How Groups Grow and Double, Rostislav Grigorchuk скачать в хорошем качестве

How Groups Grow and Double, Rostislav Grigorchuk

Rostislav Grigorchuk, 25/07/2025, Yulia’s Dream Conference. How Groups Grow and Double. “In my talk I will focus on the growth of combinatorial and algebraic objects like formal languages, graphs, and groups. I will tell a history of the solution of Milnor's problem on groups of intermediate growth (between polynomial and exponential), give concrete examples (via quite elementary construction) of such groups, and list some unusual properties of them (like self-similarity, fractalness, branchness, etc.). One application of this will be to the von Neumann–Day-type question about amenability vs. non-amenability. The latter is related to the famous Banach–Tarski paradox, the history of which and its influence on mathematics would be part of the story. The Burnside Problem will be mentioned as well. A number of exercises will be suggested, as well as a couple of research problems.” — Rostislav Grigorchuk. This lecture was delivered as part of the Yulia’s Dream Annual Conference 2025: https://math.mit.edu/research/highsch... Yulia’s Dream is a free remote mathematics research and enrichment program for exceptional high school students from Ukraine. It was established in March 2022 as an initiative under PRIMES (Program for Research in Mathematics, Engineering and Science for High School Students) at the MIT Mathematics Department. Yulia’s Dream is dedicated to the memory of Yulia Zdanovska, a 21-year-old graduate of the National University of Kyiv, a winner of the 2017 European Girls' Mathematical Olympiad and a teacher for the “Teach for Ukraine” program who was killed by a Russian-fired missile in her home city of Kharkiv. The program aims to help other Ukrainian boys and girls fulfill her dream.