The summer school will be held at the Bernoulli Center at EPFL and consists of the following 4 mini-courses:
Mauro Porta: Derived methods in representation theory
Richard Rimanyi: Characteristic classes of singularities and their 3d mirror symmetry
Characteristic classes of singularities provide a concrete and computable way to detect 3d mirror symmetry. This minicourse will introduce characteristic classes associated with singularities arising in various geometric contexts, including singularities of maps, quivers, and differential forms. We will review computational techniques (from resolution or deformation of singularities to Hall algebra-type recursions, and interpolation) and explore key applications. Our focus will be on stable envelopes, as introduced by Maulik–Okounkov, Okounkov, and Aganagic–Okounkov, and their deep connections to geometric representation theory. We will outline a proof of the 3d mirror symmetry statement for elliptic stable envelopes on bow varieties, based on a joint work with T. Botta.
Peng Shan: Vertex algebras, affine Springer fibres and 4d mirror symmetry
We will explain some results and conjectures about relationships between representation theory of simple affine Vertex algebras and the geometry of Hitchin fibrations, which is related to dualities between Higgs and Coulomb branches for 4d N=2 super conformal field theory.
Eric Chen: S-duality in arithmetic and geometric contexts
Special Lecture by Yiannis Sakellaridis:
