Yunqing Tang, Berkeley
Irrationality of periods
Periods are interesting numbers arising from algebraic geometry. Grothendieck’s period conjecture provides predictions on irrationality and transcendence of periods. There have been some systematic studies on certain periods, such as Baker’s theory on linear forms of logarithms of algebraic numbers. However, beyond special cases, we do not know the irrationality of simple-looking periods such as the product of two logs. In this talk, I will discuss the joint work with Calegari and Dimitrov on an irrationality result of certain product of two logs and some other periods. A classical prototype of the method was first used by Apéry to prove the irrationality of zeta(3). The key ingredient is an arithmetic holonomy theorem built upon earlier work by André, Bost, Charles (and others) on arithmetic algebraization theorems via Arakelov theory.
MC 5501