Third Annual Yulia's Dream Conference, June 25, 2025

Wednesday, June 25

9:10 am (Boston) [16:10 (Kyiv)]: Welcoming Remarks

• Prof. Pavel Etingof, Yulia's Dream Chief Research Advisor
• Dr. Slava Gerovitch, Yulia's Dream Program Director

9:25-10:05 am (Boston) [16:25-17:00 (Kyiv)]: Session 1

• Olena Syvachenko, Klim Garmash, “Turan’s Problem” (mentor Alina Harbuzova, MIT)
• Mykhailo Bolshakov, “Ramsey Theory on the Integers” (mentor Sasha Voitovych, MIT)

10:15-11:35 am (Boston) [17:15-18:35 (Kyiv)]: Guest lecture

• Prof. Rostislav Grigorchuk (Texas A&M University), “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.

11:45 am - 12:40 pm (Boston) [18:45-19:40 (Kyiv)]: Session 2

• Sophia Breslavets, “Fixed Points of Diffie-Hellman Permutations” (mentor Prof. Vasily Dolgushev, Temple University) (continuation of last year Yulia’s Dream project)
• Liubomyr Bielov, Dariia Balan, “Lattice structures on graphs of polytopes” (mentor Dr. Daria Poliakova, University of Hamburg)
• Oleg Puzyrkov, Sofiia Lipkevych, Mykola Kobzarenko, “Introduction to Abstract Linear Algebra” (mentor Mykola Sapronov, University of Minnesota Twin Cities)

12:50-1:25 pm (Boston) [19:50-20:25 (Kyiv)]: Session 3

• Heorhii Zhylinskyi, “Generalized Markov traces” (mentor Dr. Kostiantyn Tolmachov, University of Hamburg)
• Roman Mielamud, Anton Opulskyi, Yura Kabkov, Title TBA (mentor Prof. Anne Dranowski, University of Southern California)

Contact

With questions, contact PRIMES Program Director Slava Gerovitch at