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DESCRIPTION:Bruce Kleiner (Courant Institute\, NYU)\n\n\n\nBruce Kleiner wi
 ll give a series of three lectures\, one of which is aimed at a broad math
 ematical audience.\n\nBiography: Professor Bruce Kleiner is a world-renown
 ed expert in geometric analysis. He is a professor at the Courant Institut
 e of Mathematical Sciences at New York University. He received his Ph.D. f
 rom the University of California\, Berkeley\, in 1990. Among his many sign
 ificant contributions to the field\, Professor Kleiner proved the Cartan-H
 adamard conjecture in dimension 3 in 1992 and\, in 2007\, found a relative
 ly simple proof of Gromov's theorem on groups with polynomial growth. In 2
 013\, he received the National Academy of Sciences Award for Scientific Re
 view\, along with Professor John Lott\, for their joint explanation of Per
 elman's famous solution to the Poincaré conjecture. He was a Simons Fellow
  in 2014 and is again in 2024\, and he was an ICM speaker in 2006 and 2022
 . Recently\, in collaboration with Richard Bamler\, Professor Kleiner prov
 ed the multiplicity one conjecture for mean curvature flows of surfaces in
  R^3.\n\nFirst and second lectures\n\nMonday\, October 28\, 2024\, and Wed
 nesday\, October 30\, 2024\, at 3:30 p.m.\n\nCentre de recherches mathémat
 iques\n	Room 5340\n\n\n	Title of the first lecture: Diffeomorphism groups\, 
 moduli spaces\, and Ricci flow I\n	Title of the second lecture: Diffeomorph
 ism groups\, moduli spaces\, and Ricci flow II\n\n\nAbstract: The Smale Co
 njecture (1961) may be stated in any of the following equivalent forms:\n	 
 \n\n- The space of embedded 2-spheres in R^3 is contractible.\n\n- The inc
 lusion of the orthogonal group O(4) into the group of diffeomorphisms of t
 he 3-sphere is a homotopy equivalence.\n\n- The space of all Riemannian me
 trics on S^3 with constant sectional curvature is contractible.\n\nThis fa
 scinating conjecture inspired many subsequent advances in topology and geo
 metry over the ensuing decades\, both in the case of 3-manifolds\, and in 
 higher dimensions.  Recently\, Ricci flow was used to settle several long-
 standing conjectures which had resisted all other approaches.  After cover
 ing the necessary background\, the aim of the first two lectures will be t
 o give an account of these developments for non-experts.\n
DTSTART:20241028T193000Z
DTEND:20241028T203000Z
SUMMARY:Bruce Kleiner (Courant Institute\, NYU)
URL:/mathstat/channels/event/bruce-kleiner-courant-ins
 titute-nyu-360707
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