# Semistability, modular lattices, and iterated logarithms

Fabian Haiden (QM (SDU))
Wednesday 5 October 2022 15:00–16:00 G3.1 (1532-314)
Mathematics Seminar

I will report on joint work with Katzarkov, Kontsevich, and Pandit (arXiv:1706.01073, arXiv:1802.04123) in which we study gradient flows on spaces of representations of associative algebras. Two intriguing phenomena which we discover: 1) growth rates involve iterated logarithms log(log(… log(t)..)), and 2) the asymptotics are controlled by a filtration which is defined purely algebraically and makes sense in any modular lattice. We anticipate that the techniques can also be applied in certain infinite-dimensional cases (geometric PDEs). As a proof of concept, we determine the asymptotics of the gradient flow on the space of Hermitian metrics on a holomorphic vector bundle over a Riemann surface.

Contact: Gergely Bérczi Revised: 04.10.2022