The next meeting of the Joint Seminar of Analysis, Geometry and Topology Department will be held on October 22, 2024 at 2:00 pm (UTC+2)  in Room 478 of IMI.

A talk on:

Higher order estimates for Monge-Ampere type equations motivated by quaternionic geometry

 will be delivered by Marcin Sroka, Jagiellonian University, Kraków, Poland.

Everybody is invited.

Abstract. In the talk I will discuss obstacles for obtaining higher order a priori estimates for equation introduced by Alesker and Verbitsky in 2010 on HKT manifolds in relation to Calabi type conjecture on those manifolds (and similar type PDEs studied since on hypercomplex manifolds). After presenting the state of art, I will focus on the key second order estimate. For the real Monge-Ampere equation on Riemannian manifolds it follows essentially by Pogorelov calculation, for the complex Monge-Ampere equation, in relation to Calabi conjecture, it was proven by Aubin and Yau. I will use those two as comparison to underline new difficulties related to concavity properties of quaternionic Monge-Ampere operator.

The lecturer’s visit is supported by the Scientific Programme “Enhancing the Research Capacity in Mathematical Sciences (PIKOM)”, No. DO1-67/05.05.2022.