Yulia Zaitseva. The fourteenth Hilbert problem

Семинар лаборатории алгебраических групп преобразований, https://cs.hse.ru/latg/seminar Дата: 29.04.2026 Докладчик: Yulia Zaitseva Тема: The fourteenth Hilbert problem Аннотация: The 14th Hilbert problem is formulated as follows: is the algebra of polynomials in n variables, invariant under a subgroup G of GL(n), finitely generated? In 1958, Masayoshi Nagata presented his famous counterexample to this problem. However, at this moment, there is no complete description of the groups G for which the answer is affirmative; there are only a few constructions for counterexamples. We will survey various positive and negative results in this area.