Mellin transforms and P-recurrences, point counts over finite fields and invariants of graphs

Francis Brown (U Oxford)

Oct 15. 2024, 14:00 — 15:15

I will discuss joint work with E. Panzer on the `completion conjecture' which relates point counts mod q of graph hypersurfaces over finite fields F_q. To tackle it involves studying a general family of Mellin transforms, their P-recurrences, tropical and Apery limits, and studying points over finite fields of hypersurfaces modulo prime powers. When applied to graph hypersurfaces, this formalism reproduces a number of diverse combinatorial invariants of graphs, and organises them into a single invariant. 

Further Information
Venue:
ESI Boltzmann Lecture Hall
Associated Event:
Algebraicity and Transcendence for Singular Differential Equations (Workshop)
Organizer(s):
Alin Bostan (INRIA Paris)
Francis Brown (U Oxford)
Herwig Hauser (U of Vienna)
Shihoko Ishii (U Tokyo)
Hiraku Kawanoue (Chubu U, Kasugai City)
Michael Singer (NC State U, Raleigh)