Summer school on the Geometric Langlands Programme
(Freiburg, 2012)

Lectures by D. Nadler:

• Lecture 1 (introduction, flag varieties, loop groups, affine Grassmanian)
• Lecture 2 (sheaves as linearization of geometry, nearby and vanishing cycles, microlocal definition of perverse sheaves)
• Lecture 3 (towards (geometric) Hecke algebras)
• Lecture 4 (Geometric Satake)
• Lecture 5 (Beilinson-Drinfeld Grassmanian, convolution and nearby cycles, Gaitsgory's construction of the centre of the affine Hecke algebra via nearby cycles)

Lectures by T. Pantev:

• Lecture 1 (introduction, Bun_G, Loc, Hecke operators, Wilson operators, Drinfeld's best hope)
• Lecture 2 (why the best hope fails)
• Lecture 3 (first steps towards fixing the best hope, compact objects, perfect complexes, singular support for ind-coherent sheaves)
• Lecture 4 (more on singular support, the Arinkin-Gaitsgory result, the classical limit of the conjecture)
• Lecture 5 (proof of the classical limit of the conjecture)

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Last updated: 19 August, 2012