#MOC/resources

Class Field Theory

Advice:

• Look at global class field theory first, see book of Janusz.
• Washington’s Cyclotomic Fields.
• Harari’s book (?)
• Artin and Tate’s notes
• Interesting topics: https://www.mit.edu/~fengt/PaperF21.pdf#page=2

Resources

• Brief summary of statements of CFT #resources/summaries
• Blogpost introducing CFT “Local class field theory: a discussion”
• Milne’s Notes
• Cassels-Frohlich
• Cox: Primes of the form…
• OCW Lecture Notes

Seminar on Iwasawa theory

Galois cohomology: http://www2.math.umd.edu/~lcw/Boston.pdf

Algebraic Number Theory

See Learning Algebraic Number Theory

Modular Forms

• AWS 2021

Arithmetic Geometry

• https://math.mit.edu/nt/index_stage
• Seminar talks on the Weil conjectures
• Seminar on unlikely intersections and o-minimality

Abelian Varieties

• http://www.math.columbia.edu/~chaoli/docs/AbelianVarieties.html
• See Haiyang’s notes: moduli stack of abelian varieties > ^7cc3c7

Rational Points

• https://web.math.princeton.edu/~shouwu/publications/iccm98.pdf

Langlands

• See The Langlands Program

• attachments/Geometric Langlands, Perfectoid Spaces, Fargues-Fontaine Overview.pdf

• attachments/Friedberg - 2018 - WHAT IS …the Langlands Program.pdf

• MSRI Summer School on automorphic forms and the Langlands program

• Projects/2022 AWS/Automorphic Forms and Langlands Kevin Buzzard Notes

Misc

Some Courses at Stanford, 2014-2019

Course

Title

Lecturer

249A (2018)

Automorphy Lifting (in progress)

Richard Taylor

249C (2017)

Geometric Quantization and Representation Theory (in progress)

Akshay Venkatesh

249B (2017)

Alterations. (Due to a broken hand, this was picked up by Aaron Landesman.)

Brian Conrad

245C (2016)

Geometry of Numbers

Akshay Venkatesh

249B (2016)

Reductive Groups over Fields

Brian Conrad

245B (2016)

Enumerating Curves in Calabi-Yau Threefolds (under revision)

Jun Li

258 (2016)

Higgs Bundles and Non-Abelian Hodge Theory (under revision)

Rafe Mazzeo

263C (2015)

The Analytic Class Number Formula and L-functions (Under revision)

Akshay Venkatesh

245C (2015)

Automorphic Forms on Shimura Varieties (Under revision)

Zhiyuan Li

249C (2015)

Abelian Varieties (Under revision)

Brian Conrad

282C (2015)

Fiber Bundles and Cobordism (Under revision)

Dan Berwick-Evans

245B (2015)

Equivariant Algebraic Geometry

Ravi Vakil

263B (2015)

Modular Representation Theory

Dan Bump

249B (2015)

The Langlands Correspondence for Global Function Fields

Zhiwei Yun

248 (2014)

Introduction to Ergodic Theory

Maryam Mirzakhani