报告人 ：Dmitri Piontkovski（HSE University, Moscow）

时间：2023年02月28日 19:00-

Zoom会议ID： https://us06web.zoom.us/j/82172248394?pwd=YlBpaGplbnpBZFNwOVJxekcwVXVDQT09

摘要：In 1964 E. S. Golod and I. R. Shafarevich introduced an approach that allowed them to solve several outstanding problems: the construction of infinite-dimensional finitely generated algebraic algebra, the construction of infinite finitely generated p-group or the construction of a number field having infinite Hilbert tower. 

The construction of Golod and Shafarevich combines asymptotic and homological methods in ring theory. In the course we present both the original construction and consider related algebraic topics that use such methods. We start introducing the concept of growth for formal languages as well as of filtered and graded rings and discuss the rationality problem for the Hilbert series and formal languages. Using Grobner—Shirshov bases theory, we extend a homological method of enumerating words in a hereditary language to Hilbert series of graded algebras. Even the first steps toward understanding homology over graded rings will give us the Golod-Shafarevich theorem. Then we discuss relations between growth and other properties of algebras, including some open problems. Finally, we plan to give a brief introduction to ideas of noncommutative projective algebraic geometry and discuss a very recent connection of growth rate in some algebras and entropy in derived categories of corresponding noncommutative varieties.

简介：Dmitri Piontkovski is a Senior Researcher and Professor at HSE University, Moscow (Russia). He obtained his Ph.D. at Lomonosov University in 1998 under the supervision of Prof. Evgeni Golod. He was a research visitor at University Autonoma de Madrid, University of Bari, (Italy), Rutgers (USA), Bar Ilan (Israel), and others. He is an author of more than 40 articles on graded rings, homological algebra, operads, and applications to economics and physics.

邀请人：鲁澧

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