## The geometric Langlands program,

abelianization and the Hitchin fibration

### Time and venue

Seminar | Tuesday 16-18h, SR 6, Mathematikon |

Summer School | 5 - 12 August, HS 1, Mathematikon |

### Seminar topics

In the 1960's Robert Langlands formulated a series of deep conjectures which relate arithmetic and representation theory. If in these conjectures the role of number fields is replaced by function fields of curves, one arrives at the geometric Langlands program due to Beilinson, Deligne, Drinfeld and Laumon. In the seminar we will focus on the idea of abelianization which relates the geometric Langlands conjectures to a statement for Higgs bundles and has seen recent progress in the work of Donagi-Pantev, Chen-Zhu and others.

### Summer School

At the beginning of August we will have a Summer School with lectures by Ron Donagi and Tony Pantev (University of Pennsylvania) about Hitchin fibrations, geometric Langlands and nonabelian Hodge theory.

### Notes

Here are some handwritten notes for the seminar talks:

Talk 0 - From arithmetic to geometric Langlands (Rainer Weissauer)

Talk 1 - Drinfeld's best hope and abelianization (T.K.)

Talk 2 - Algebraic stacks (Katharina Hübner)

Talk 3 - Rigidification and duality for Picard stacks (Katharina Hübner)

Talk 4 - The Hitchin fibration I (Johannes Anschütz)

Talk 5 - The universal centralizer group scheme I (A.P.)

Talk 6 - The universal centralizer group scheme II (A.P.)

Talk 7 - The Hitchin fibration II (T.K.)

Talk 8 - Isogenies and cocycles (T.K.)

Talk 9 - The duality morphism (T.K.)

Talk 10 - Proof of the duality I (Uwe Weselmann)

Talk 11 - Proof of the duality II (Uwe Weselmann)

Talk 12 - Proof of the duality III (T.K.)