# A survey of Literature on Gauge Theory approach to Geometric Langlands and allied topics

## Table of Contents

## 1 Introduction

This page aims to be an entry point of sorts for the literature on the gauge theory approach to geometric Langlands and some other allied topics. Currently, it is just a list of papers (ordering within each heading is influenced but not determined by chronology). This is still woefully incomplete and I will try to update it once in a while. Many trends of the physically motivated research (esp those related to N=2 theories in four dimensions) are currently missing in my list. The list on the mathematical side is also missing several trends. In future, I also hope to add a few words of introduction linking the different works. Any Email comments are welcome. I should note that the broader Langlands program is a vast research program at the intersection of several different themes (for ex : Number Theory, Algebraic Geometry, Topology, Representation Theory and more recently, Quantum Field Theories, Differential, Symplectic Geometry and Mirror Symmetry). Its vastness is simultaneously inspiring and forbidding. In practice, it helps to have an interest and background knowledge in atleast one or more of the themes before begining one's trek into the literature on Langlands. The literature collected here is undoubtedly biased by my own trajectory which is still one of learning.

## 2 The Physics literature since Kapustin-Witten (KW)

## 3 The Mathematical literature since Beilinson-Drinfeld (BD)

**Note** : This set includes works that are close to the framework of BD, those that are closer to KW and other independent approaches.

- Beilinson-Drinfeld (
**pdf**; Preliminary version. Link active as of mid 2014) - Ginzburg I
- Mirkovic-Vilonen (
**pdf**) - Ben-Zvi and Frenkel (book)
- Hausel-Thaddeus
- Nadler-Zaslow
- Nadler I, II
- Bezrukavnikov I
- Donagi-Pantev I , II (
**pdf**) - Frenkel-Gaitsgory I
- Frenkel I (book)
- Frenkel reviews I, II , III
- Ben-Zvi and Nadler I , II, III, IV
- Hausel survey
- Frenkel-Ngo-Langlands
- Frenkel-Ngo

## 4 Background on Langlands (more elementary, not in research papers)

- Articles on Representation Theory, Fourier Transform and Moduli Spaces in the Princeton Companion to Math
- Several useful questions on MO.
- Frenkel's `Love and Math'

## 5 Resources

There are many other resources on the web that collect very useful material on the Langlands program and allied topics. Some of them are :

- UChicago page on Langlands is here.
- David Ben-Zvi's Langlands page is here.
- Northwestern's page on Langlands is here.
- Dennis Gaitsgory's GL page is here.

Other useful resources where the Langlands program over more general fields (the geometric case being the specialization over C or R) is discussed : (Warning : If your primary research interest is the Langlands program over general fields, this list is likely to look very limited. My goal here is to only give a flavor of the work done in the more general context to someone whose primary interest is in the geometric setting. Additionally, my ability to link to something is also limited by the availability of something to link to. These are the links I could find.)

- Bill Casselmann's courses , essays (many of which are of a very accessible nature to a non-expert) and his collection of useful lecture notes .
- Eisenstein Series and Automorphic Representations - A book aimed at physicists, explaining the role of Eisenstein Series in the original setting of the Langlands program, namely that of Number Theory. The physics context relevant for this book is quite different from that for Geometric Langlands but the book is valuable because it presents material that is otherwise quite hard to access.
- The works of Langlands .
- The works of Arthur .
- The works of Gan .
- The works of Gross .
- The articles and works of Harris .
- Lecture Notes of Kazhdan .
- The works of Lusztig.
- The works of Prasad .
- The works of Shelstad .
- The works of Vogan .