London School of Geometry and Number Theory (LSGNT) 

Topics in Number Theory 2022/23

Topics in Number Theory is a year-long course taught every year to the first-year LSGNT students. This version of the course is designed by Fred Diamond and Payman Kassaei (and organized by PK).  It is taught collaboratively by academics in London. Each lecture is followed by a wrap-up session in which students (the owners) are in charge of organizing presentations where solutions to problem sets or other aspects of the topic are discussed. A senior student (the supervisor) will be present at each wrap-up session.

Date 

Lecturer 

Title 

Owner 

Supervisor 

Oct 19

Owen Patashnick

Counting points on varieties in characteristic p  

 M. Masters 

M. Ortiz

Oct 26

Chris Birkbeck

The Weil conjectures  

S. Vassiliadis

D. Mamaev

Nov 9

Luis Garcia Martinez

L functions 

H. Singh

S. Yang

Nov 16

Peter Jossen

Elliptic curves and abelian varieties 

C. Rudrum

A. Livingston

Nov 23

Fred Diamond

Galois representations  

H. Spencer

A. Satoskar

Nov 30

  Vladimir Dokchitser

From the Class number formula to the Birch-Swinnerton-Dyer Conjecture  

J. Tilley

D. Angdinata

Dec 7

 Robert Rockwood

An introduction to Iwasawa theory/special values conjectures 

A. Varshney +  I. Rendell

S. Monnet

Dec 14

 Alexei Skorobogatov

Diophantine Equations 

A. Bozovich

D. Puignau-Chacon

Jan 25

Lassina Dembele

Modular forms 

G. Navone

D. Gordo Chicharro

Jan 31

 Stephen Lester

Introduction to the theory of the Riemann zeta function 

M. Haghshenas

Y. Yang

Feb 8

 Netan Dogra

Rigid Geometry and p-adic integration

Y. Yang

M. Christensen

Feb 15 

 Ian Petrow

The fourth moment of the Riemann zeta function 

S. Vazquez Saez  + A. Wolf

M. Levin

Feb 22 

 George Boxer

An introduction to the geometry of Shimura varieties in characteristic p 

Y. Zhao

J. Zhang

March 1 

 Aled Walker

Pair correlation of zeros of the Riemann zeta function 

Z. Tan

N. Cavalleri

The lectures take place 10-12 am.