Higgs Bundles and Relations to Langlands Programme

Programme

 

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