SGGTC this Friday: Jun Li and Dan Cristofaro-Gardiner
Oleg Lazarev
Dear all,
This Friday we have two speakers. Jun Li from the University of Michigan will give a talk at 10:30 am in Math 520. Dan Cristofaro-Gardiner from UC Santa Cruz will give a talk at 1:00 pm in Math 407. We will meet at 11:35 in the lobby and go out for lunch.
Best, Oleg
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Jun Li: Smooth and symplectic isotopy on rational 4-manifolds
Abstract: We study rational 4-manifolds and their symplectomorphism groups. Analogous to the 2-dimensional case, one can think about the symplectic Torelli group and symplectic mapping class group, where the former is the subgroup of the symplectomorphism group fixing homology and the latter is the symplectomorphism group mod symplectic isotopy. We’ll show how the symplectic mapping class groups of rational 4-manifolds are related to braid groups. Also, McDuff-Salamon asked whether any Torelli symplectomorphism on a rational 4-manifold is smoothly isotopic to identity. And we answer it in the positive. This is based on joint works with T-J Li and Weiwei Wu.
Dan Cristofaro-Gardiner: Two or infinity
Abstract: We study rational 4-manifolds and their symplectomorphism groups. Analogous to the 2-dimensional case, one can think about the symplectic Torelli group and symplectic mapping class group, where the former is the subgroup of the symplectomorphism group fixing homology and the latter is the symplectomorphism group mod symplectic isotopy. We’ll show how the symplectic mapping class groups of rational 4-manifolds are related to braid groups. Also, McDuff-Salamon asked whether any Torelli symplectomorphism on a rational 4-manifold is smoothly isotopic to identity. And we answer it in the positive. This is based on joint works with T-J Li and Weiwei Wu.
Dan Cristofaro-Gardiner: Two or infinity
Abstract: The Weinstein conjecture states that any Reeb vector field on a closed manifold has at least one closed orbit. The three-dimensional case of this conjecture was proved by C. Taubes in 2007. I will discuss joint work showing that for a wide class of Reeb vector fields on closed three-manifolds, there are either two, or infinitely many, distinct closed orbits. I will also say a few words about how one might extend this result to all Reeb vector fields on closed three-manifolds.
Abstract: The Weinstein conjecture states that any Reeb vector field on a closed manifold has at least one closed orbit. The three-dimensional case of this conjecture was proved by C. Taubes in 2007. I will discuss joint work showing that for a wide class of Reeb vector fields on closed three-manifolds, there are either two, or infinitely many, distinct closed orbits. I will also say a few words about how one might extend this result to all Reeb vector fields on closed three-manifolds.