Higher moments of elliptic curves
Algebraic Geometry and Number Theory Seminar
Date
Thursday, December 14, 2023 13:00 - 15:00
Speaker
Bartosz Naskręcki (Adam Mickiewicz University)
Location
Heinzel Seminar Room (I21.EG.101), Office Building West, ISTA
Series
Seminar/Talk
Tags
Mathematics and CS Seminar, mathematical_seminar_ics
Host
Tim Browning
Contact
In this talk we will discuss some new developments in higher moment sums of 1-parametric families of elliptic curves. These sums have connections to modular forms and algebraic curves. I will sketch a result about the second moment of cubic curves leading to a connection with intermediate Jacobians in threefolds. Next we will discuss proofs of modularity of certain rigid Calabi-Yau threefolds which uses directly higher moments, universal families of elliptic curves and Deligne’s results, avoiding completely the standard approach via Faltings-Serre method.