The inaugural lecture by Assoc. Prof. Mikhail Shkolnikov at the Analysis, Geometry and Topology Department will be held on May 13, 2025, at 3:15 pm in Room 403 of IMI – BAS.

Speaker: Mikhail Shkolnikov (IMI – BAS)

Title: Introduction to amoebas and tropicalization

Abstract: We will start by reviewing the most classical aspects of the theory of amoebas deeply rooted in complex analysis and geometry. Next, we will pass to the notion of a tropical limit of amoebas, and will see how restoring the phase allows to recover topology and deduce intersection-theoretic results. After that, we will discuss some results (and their limitations) obtained with Grigory Mikhalkin in the context of non-commutative versions of amoebas of surfaces and tropical limits of curves inside the special matrix group SL(2,C). I will conclude by sketching a proof of the complete description of possible tropicalizations of families of analytic surfaces in SL(2,C) recently obtained with Peter Petrov, in particular, motivating our ongoing project on the non-commutative phase tropicalization, a few words about which will be said if time permits.