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DESCRIPTION:Joshua Zahl (Nankai University)\n\nBiography: 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 classic
 al harmonic analysis\, geometric measure theory\, discrete geometry and co
 mbinatorial geometry. After receiving his Ph.D. from the University of Cal
 ifornia\, Los Angeles\, in 2013\, Joshua Zahl held an NSF postdoctoral pos
 ition at the Massachusetts Institute of Technology. He received the PIMS/U
 BC Mathematical Sciences Early Career Award in 2023\, the ICBS Frontiers o
 f Science Award in Mathematics in 2024\, and will be an invited speaker at
  the 2026 International Congress of Mathematicians (ICM) in Philadelphia..
 \n\nLecture 1 - This talk is aimed at a general mathematical audience. \n
 \nMonday\, September 22\, 2025\, 3:30pm  \n	Room 6214 (CRM).\n	\n	A wine and 
 cheese reception will follow.\n\nTitle: The Besicovitch compression phenom
 enon and the Kakeya set conjecture\n\nAbstract: In 1919\, Besicovitch cons
 tructed a compact set in the plane with Lebesgue measure 0 that contains a
  unit line segment pointing in every direction. Such objects are now calle
 d measure 0 Besicovitch sets (aka Kakeya sets). By replacing a measure zer
 o Besicovitch set by its \delta-thickening\, one obtains a collection of 1
  x \delta rectangles pointing in different directions\, the sum of whose a
 reas is 1\, but whose union has very small volume. The existence of such c
 ollections of rectangles is called the Besicovitch compression phenomenon.
 \n	The Kakeya set conjecture is a quantitative statement controlling the st
 rength of the Besicovitch compression phenomenon. In this talk\, I will di
 scuss connections between the Besicovitch compression phenomenon\, the Kak
 eya set conjecture\, and questions in harmonic analysis and PDE.\n\nLectur
 e 2 \n\nTuesday\, September 23\, 2025\, 2:30pm (Note the different time.)
 \n	Room 6214 (CRM)\n	\n	A coffee get-together will follow.\n\nTitle: Sticky K
 akeya sets\n\nAbstract: Sticky Kakeya sets are a special class of Kakeya s
 ets that are approximately self-similar at every location and scale. The s
 ticky Kakeya conjecture asserts that every sticky Kakeya set in R^n has Ha
 usdorff dimension n. In 2022\, Hong Wang and I proved this conjecture in d
 imension 3\; this was an important ingredient in our subsequent proof of t
 he Kakeya set conjecture in dimension 3. In this talk I will discuss progr
 ess on the Kakeya conjecture over the past several decades\, leading to th
 e proof of the sticky Kakeya conjecture in dimension 3. This is joint work
  with Hong Wang.\n\n \n\nHong Wang (IHES and Courant Institute\, NYU)\n\nB
 iography: Beginning this fall\, Hong Wang will join the Institut des Haute
 s Études 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 g
 eometric measure theory. She received her Ph.D. from the Massachusetts Ins
 titute of Technology in 2019\, and held a postdoctoral position at the Ins
 titute for Advanced Study. Before joining the Courant Institute in 2023\, 
 she was at the University of California\, Los Angeles. In 2022 she receive
 d the Maryam Mirzakhani New Frontiers Prize “for advances on the restricti
 on conjecture\, the local smoothing conjecture\, and related problems”. Wa
 ng will be an invited speaker at the 2026 International Congress of Mathem
 aticians (ICM) in Philadelphia.\n\nLecture 1\n\nThursday\, September 25\, 
 2025\, 2:30pm \n	Room 6214 (CRM).\n	\n	A coffee get-together will follow.\n\n
 Title: Kakeya sets in R^3\n\nAbstract: A Kakeya set is a compact set of R^
 n that contains a unit line segment pointing in every direction. Kakeya se
 t conjecture asserts that every Kakeya set has Hausdorff dimension n. In t
 his 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.\n\nLecture 2 - This talk is aimed at a gener
 al mathematical audience\n\nFriday\, September 26\, 2025\, 2023\, 3:30pm (
 Note the different time.) \n	Room 6214 (CRM).\n	\n	A wine and cheese receptio
 n will follow.\n\nTitle: Restriction theory and projection theorems \n\nAb
 stract: Restriction theory studies functions whose Fourier transforms are 
 supported on some curved manifold in R^n (for example\, solutions to the l
 inear Schrodinger equation or to the wave equation). Projection theorems s
 tudy 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.\n
DTSTART:20250922T171500Z
DTEND:20250926T171500Z
SUMMARY:Nirenberg Lectures in Geometric Analysis
URL:/qls/channels/event/nirenberg-lectures-geometric-a
 nalysis-366869
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