# Langlands correspondence and Bezrukavnikov's equivalence

**Authors:** Anna Romanov, Geordie Williamson  
**arXiv:** [2103.02329](https://arxiv.org/abs/2103.02329)  
**Date:** 2021-03-03  
**Summary page:** https://www.summarizepaper.com/en/paper/2103.02329v1/

## Key points

- The paper is titled "Langlands correspondence and Bezrukavnikov's equivalence" and was authored by Anna Romanov and Geordie Williamson.
- It was written as part of a course taught over two extended semesters at the University of Sydney.
- The first provides an introduction to the Langlands correspondence from an arithmetical point of view.
- The second introduces enough background in geometric representation theory to understand Bezrukavnikov's equivalence, which is a categorification of Kazhdan and Lusztig's two realizations of the affine Hecke algebra, a key object in representation theory.
- Throughout both parts, detailed explanations and examples are provided to make it accessible for readers with varying levels of familiarity with these topics.
- Overall, this 274-page preliminary draft serves as an excellent resource for those interested in exploring further into the Langlands correspondence and its connections to geometric representation theory.
- The authors welcome comments on their work, indicating their openness to feedback and potential improvements on their already comprehensive treatment of these complex mathematical concepts.

## Summary

The paper titled "Langlands correspondence and Bezrukavnikov's equivalence" is an extensive set of lecture notes authored by Anna Romanov and Geordie Williamson. It was written as part of a course taught over two extended semesters at the University of Sydney. The paper is divided into two parts: the first provides an introduction to the Langlands correspondence from an arithmetical point of view, while the second introduces enough background in geometric representation theory to understand Bezrukavnikov's equivalence. This equivalence is a categorification of Kazhdan and Lusztig's two realizations of the affine Hecke algebra, which is a key object in representation theory. Throughout both parts of the paper, the authors provide detailed explanations and examples that make it accessible for readers with varying levels of familiarity with these topics. Overall, this 274-page preliminary draft serves as an excellent resource for those interested in exploring further into the Langlands correspondence and its connections to geometric representation theory. The authors welcome comments on their work, indicating their openness to feedback and potential improvements on their already comprehensive treatment of these complex mathematical concepts.