To be held from July 21 to August 22, 2025 at Bernoulli Center
the programme "Representations, Moduli and Duality"
Description:
The notion of duality in physics has a rich history, going back at least as far as the observation that Maxwell’s theory of elctromagnetism is symmetric after swapping electric and magnetic fields. More generally, dualities in physics can provide a way of relating two seemingly very different physical theories via a nontrivial duality transformation. For instance, S-duality in physics provides a way to swap strongly coupled physical theories for weakly coupled ones [MO77], for which we may use perturbative methods to exactly solve the equations governing the system. Such dualities in physics are often translated into deep conjectures and programs of research in mathematics [KW07]. This proposal centers on one in particular: 3d mirror symmetry [IS96]. Via this symmetry, the Coulomb branch of the physical theory is exchanged 1 with the Higgs branch. This idea has deep implications, cutting across multiple areas of mathematics, since various spaces that have become central objects in mathematics over the last forty years turn out to be moduli spaces of states in these two branches. Moduli spaces arise in mathematics from the observation that a set of objects that we may be studying (be they representations, sheaves, or spaces themselves) can often be naturally arranged into something richer than a set: a space, with perhaps an algebraic, or symplectic, or even “higher” structure. The subject of geometric representation theory is the study of these spaces, along with geometrically defined homomorphisms between the invariants of these spaces [CG97]. Tracking through all this mathematics, the study of dualities in mathematics which formalise 3d mirror symmetry in physics provides deep new insights into moduli spaces and representation theory.
The programme consists of 5 weeks of research collaborations with one week-long school, one week-long conference and one workshop.
More information on the scientific programme here.
Details on the support
The 2 laureates selected to participate in the programme will receive financial support including:
- Roundtrip travel between your home country and Switzerland (up to a maximum amount of 1600 euros, including visa fees).
- Full board accommodation at Bernoulli Center in Lausanne (Switzerland).
- Per diem allowance of 250€/week.
Admission requirements
- Bernoulli Center and CIMPA support the participation of young mathematicians less or equal to 36 years old or with the highest academic diploma during the last 5 years affiliated in a developing country (IMU list).
- A candidate will commit to spend at least 2/3 of the time of the programme at Bernoulli Center to be admissible.
How to apply
Applications must be submitted before the deadline. Applications shall include a cover letter and two recommendation letters that will be sent electronically by the referees. Candidates are advised to complete their applications early enough and to ask the referees to send the letters long before the deadline. CIMPA will not assume responsibility for any last-minute application which cannot be completed due to technical reasons.
The candidates have to apply on the web page: https://application.cimpa.info
The applications must be submitted by April 6, 2025.