Faculty of Science

Proof of the Geometric Langlands Conjecture
Provider: Faculty of Science

Activity no.: 7014-25-07-31
	Enrollment deadline: 13/08/2025

Place

Department of Mathematical Sciences

Date and time

18.08.2025, at: 00:00 - 22.08.2025, at: 16:00

Regular seats

120

ECTS credits

2.50

Contact person

Robert Wayne Burklund E-mail address: rb@math.ku.dk

Enrolment Handling/Course Organiser

PhD Administration SCIENCE E-mail address: phdcourses@science.ku.dk

Written language

English

Teaching language

English

Exam requirements

Attending the lecture series, active participation in the exercise sessions.

Exam form

Course participation

Course workload

Course workload category	Hours
Preparation	35.00
Lectures	18.00
Practical exercises	8.00
Theoretical exercises	8.00

Sum	69.00

Enrolment guidelines

The course aims to provide an overview of the recently announced proof the geometric langlands conjecture with lecture series given by the team who proved the conjecture. These developments have already been covered by an article in Quanta (*) and the timing is ideal for an event which aims to make these developments accessible for a wider mathematical audience.

The guest lecturers are each experts in the field and all are members of the team that has announced a proof of the conjecture. There will be one lecture series on the construction of the GL functor. This will partly focus on the difficult issue of formulating the appropriate source and target categories. There will be another lecture series devoted to studying the coefficient functor and deducing conservativity of the GL functor from this. The third lecture series will provide an overview of the proof, assembling all the necessary pieces into a complete proof.

(*) https://www.quantamagazine.org/monumental-proof-settles-geometric-langlands-conjecture-20240719/

Formal requirements

Recommended Academic Qualifications:
Knowledge about algebraic geometry, representation theory and six functor formalisms.

Learning outcome

Knowledge:
• Participants will understand the formulation of the geometric langlands conjecture (GLC) and related technical issues.
• Participants will understand the key ideas and techniques used in proving the GLC.
• Participants will know how the GLC can be used to analyze related questions in representation theory and the connection with arithmetic langlands.

Skills:
• To be able to use acquired knowledge within the participants own research.
• To be able to analyze the geometry of stacks of local systems on complex curves.
• To be able to effectively manipulate categories of D-modules on stacks and Ind-coherent sheaves with singular support restrictions.

Competences:
• To be able to produce independent proofs of results in geometric representation theory and algebraic geometry more broadly using the tools developed to prove the GLC.
• To be able to produce independent proofs of results in geometric representation theory using the GLC as an input.

Teaching and learning methods

The masterclass will consist of three lecture series each highlighting different facets of the proof of the geometric langlands conjecture, together with several one hour talks on more specialized topics.
This will be accompanied by exercise sessions and informal discussion sessions in which the participants can practice the techniques which are discussed theoretically in the lectures.

Lecturers

Guest Lecturers:
Dennis Gaitsgory, MPIM Bonn
Sam Raskin, Yale
Nick Rozenblyum, University of Toronto

Remarks

Registration will open soon here:
https://www.math.ku.dk/english/calendar/events/geometric-langlands/

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