Modular forms and Eisenstein series

Abstract: I’ll discuss some recent work on defining modular forms and Eisenstein series in LEAN. Modular forms are some of the most important objects in number theory due in part to their role in the proof of Fermat’s Last Theorem. These special functions act as glue between algebra, geometry and analysis, it is therefore tempting to begin formalizing them. Moreover one wants to formalise interesting examples, such as Eisenstein series. In the talk I will discuss the mathematics behind there definitions and highlight the main challenges in formalising them.

general mathematicsnumber theory

Audience: advanced learners

Comments: This talk will be a Zoom talk. I (Kevin Buzzard) am not in London this week so I will not be running the show in the usual room, and do not know if anyone will be there to run it because I was too disorganised to sort anything out before I left London. See you on Zoom!

London Learning Lean

Series comments: London Learning Lean is an in-person informal seminar where people in the Lean community give 10-minute presentations on things they're doing with the Lean theorem prover. It runs on the last Friday of the month, typically either at Imperial College or UCL. Please contact Kevin Buzzard on the Lean Zulip if you want to reserve a slot for a ten-minute presentation!