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Geometry & Topology Seminar

Title: Positivity properties of the vector bundle Monge-Ampere equation
Speaker: Aashirwad Ballal (IISc)
Date: 21 October 2024
Time: 04:00 pm
Venue: LH-1, Mathematics Department

Monge-Ampere-positivity (MA-positivity) is a notion of positivity which arises naturally in the study of a generalization the complex Monge-Ampere equation to vector bundles. In particular, preservation of MA-positivity along a continuity path turns out to be crucial in proving the existence of solutions to the vector bundle Monge-Ampere (vbMA) equation. In this talk, we briefly introduce the vbMA equation and discuss some recent results such as the preservation of MA-positivity for rank-two holomorphic bundles over complex surfaces and the existence of counterexamples to an algebraic version of MA-positivity preservation for vector bundles of rank-three and higher over complex manifolds of dimension greater than one.


Contact: +91 (80) 2293 2711, +91 (80) 2293 2265 ;     E-mail: chair.math[at]iisc[dot]ac[dot]in
Last updated: 23 Oct 2024