[Aalto AGC Seminar] Anthony Mäkelä (University of Gothenburg) | Moduli of P-critical connections via moment maps and analytic GIT | Mon 15.6. at 14:15

[Aalto Algebra, Geometry and Combinatorics Seminar]

We would like to invite you to a talk in the Aalto AGC (Algebra, Geometry and Combinatorics) Seminar.

The talk is on
Mon 15.6. at 14:15-15:00
in
M3 (M234), Otakaari 1.

The speaker is
Anthony Mäkelä (University of Gothenburg)
giving the talk
Moduli of $P$-critical connections via moment maps and analytic GIT


Abstract: The Kobayashi--Hitchin correspondence relates stable holomorphic vector bundles to special connections, and can be viewed as a prototype for a broader principle: extremal objects in differential geometry should correspond to stable objects in algebraic geometry. Motivated by Bridgeland stability conditions, recent work has introduced polynomial curvature equations for Hermitian vector bundles, including (Z)-critical and (P)-critical connections, which generalize the Hermite--Einstein equation and admit moment-map interpretations. In this talk, I will describe a construction of moduli spaces for (P)-critical connections using local deformation theory and analytic geometric invariant theory. The construction produces finite-dimensional analytic GIT quotient charts around a (P)-critical connection and glues them into a Hausdorff complex space carrying a natural Weil--Petersson-type geometry.

The webpage of the seminar is at
math.aalto.fi/en/research/discrete/seminars/agc/<https://math.aalto.fi/en/research/discrete/seminars/agc/>
and we have a mailing list at
https://list.aalto.fi/mailman/listinfo/agc-math-aalto


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