The workshop is organized as a part of IMPANGA.
Timetable:
8th October 2015:
10:30-11:30: Adrian Langer, Mini-course on Higgs bundles (I)
13:00-14:00: Adrian Langer, Mini-course onHiggs bundles (II)
14:30-15:30: Przemyslaw Chojecki, Geometric interpretation of fundamental lemma
9th October 2015:
10:30-11:30: Adrian Langer, Mini-course on Higgs bundles (III)
13:00-14:00: Piotr Achinger, Hitchin's fibration and P=W conjecture
Programme of the mini-course given by Adrian Langer:
Lecture 1
Local systems, flat bundles, Higgs bundles
Simpson's correspondence (non-abelian Hodge theory)
Examples and applications: Rank 1 case and relation to generic vanishing theorems
Lecture 2
Moduli spaces of representations of the fundamental group and hyperk\"ahler structure
Multiplicative group action and complex variation of the Hodge structure
Hitchin's fibration
Examples and applications: rigidity results for representations of the fundamental group
Lecture 3
Spectral covers and generic fibres of Hitchin's fibration
Langlands duality as mirror symmetry (after Hausel-Thaddeus)
Geometric Langlands conjecture