报告题目: Burnside-Type Problems for Finitely Presented Structures
报 告 人：Alexei Kanel-Belov 教授（巴伊兰大学、莫斯科物理技术学院）
时 间：2026年10月10日 14:40
地 点：旭日教学大楼328会议室
摘 要:
This talk addresses Burnside-type problems for finitely presented structures. We consider the finitely presented Burnside conjecture and analogous conjectures for nil-rings and nil-semigroups. We review tools for controlling defining relations: Gröbner bases with the diamond lemma, small cancellation theory, and the automata approach, where words are viewed as states of finite automata and relations as local interactions. Using this approach, we construct finitely presented semigroups with non-integer Gelfand–Kirillov dimension and finitely presented associative algebras with finite Gröbner bases but undecidable zero divisor problems. We also present a geometric method, connecting finitely presented nil-semigroups to aperiodic tilings via uniformly elliptic complexes, local path convertibility, and determinism. This yields an infinite finitely presented nil-semigroup. Finally, we discuss a two-way bridge between algebra and computer science, inspired by Gács' work on reliable computation with cellular automata.
