Convergence of Riemannian Manifolds Workshop
Institute of Mathematics, UNAM, Mexico City, April 3-6, 2018
organized by Raquel del Carmen Perales Aguilar and Christina Sormani
Tuesday 3 April - Thursday 5 April: Research Workshop
Raquel Perales (CONACYT Fellow at IMATE UNAM, MEXICO) will lead a team of postdocs and graduate students on a project related to intrinsic flat convergence and scalar curvature. This project was initiated by Christina Sormani (Professor at CUNY, USA) at the Fields Institute in Toronto Canada and is funded by Sormani's NSF research grants on Intrinsic Flat Convergence. The participants in this research workshop are all postdocs directly involved in this project: Armando Cabrera (Postdoc at University Tubingen, GDR), Christian Ketterer (Postdoc at University of Toronto, CA) and Robin Neumayer (Postdoc at Northwestern University, USA). Lan-Hsuan Huang (Professor at University of Connecticut, USA) and Christina Sormani (Professor at CUNY, USA) will provide advice and mentoring to the team.
Presentations by Participants:
Robin Neumayer (Postdoc at Northwestern University)
Tuesday 3 of April: 11:00am-12:00noon. Differential Equations Seminar, Institute of Mathematics. UNAM, Mexico City
Titulo: TBA
Abstract: TBA
Christian Ketterer (Postdoc at University of Toronto, CANADA)
Friday 6 of April: 10:30-11:30am. Auditorium of the Institute of Mathematics. UNAM, Mexico City
Titulo: Lott, Sturm and Villani meet Alexandrov
Abstract: We consider a noncollapsed metric measure space which satisfies both a synthetic Ricci lower curvature bound in the sense of Lott-Sturm-Villani, and a synthetic sectional upper curvature bound in the sense of Alexandrov. Our main theorem says that in this case one obtains a metric space of lower bounded sectional curvature in the sense of Alexandrov, and consequently - by a theorem of Berestovsky-Nikolaev - a C^{1,\alpha}-Riemannian manifold. This is a joint work with V. Kapovitch.
Armando Cabrera (Postdoc at University Tubingen, ALEMANIA)
Friday 6 of April: 12-1pm. Auditorium of the Institute of Mathematics. UNAM, Mexico City
Título: On the stability of the positive mass theorem for asymptotically hyperbolic graphs
Abstract: The Positive Mass theorem asserts that the ADM mass of an asymptotically flat Riemannian manifold with non-negative scalar curvature is non-negative; moreover, the ADM mass equals zero if and only if the manifold is isometric to the Euclidean space. It is then natural to ask about the stability of the Positive Mass theorem, i.e, if the ADM of a given manifold mass is close to zero, is the manifold close to being the Euclidean space in some sense? Huang and Lee proved the stability (in the sense of currents) of the Positive Mass theorem for asymptotically flat graphs. We will describe how to use results of Dahl, Gicquaud and Sakovich to adapt Huang and Lee's ideas to establish the stability of the Positive Mass theorem for asymptotically hyperbolic graphs.
Friday Participants: Alejandro Betancourt de la Parra (Postdoc at CIMAT), Juan Carlos Fernández (Postdoc at CIMAT), Isidro Munive (Postdoc at CIMAT), Juan Miguel Ruíz (UNAM, ENES León), Areli Vázquez (UNAM, ENES León). Friday Poster.
Contacts: Dr. Raquel Perales CONACYT Fellow at IMATE UNAM, MEXICO) and Prof. Christina Sormani (Professor at CUNY, NYC, USA)
Travel funded in part by Prof Sormani’s NSF grant DMS 1309360. Facilities provided by UNAM.