Yasha Savelyev

I will outline, in the special case of the torus, an ongoing research program studying the arithmetic of counts of closed geodesics on Riemann-Finsler manifolds. I will first explain some of the results, and their connection with the hugely influential Kolmogorov-Arnold-Moser theorem. With this motivation in hand, I will describe a basic conjecture that students can think about – and perhaps even attack with computer assistance (LLMs).