Geometric Analysis and Topology Seminar

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On the conjecture of Alesker-Verbitsky and some new geometric PDEs

Speaker: Marcin Sroka, UQAM

Location: Warren Weaver Hall 512

Date: Friday, November 17, 2023, 11 a.m.

Synopsis:

More than a decade ago Alesker and Verbitsky introduced the analogue of Calabi’s (volume prescribing) conjecture for hypercomplex manifolds. This problem also reduces to the solvability of a certain second order PDE called the quaternionic Monge-Ampere equation. Despite the conjecture remaining open, recent years have witnessed some partial results. I will outline these advances as well as discuss more general PDEs motivated by quaternionic geometry and the relations between the latter and existing real and complex PDEs.