Bruce Kleiner (Courant Institute, NYU)
Bruce Kleiner (Courant Institute, NYU)
Bruce Kleiner will give a series of three lectures, one of which is aimed at a broad mathematical audience.
叠颈辞驳谤补辫丑测:听Professor Bruce Kleiner is a world-renowned expert in geometric analysis. He is a professor at the Courant Institute of Mathematical Sciences at New York University. He received his Ph.D. from the University of California, Berkeley, in 1990. Among his many significant contributions to the field, Professor Kleiner proved the Cartan-Hadamard conjecture in dimension 3 in 1992 and, in 2007, found a relatively simple proof of Gromov's theorem on groups with polynomial growth. In 2013, he received the National Academy of Sciences Award for Scientific Review, along with Professor John Lott, for their joint explanation of Perelman's famous solution to the Poincar茅 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 proved the multiplicity one conjecture for mean curvature flows of surfaces in R^3.
First and second lectures
Monday, October 28, 2024, and Wednesday, October 30, 2024, at 3:30 p.m.
Centre de recherches math茅matiques
Room 5340
- Title of the first lecture:听Diffeomorphism groups, moduli spaces, and Ricci flow I
- Title of the second lecture:听Diffeomorphism groups, moduli spaces, and Ricci flow II
Abstract:听The Smale Conjecture (1961) may be stated in any of the following equivalent forms:
听
- The space of embedded 2-spheres in听R^3听is contractible.
- The inclusion of the orthogonal group听O(4) into the group of diffeomorphisms of the 3-sphere is a homotopy equivalence.
- The space of all Riemannian metrics on听S^3听with constant sectional curvature is contractible.
This fascinating conjecture inspired many subsequent advances in topology and geometry over the ensuing decades, both in the case of 3-manifolds, and in higher dimensions. 听Recently, Ricci flow was used to settle several long-standing conjectures which had resisted all other approaches. 听After covering the necessary background, the aim of the first two lectures will be to give an account of these developments for non-experts.