From the first announcement: "The goal is to study Etale Cohomology, with the hope to understand Grothendieck's sheaf-function dictionary, Lefschetz fixed point formula, and perhaps the idea of the proof of Weil conjectures by Deligne (though this is unlikely to be included in the seminar itself). The basic idea is that one can express functions on all kinds of spaces (e.g., those arising in number theory), by means of geometry. Thus, etale cohomology has wide applications in algebraic geometry, arithmetic geometry, number theory, and representation theory of finite and p-adic groups (eg., character theory of finite groups of Lie type is stated entirely in these terms), and automorphic forms. For example, automorphic sheaves are the sheaf-theoretic analogues of automorphic functions, via this sheaf-function dictionary, and are important in the formulation of the geometric Langlands conjectures."

References, links, etc:

• The main source is J. Milne's notes.
• Grothendieck Topologies, Notes on a seminar by M. Artin, 1962.
• Grothendieck's TOHOKU paper (on Project Euclid) Part I ; Part II
• Notes on character sheaves by Anne-Marie Aubert.
• Laumon's 1987 paper (at Numdam)
• Notes by Sug Woo Shin on sheaf-function correspondence.
• An interesting blog post, Part I ; Part II . (communicated by Robert).

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Talks:

• September 14. Masoud gave an overview/introduction to the idea of geometrization.
  
• September 22. Robert Klinzmann, introduction to sheaves I.
• September 29. Robert Klinzmann, introduction to sheaves and cohomology II.
• October 6. Alex Duncan, Introduction to Grothendieck topologies.
• October 13. Aurel Meyer, The etale fundamental group.
• October 20. STUDY BREAK (that is, no talk).
• October 27. Robert Klinzmann, TBA.
• Further topics:
  • Sheaves of abelian groups on the etale site; cohomology
  • Sheaves of $\Z_l$ and $\bar \Q_l$-modules;
  • The formalism of 6 functors;
  • Grothendieck-Lefschetz fixed point formula.
  • Sheaf-function dictionary.
  • All of the above already happened, in some order. Sorry about neglecting this page.
• On December 1, I should finish the correspondence between characters of abelian groups and character sheaves, and probably define Fourier-Deligne transform, following Laumon's paper. The rest is informal discussion.