Masterclass: Proof of the geometric Langlands conjecture

University of Copenhagen
18-22 August 2025

The masterclass aims to provide an overview of the recently announced proof of the geometric Langlands conjecture with a series of lectures given by the team that proved the conjecture. An article in Quanta has already covered these developments. The timing is ideal for an event that aims to make these developments accessible to a wider mathematical audience.

All registration process has ended. We cannot answer every email inquiring late registration.

If you have registered before, fill in this form to confirm that you will come to the masterclass.

We plan to record the lectures.

 

 

Dima Arinkin (University of Wisconsin – Madison)
Dario Beraldo (University College London)
Justin Campbell (University of Chicago)
Lin Chen (Tsinghua University)
Joakim Færgeman (Yale University)
Dennis Gaitsgory (MPIM)
Andreas Hayash (Aristotle University of Thessaloniki)
Kevin Lin (University of Chicago)
Sam Raskin (Yale University)
Nick Rozenblyum (University of Toronto)
Yifei Zhao (University of Münster)

 

 

 

 

 

 

 

Day 1, Fun(ctor) day:
Tutorial 1.1 (Justin): all you need to know about Bun_G
Tutorial 1.2 (Dima): all you need to know about LocSys
Lecture 1 (Sam): coarse version of the Langlands functor 
Tutorial 1.3 (Dima): IndCoh and coherent singular support
Lecture 2 (Dennis): the actual Langlands functor + road map to the proof (1st approximation)
Bonus Material A (Joakim): Tempered, restricted and Betti 
versions of geometric Langlands 
Day 2, (Kac-)Moody day:
Tutorial 2.1 (Andreas): The Whittaker category
Tutorial 2.2 (Sam): Kac-Moody modules 
Lecture 3 (Dima): Monodromy-free opers
Tutorial 2.3 (Kevin): introduction to factorization
Lecture 4 (Yifei): Feigin-Frenkel isomorphism and construction of the FLE functor
Bonus Material B (Dennis): proof of the FLE 
Day 3, Loca(lization) day:
Tutorial 3.1 (Sam): KM localization on Bun_G
Tutorial 3.2 (Nick): unitality
Lecture 5 (Lin): Making branes interact (localization vs Whittaker) 
Tutorial 3.3 (Kevin): Spectral Poincaré functors 
Lecture 6 (Nick): Compatibility of the Langlands functor with critical localization + road map to the proof (next approximation) 
Bonus Material C (Lin): Hecke eigen-property of the critical localization
Day 4, Eis(enstein) day:
Tutorial 4.1 (Andreas): local semi-inf category 
Tutorial 4.2 (Yifei): spectral semi-inf category 
Lecture 7 (Justin): the Sith theory
Lecture 8 (Dennis): Jacquet functors and the FLE
Lecture 9 (Joakim): Compatibility of the Langlands functor with Eisenstein 
and constant term functors
Day 5, Doomsday: 
Bonus Material D (Joakim): Langlands functor is conservative
Lecture 10 (Dario): summary + final road map to the proof 
Lecture 11 (Lin): ambidexterity 
Lecture 12 (Kevin): end of the argument
Bonus Material E (Sam): after GLC... 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

We kindly ask the participants to arrange their own accommodation.

We recommend Hotel 9 Små Hjem, which is pleasant and inexpensive and offers rooms with a kitchen. Other inexpensive alternatives are Steel House Copenhagen (close to city centre), and CabInn, which has several locations in Copenhagen: the Hotel City (close to Tivoli), Hotel Scandinavia (Frederiksberg, close to the lakes), and Hotel Express (Frederiksberg) are the most convenient locations; the latter two are 2.5-3 km from the math department. Somewhat more expensive – and still recommended – options are Hotel Nora and  Ibsen's Hotel.

An additional option is to combine a stay at the CabInn Metro Hotel with a pass for Copenhagen public transportation (efficient and reliable). See information about tickets & prices.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Qingyuan Bai <qb@math.ku.dk>

Robert Burklund <rb@math.ku.dk>

Florian Riedel <florian.riedel@pm.me>

 

 

butterfly
胡蝶の舞 -  柳川重信

“Demazure tells us that, behind this terminology [pinning], there's the image of the butterfly (provided to him by Grothendieck): the body is a maximal torus T, the wings are two opposite Borel subgroups with respect to T, we unfold the butterfly by spreading the wings, then we fix elements in the additive groups (pins) to rigidify the situation (i.e., to eliminate automorphisms).” (SGA 3, XXIII, p.177, new edition.)