BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Memento EPFL//
BEGIN:VEVENT
SUMMARY:Summer school: Recent perspectives on geometry and representation 
 theory
DTSTART:20250721T090000
DTEND:20250725T170000
DTSTAMP:20260405T193012Z
UID:9f550b768cd38c63cef24675414ac008227f2d99bfa2e8de51ce1e98
CATEGORIES:Conferences - Seminars
DESCRIPTION:Mauro Porta (Université de Strasbourg and IUF)\, Richard Rima
 nyi (UNC Chapel Hill)\, Peng Shan (Tsinghua University)\, Eric Chen (EPFL 
 / Kavli IPMU)\, Yiannis Sakellaridis (Johns Hopkins University)\nThe summe
 r school is part of the programme "Representations\, Moduli and Duality" a
 nd will be held at the Bernoulli Center at EPFL and consists of the follow
 ing 4 mini-courses:\n\nMauro Porta: Derived methods in representation theo
 ry\nIn this mini-course\, I will provide an introduction to derived algebr
 aic geometry\, with special emphasis on the construction of moduli stacks 
 and spaces relevant for geometric representation theory. I will discuss ho
 w to obtain homological and motivic invariants\, and introduce cohomologic
 al Hall algebras as consequence of the formalism of 2-Segal objects of Kap
 ranov and Dyckerhoff. If time permits\, I will outline some recent advance
 s of the theory.\n\nRichard Rimanyi: Characteristic classes of singulariti
 es and their 3d mirror symmetry\nCharacteristic classes of singularities p
 rovide a concrete and computable way to detect 3d mirror symmetry. This mi
 nicourse will introduce characteristic classes associated with singulariti
 es arising in various geometric contexts\, including singularities of maps
 \, quivers\, and differential forms. We will review computational techniqu
 es (from resolution or deformation of singularities to Hall algebra-type r
 ecursions\, and interpolation) and explore key applications. Our focus wil
 l be on stable envelopes\, as introduced by Maulik–Okounkov\, Okounkov\,
  and Aganagic–Okounkov\, and their deep connections to geometric represe
 ntation theory. We will outline a proof of the 3d mirror symmetry statemen
 t for elliptic stable envelopes on bow varieties\, based on a joint work w
 ith T. Botta.\n\nPeng Shan: Vertex algebras\, affine Springer fibres and 4
 d mirror symmetry\nWe will explain some results and conjectures about rela
 tionships between representation theory of simple affine Vertex algebras a
 nd the geometry of Hitchin fibrations\, which is related to dualities betw
 een Higgs and Coulomb branches for 4d N=2 super conformal field theory.\n\
 nEric Chen: S-duality in arithmetic and geometric contexts\nThe seminal wo
 rk of Kapustin--Witten posits that various Langlands-type equivalences can
  be organized under the framework of S-duality for a family of 4d gauge th
 eories. Following this assertion\, one would optimistcally expect the exis
 tence of a category L of boundary conditions which underlies calculations 
 of interest in this family of theories. Following an introduction to these
  ideas\, we will explain their relation to the recently emergent relative 
 Langlands program of Ben-Zvi—Sakellaridis--Venkatesh\, and survey some e
 xperiments one can conduct to further our understanding of S-duality on th
 e category L. \n\nSpecial Lecture by Yiannis Sakellaridis: L-functions a
 nd harmonic analysis\n The goal of this talk will be to explain the arith
 metic origins of the "relative" Langlands duality presented in the mini-co
 urse by Eric Chen. In particular\, I will give an overview of the role pla
 yed by harmonic analysis on spherical varieties and other interesting spac
 es in the study of (automorphic) L-functions\, and explain the relations b
 etween numerical and geometric statements. If time allows\, I will also di
 scuss possible extensions of this program that we currently do not underst
 and.
LOCATION:GA 3 21 https://plan.epfl.ch/?room==GA%203%2021
STATUS:CONFIRMED
END:VEVENT
END:VCALENDAR