Nirenberg Lectures in Geometric Analysis
Joshua Zahl (Nankai University)
Biography:听Joshua Zahl is a professor at the Chern Institute of Mathematics, Nankai University, and was previously a faculty member at the University of British Columbia from 2016 to 2025. He is an internationally renowned leading expert in classical harmonic analysis, geometric measure theory, discrete geometry and combinatorial geometry. After receiving his Ph.D. from the University of California, Los Angeles, in 2013, Joshua Zahl held an NSF postdoctoral position at the Massachusetts Institute of Technology. He received the PIMS/UBC Mathematical Sciences Early Career Award in 2023, the ICBS Frontiers of Science Award in Mathematics in 2024, and will be an invited speaker at the 2026 International Congress of Mathematicians (ICM) in Philadelphia..
Lecture 1 - This talk is aimed at a general mathematical audience.听
Monday, September 22, 2025, 3:30pm 听
Room 6214 (CRM).
A wine and cheese reception will follow.
Title: The Besicovitch compression phenomenon and the Kakeya set conjecture
Abstract: In 1919, Besicovitch constructed a compact set in the plane with Lebesgue measure 0 that contains a unit line segment pointing in every direction. Such objects are now called measure 0 Besicovitch sets (aka Kakeya sets). By replacing a measure zero Besicovitch set by its \delta-thickening, one obtains a collection of 1 x \delta rectangles pointing in different directions, the sum of whose areas is 1, but whose union has very small volume. The existence of such collections of rectangles is called the Besicovitch compression phenomenon.
The Kakeya set conjecture is a quantitative statement controlling the strength of the Besicovitch compression phenomenon. In this talk, I will discuss connections between the Besicovitch compression phenomenon, the Kakeya set conjecture, and questions in harmonic analysis and PDE.
Lecture 2听
Tuesday, September 23, 2025, 2:30pm (Note the different time.)
Room 6214 (CRM)
A coffee get-together will follow.
Title: Sticky Kakeya sets
Abstract: Sticky Kakeya sets are a special class of Kakeya sets that are approximately self-similar at every location and scale. The sticky Kakeya conjecture asserts that every sticky Kakeya set in R^n has Hausdorff dimension n. In 2022, Hong Wang and I proved this conjecture in dimension 3; this was an important ingredient in our subsequent proof of the Kakeya set conjecture in dimension 3. In this talk I will discuss progress on the Kakeya conjecture over the past several decades, leading to the proof of the sticky Kakeya conjecture in dimension 3. This is joint work with Hong Wang.
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Hong Wang (IHES and Courant Institute, NYU)
Biography:听Beginning this fall, Hong Wang will join the Institut des Hautes 脡tudes Scientifiques (IHES), on a joint professorship with the Courant Institute of Mathematical Sciences at New York University. Hong Wang is an outstanding mathematician working in the fields of Fourier analysis and geometric measure theory. She received her Ph.D. from the Massachusetts Institute of Technology in 2019, and held a postdoctoral position at the Institute for Advanced Study. Before joining the Courant Institute in 2023, she was at the University of California, Los Angeles. In 2022 she received the Maryam Mirzakhani New Frontiers Prize 鈥渇or advances on the restriction conjecture, the local smoothing conjecture, and related problems鈥�. Wang will be an invited speaker at the 2026 International Congress of Mathematicians (ICM) in Philadelphia.
Lecture 1
Thursday, September 25, 2025, 2:30pm听
Room 6214 (CRM).
A coffee get-together will follow.
Title: Kakeya sets in R^3
Abstract: A Kakeya set is a compact set of R^n that contains a unit line segment pointing in every direction. Kakeya set conjecture asserts that every Kakeya set has Hausdorff dimension n. In this talk, we present the ideas in proving the Kakeya set conjecture in R^3 assuming our previous result on sticky Kakeya sets as a black box. This is joint work with Josh Zahl.
Lecture 2 - This talk is aimed at a general mathematical audience
Friday, September 26, 2025, 2023, 3:30pm (Note the different time.)听
Room 6214 (CRM).
A wine and cheese reception will follow.
Title:听Restriction听theory and听projection听theorems听
Abstract: Restriction theory studies functions whose Fourier transforms are supported on some curved manifold in R^n (for example, solutions to the linear Schrodinger equation or to the wave equation). Projection theorems study the Hausdorff dimension of fractal sets under orthogonal projections from R^n to its subspaces. We will survey some recent works in both fields and discuss their interactions.