Workshop on Higgs bundles and their relations to Langlands program

organizers: Piotr Achinger, Przemyslaw Chojecki and Adrian Langer


Date: 8th-9th October 2015
Place:  room 403,  IMPAN, ul. Śniadeckich 8, Warsaw, Poland.



Description of the workshop:
   
    The mini-course will be given by Adrian Langer on Higgs bundles and their moduli space with connections to Langlands program:

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

There will be also a talk by Piotr Achinger on Hitchin's fibration and P=W conjecture and a talk by Przemyslaw Chojecki on geometric interpretation of fundamental lemma.   

The workshop is organized as a part of IMPANGA.




Timetable



8th October 2015:

10:30-11:30: Adrian Langer (I)

13:00-14:00: Adrian Langer (II)

14:30-15:30: Przemyslaw Chojecki



9th October 2015:

10:30-11:30: Adrian Langer (III)

13:00-14:00: Piotr Achinger