Arithmetic Occult Periods

Explore the intriguing world of arithmetic ball quotients and their connection to complex configuration spaces in this Fields Number Theory Seminar talk. Delve into Jeff Achter's presentation on how certain complex configuration spaces can be uniformized as arithmetic ball quotients through the identification of parametrized objects with periods of auxiliary objects. Examine the role of Shimura varieties in providing algebraic structure to these ball quotients over cyclotomic integer rings. Discover how transcendentally-defined period maps respect these algebraic structures, leading to their arithmetic nature. Gain insights into this fascinating intersection of complex analysis, algebraic geometry, and number theory.