During Summer Term 2022, I and Alvaro Gonzalez Hernandez are running a study group on Hasse-Weil zeta functions. The plan is to study the proofs of the Weil Conjectures for curves and then to get a glimpse of the theory for higher-dimensional varieties. The talks take place in room B3.03 (Zeeman building) on Fridays from 1pm to 2pm.

The planned schedule is as follows.

Topic	Speaker	Date
Introduction, basic facts and definitions	Óscar Salgado	6th May
Rationality and Functional Equation of zeta functions of curves	Elvira Lupoian	13th May
Background on Intersection Theory on surfaces	Alvaro Hernandez	20th May
The Riemann Hypothesis for curves via Intersection Theory	Steven Groen	27th May
The Riemann Hypothesis for curves via the Bombieri-Stepanov method	Phil Holdridge	3rd June
Survey of Étale Cohomology and its role in the Weil Conjectures	Arshay Sheth	10th June
The Lang-Weil estimates	Sam Chow	17th June
Dwork's p-adic proof of rationality of zeta functions, part I	Katerina Santicola	24th June
Dwork's p-adic proof of rationality of zeta functions, part II	Nuno Arala	1st July

Useful resources:

• Zeta functions in algebraic geometryLink opens in a new window, by Mircea Mustata
• The Weil Conjectures for curvesLink opens in a new window, by Sam Raskin