The Geometric Andre-Grothendieck Period Conjecture Over Complex Function Fields

Explore a 55-minute mathematical seminar presentation where Jacob Tsimerman from the University of Toronto delves into the geometric Andre-Grothendieck period conjecture. Learn about periods of algebraic varieties defined over number fields K, focusing on the integrals of K-rational differential forms over topological cycles. Understand how algebraic relations between periods are expected to arise from geometry, as formalized in the Grothendieck period conjecture. Discover Andre's broader generalization covering finitely generated fields, which encompasses the Schanuel conjecture and explains the transcendence of numbers like e. Examine recent advances in transcendence theory of period maps over the past twenty years, with particular attention to the complex function field case where more comprehensive results are known. Follow along as Tsimerman presents joint work with B.Bakker, demonstrating the proof of the Andre-Grothendieck Period conjecture analog over complex function fields.