The Geometry/Topology seminar is organized this academic year (2016-2017) by Gonçalo Oliveira and Michael Abel

- Monday, September 25, 2017, 3:15pm, 119 Physics, Geometry/topology Seminar
*Binet-Legendre metric and applications of Riemannian results in Finsler geometry*

Vladimir Matveev (Jena University)- We introduce a construction that associates a Riemannian metric $g_F$ (called the \emph{Binet-Legendre} metric) to a given Finsler metric $F$ on a smooth manifold $M$. The transformation $F \mapsto g_F$ is $C^0$-stable and has good smoothness properties, in contrast to previously considered constructions. The Riemannian metric $g_F$ also behaves nicely under conformal or isometric transformations of the Finsler metric $F$ that makes it a powerful tool in Finsler geometry. We illustrate that by solving a number of named problems in Finsler geometry. In particular, we extend a classical result of Wang to all dimensions. We answer a question of Matsumoto about local conformal mapping between two Berwaldian spaces and use it to investigate essentially conformally Berwaldian manifolds. We describe all possible conformal self maps and all self similarities on a Finsler manifold, generalizing the famous result of Obata to Finslerian manifolds. We also classify all compact conformally flat Finsler manifolds. We solve a conjecture of Deng and Hou on locally symmetric Finsler spaces. We prove smoothness of isometries of Holder-continuous Finsler metrics. We construct new `easy to calculate' conformal and metric invariants of Finsler manifolds. The results are based on the papers arXiv:1104.1647, arXiv:1409.5611, arXiv:1408.6401, arXiv:1506.08935, arXiv:1406.2924 partially joint with M. Troyanov (EPF Lausanne) and Yu. Nikolayevsky (Melbourne)

- Monday, October 16, 2017, 3:15pm, 119 Physics, Geometry/topology Seminar
*TBA*

Ziva Myer (Duke University)- TBA

- Monday, October 23, 2017, 3:15pm, 119 Physics, Triangle Topology Seminar
*Complex curves through a contact lens*

Kyle Hayden (Boston College)- Every four-dimensional Stein domain has a height function whose regular level sets are contact three-manifolds. This allows us to study complex curves in the Stein domain via their intersection with these contact level sets, where we can comfortably apply three-dimensional tools. We use this perspective to characterize the links in Stein-fillable contact manifolds that bound complex curves in their Stein fillings. (Some of this is joint work with Baykur, Etnyre, Hedden, Kawamuro, and Van Horn-Morris.)

- Monday, October 30, 2017, 3:15pm, 119 Physics, Geometry/topology Seminar
*TBA*

Daniel Scofield (North Carolina State University)- TBA

- Monday, November 6, 2017, 3:15pm, 119 Physics, Geometry/topology Seminar
*TBA*

Tori Akin (Duke University) - Monday, November 13, 2017, 3:15pm, 119 Physics, Geometry/topology Seminar
*TBA*

Chen-Yun Lin (Duke University)

Generated at 2:04pm Saturday, September 23, 2017 by Mcal. Top * Reload * Login