Nahm's problem and cluster algebras

Abstract: Nahm, Terhoeven, and Zagier studied the intersection of the set of q-hypergeometric series and the set of modular functions, and they found that the problem of finding an element of this intersection is related to the dilogarithm function and algebraic K-theory. In this talk, I will explain this problem is also related to the periodicity of T-systems (and Y-systems), which are difference equations that appear in the theory of cluster algebras. I will give a systematic construction of q-hypergeometric series that are expected to be modular using the theory of cluster algebras.

number theory

Audience: researchers in the discipline

Dublin Algebra and Number Theory Seminar

Series comments: Passcode: The 3-digit prime numerator of Riemann zeta at -11