This seminar is jointly organized by Bjoern Bringmann (at Caltech) and Sehyun Ji, Stepan Malkov, and Terence Tao (at UCLA). It is held roughly every other week, typically on Fridays from 3-5 pm (Pacific time). Its physical location alternates between Caltech (Linde 310) and UCLA (MS 6221).
Fall 2026
October 9th (at Caltech, note the unusual time):
2-3 pm: Sung-Jin Oh (UC Berkeley)
Title: An h-principle for general relativistic initial data sets.
Abstract: I will discuss a new flexibility result for the Einstein constraint equations, which may be interpreted as an analogue of the Nash-Kuiper theory for isometric embeddings. As an application, we generalize smooth obstruction-free gluing theorems of Czimek-Rodnianski (later sharpened by Mao-Oh-Tao). This is joint work with Jonathan Luk, Yuchen Mao, and Zhongkai Tao.
3-4 pm: Kevin Ren (Princeton)
Title: Bounding the Euclidean Distortion of Negative-Type Metric Spaces, revisited.
Abstract: We show that any N-point negative-type metric space admits a bi-Lipschitz embedding into Euclidean space with distortion O(sqrt(log N)), which is sharp up to constant factors. This was previously done in joint work with Assaf Naor and Alan Chang via a refinement of the chaining argument of Arora-Rao-Vazirani. In this talk, we present an alternative metric-based argument with surprising connections to Ball's extension theorem and Markov type. Joint work with Assaf Naor.
October 23rd (at UCLA):
3-4 pm: Will Feldman (University of Utah)
Title: Perron extremal solutions of the Bernoulli one-phase problem
Abstract: I will give some background about various notions of solution of the Bernoulli one-phase problem, their history, interest and connections. Then I will talk in more detail about the Perron extremal solutions. We show that the Perron solutions are also variational solutions and have some additional energetic structure. This allows the first analysis of the fine structure of the free boundary for Perron solutions in $d=2$. This is a joint work with Kerrek Stinson (Utah) and Farhan Abedin (Lafayette College).
4-5 pm: Lars Becker (Princeton University)
Title: On the triangular Hilbert transform
Abstract: The triangular Hilbert transform is a bilinear singular integral operator whose boundedness is known to imply several landmark results
in harmonic analysis, including Carleson's theorem on pointwise convergence of Fourier series and uniform bounds for the bilinear
Hilbert transform. OpenAI recently announced a proof of its boundedness. This talk discusses their proof, along with background and various extensions that are missing from their announcement.
November 13th (at Caltech):
3-4 pm: Paata Ivanisvili (UC Irvine)
Title: Several problems in analysis in the AI era
Abstract: I will discuss several recent results in analysis, including results on Landis’ conjecture, the Hayman–Wu constant, Carbery’s problem, and sharp Markov–Bernstein inequalities. These results involve AI at different stages of its development.
4-5 pm: Ben Pineau (NYU)
Title: Global well-posedness for non-localized 3D gravity water waves.
Abstract: I will describe a work in progress on the problem of well-posedness for small data in $H^s$ based (i.e. non-localized) Sobolev spaces for gravity water waves in a fluid of infinite depth in spatial dimension $d\geq 3$ and higher. Our main result establishes global well-posedness in low regularity, non-localized $H^s$ based Sobolev spaces assuming only smallness of the data in a critical Sobolev (more precisely, Besov) norm. All previous global well-posedness results required the data to be localized and much more regular. This is joint work with Mihaela Ifrim and Daniel Tataru.
November 20th (at UCLA):
3-4 pm: Wilhelm Schlag (Yale)
Title: TBD
4-5 pm: Jason Zhao (UC Berkeley)
Title: The Cauchy problem for Manton’s Chern-Simons-Schrödinger equation
Abstract: Manton (1997) introduced the Chern-Simons-Schrödinger equation as a model for the dynamics of abelian Higgs vortices. After briefly motivating the equation by discussing some of Manton’s predictions, the main goal of this talk will be to formulate the Cauchy problem within the natural energy space and prove global well-posedness. The heart of the analysis lies in developing a geometric Littlewood-Paley theory based on the covariant heat equation in caloric gauge, which we use to perform a paradifferential-style decomposition of the Chern-Simons-Schrödinger equation.