Past Events
Please note, this is a live-stream of an in-person talk to be given at Harvard University.
In this talk I will discuss recent progress on finite-time singularity formation for several fluid equations, from model problems to the Navier–Stokes and Euler systems themselves. I…
In applications, it is often impossible to measure the phase of a signal, and one must recover it from some additional physical "redundancy" present in the problem. Phase retrieval problems arise in diverse fields, ranging from crystallography to quantum mechanics. Mathematically, the analysis…
Recent developments in scalar curvature geometry have revealed that positive scalar curvature (PSC) imposes quantitative restrictions on various geometric invariants. In this talk, I will present two results in this direction: an estimate for the stable two-dimensional systole of compact PSC…
The Ginzburg–Landau energy is often used to approximate the Dirichlet energy. As the perturbation parameter tends to zero, critical points of the Ginzburg–Landau energy converge, in an appropriate (bubbling) sense, to harmonic maps. In this talk I will first explain key analytical properties of…
My first productive experience using large language models occurred in October 2024. At the time, we were thinking about the hot spots conjecture, and a very lucky prompt gave us a key insight that helped us establish an interesting result on the extremal failure of this conjecture. I will…
An old result of Nathanson shows that every n-element set of positive reals has at least n(n+1)/2+1 distinct subset sums, with equality exactly for homogeneous arithmetic progressions. We establish stability versions of this inverse theorem in two regimes. First, for any parameter M at most n-4…
Permutons, which are probability measures on [0, 1]^2 with uniform marginals, are the natural scaling limits for sequences of (random) permutations. In particular, various classes of permutations arising from combinatorics and pattern avoidance have been shown to converge to universal permuton…
Abstract: We study Lagrangian isotopy of tori in S^2 \times S^2 and CP^2 from Dimitroglou Rizell, Goodman, and Ivrii's paper.