Suggested reading and references

What follows is the list of mathematical ideas that are important for the workshop, with references for each. Note that only the first few are assumed known; the rest will be introduced in the talks. So familiarity with the material from most references is by no means required to understand the talks, and in fact some of the texts might work better as a follow-up to the workshop. On the other hand, even for the material that is going to be introduced, it may be worth it to glance through the references before the workshop. More detailed suggestions are given for the topics.

• 1. Infinity-categories (assumed known, necessary throughout)

  2. DG categories (assumed known, necessary throughout)

  3. Algebraic stacks (assumed known, necessary throughout)

     1. • The stack Bun(G) (assumed known, necessary throughout)

  4. D-modules (assumed known, necessary throughout)

     1. • D-modules on algebraic stacks (necessary near the end: talks 4.3 and 5.4)

  5. Derived algebraic geometry (assumed known, necessary for talks about the spectral side of the Langlands correspondence)

  6. Ind-coherent sheaves (will be introduced, necessary for talks about the spectral side of the Langlands correspondence)

  7. Affine Grassmannian (will be introduced, necessary for talks about the geometric (aka automorphic) side of the Langlands correspondence)

  8. Geometric Satake correspondence (will be introduced, necessary for the talks 3.2 and 5.1-5.3)

  9. Automorphic functions on adele groups (will be introduced; serves as crucial piece of motivation)

  10. Loop groups (will be introduced, necessary for several talks)

  11. Factorization algebras (will be introduced; serve as motivation for talks on factorization)

  12. Beilinson-Bernstein localization (assumed; serves as crucial piece of motivation for talk 4.3)

  13. Affine Beilinson-Bernstein localization (will be explained; used in talk 4.3)

  14. Opers (will be explained; used in talk 5.1)

Additionally, there are a number of potentially useful notes and links that can be found at the graduate seminar webpage.

Finally, some of the talks will be loosely based on parts of "Outline of the proof of the Geometric Langlands Conjecture for GL(2)" and "Singular support of coherent sheaves and the Geometric Langlands Conjecture". Precise references are given next to the description of the individual talks. (But reading these papers is by no means a prerequisite for following the talks: in fact if you have read the papers, the talks might be boring!)