalization group method and its applications in probability theory.
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…
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…
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…
A refinement of the tropical limit (Section 2.5.8–9 of [IMS09])
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 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…