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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). Location: Cent
 re de recherches mathématiques (CRM)\, Pavillon André-Aisenstadt\, Univers
 ité de Montréal\n	\n	A wine and cheese reception will follow.\n\nTitle: The 
 Besicovitch compression phenomenon and the Kakeya set conjecture\n\nAbstra
 ct: In 1919\, Besicovitch constructed a compact set in the plane with Lebe
 sgue measure 0 that contains a unit line segment pointing in every directi
 on. Such objects are now called measure 0 Besicovitch sets (aka Kakeya set
 s). By replacing a measure zero Besicovitch set by its \delta-thickening\,
  one obtains a collection of 1 x \delta rectangles pointing in different d
 irections\, the sum of whose areas is 1\, but whose union has very small v
 olume. The existence of such collections of rectangles is called the Besic
 ovitch compression phenomenon.\n	The Kakeya set conjecture is a quantitativ
 e statement controlling the strength of the Besicovitch compression phenom
 enon. In this talk\, I will discuss connections between the Besicovitch co
 mpression phenomenon\, the Kakeya set conjecture\, and questions in harmon
 ic analysis and PDE.\n\nLecture 2 \n\nTuesday\, September 23\, 2025\, 2:30
 pm (Note the different time.)\n	Room 6214 (CRM). Location: Centre de recher
 ches mathématiques (CRM)\, Pavillon André-Aisenstadt\, Université de Montr
 éal\n	\n	A coffee get-together will follow.\n\nTitle: Sticky Kakeya sets\n\n
 Abstract: Sticky Kakeya sets are a special class of Kakeya sets that are a
 pproximately self-similar at every location and scale. The sticky Kakeya c
 onjecture asserts that every sticky Kakeya set in R^n has Hausdorff dimens
 ion n. In 2022\, Hong Wang and I proved this conjecture in dimension 3\; t
 his 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 Kak
 eya conjecture over the past several decades\, leading to the proof of the
  sticky Kakeya conjecture in dimension 3. This is joint work with Hong Wan
 g.\n\n \n\nHong Wang (IHES and Courant Institute\, NYU)\n\nBiography: Begi
 nning this fall\, Hong Wang will join the Institut des Hautes Études Scien
 tifiques (IHES)\, on a joint professorship with the Courant Institute of M
 athematical Sciences at New York University. Hong Wang is an outstanding m
 athematician working in the fields of Fourier analysis and geometric measu
 re theory. She received her Ph.D. from the Massachusetts Institute of Tech
 nology in 2019\, and held a postdoctoral position at the Institute for Adv
 anced Study. Before joining the Courant Institute in 2023\, she was at the
  University of California\, Los Angeles. In 2022 she received the Maryam M
 irzakhani New Frontiers Prize “for advances on the restriction conjecture\
 , the local smoothing conjecture\, and related problems”. Wang will be an 
 invited speaker at the 2026 International Congress of Mathematicians (ICM)
  in Philadelphia.\n\nLecture 1\n\nThursday\, September 25\, 2025\, 2:30pm 
 \n	Room 6214 (CRM). Location: Centre de recherches mathématiques (CRM)\, Pa
 villon André-Aisenstadt\, Université de Montréal\n	\n	A coffee get-together 
 will follow.\n\nTitle: Kakeya sets in R^3\n\nAbstract: A Kakeya set is a c
 ompact set of R^n that contains a unit line segment pointing in every dire
 ction. Kakeya set conjecture asserts that every Kakeya set has Hausdorff d
 imension 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.\n\nLecture 2 - This talk is 
 aimed at a general mathematical audience\n\nFriday\, September 26\, 2025\,
  2023\, 3:30pm (Note the different time.) \n	Room 6214 (CRM). Location: Cen
 tre de recherches mathématiques (CRM)\, Pavillon André-Aisenstadt\, Univer
 sité de Montréal\n	\n	A wine and cheese reception will follow.\n\nTitle: Res
 triction theory and projection theorems \n\nAbstract: Restriction theory s
 tudies functions whose Fourier transforms are supported on some curved man
 ifold in R^n (for example\, solutions to the linear Schrodinger equation o
 r to the wave equation). Projection theorems study the Hausdorff dimension
  of fractal sets under orthogonal projections from R^n to its subspaces. W
 e will survey some recent works in both fields and discuss their interacti
 ons.\n
DTSTART:20250922T171500Z
DTEND:20250926T171500Z
SUMMARY:Nirenberg Lectures in Geometric Analysis
URL:/science/channels/event/nirenberg-lectures-geometr
 ic-analysis-366869
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