Large N Program Series: Tamas Darvas, Purdue University

Title: The metric completion of the space of Kahler potentials and applications, part 1
Program Website: Large N limit problems in Kahler Geometry
Speaker: Tamas Darvas, Purdue University
Date: Thursday, June 04, 2015
Time: 10:00am – 11:00am
Place: Seminar Room 313, Simons Center


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Abstract: In connection with canonical Kahler metrics, the study of the L^2 Riemannian geometry of the space of Kahler potentials goes back to Mabuchi and Donaldson. In the first part of this series of talks we introduce the associated path length metric space and characterize the metric completion. Barring some difficulties, the techniques we use allow greater generality and we will end up characterizing the metric completion of the analogous L^p Finsler geometries instead. In the second part I will show how one can use the L^1 Finsler geometry to resolve a long standing question in Kahler geometry relating properness of Energy functionals to existence of KE metrics on general Fano manifolds.