Встъпителната лекция на доцент Михаил Школников в секция Анализ, геометрия и топология на ИМИ-БАН ще се проведе на 13.05.2025 г. (вторник) от 15:15 ч. в зала 403 на ИМИ – БАН.

Докладчик: Михаил Школников (ИМИ – БАН)

Доклад: Introduction to amoebas and tropicalization

Резюме: 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.