Dear all, 

The Number Theory-Algebraic Geometry "lunch" seminar (80943) this semester will be a student's learning seminar on Galois representations and modular forms (see description below). 

First meeting:  Mon, 22 Mar 2021, 13-14 
Speaker: Ari Shnidman
Title:Introduction

The first meeting will be via ZOOM

https://huji.zoom.us/j/86725837215?pwd=bmh3VTg3UlhvejQ1bkFiYlZ2OTN6UT09
Meeting ID: 867 2583 7215
Passcode: 620671

while after Passover it might move to Ross 70 with a live broadcast.    

Our intention is to make accessible to motivated master and PhD students, and that most of talks will  be given by students or post-docs. HUJI students can register and get a credit for this. 

Students with background in either number theory or algebraic geometry are encouraged to attend, and especially encouraged to give talks. Please contact one of us if you are interested in giving a talk.  

Best,

Ari and Yakov. 

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Description: The ultimate goal for the semester is to understand Deligne's construction of Galois representations associated with modular forms of even weight.  We will start at the beginning, by defining modular forms, modular curves, Hecke operators, and then discuss Galois representations, L-functions, and the Eichler-Shimura relation.
 
We will use the geometry of modular curves, and the formalism of etale cohomology (which we will go over), to attach a Galois representation to each modular form of even weight, so that the L-function of the Galois representation agrees with the L-function of the modular form.

References: Most likely our main reference will be 

https://www.math.wisc.edu/~boston/Diamond-Im-Modular_forms_and_modular_curves.pdf