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SUMMARY:Holomorphic-topological field theories and representation theory
DTSTART:20251103T130000Z
DTEND:20251107T220000Z
DTSTAMP:20260312T132700Z
UID:indico-event-1214@events.perimeterinstitute.ca
CONTACT:conferences@perimeterinstitute.ca
DESCRIPTION:\nHolomorphic-topological field theories and representation th
 eory\n \nHolomorphic-topological (HT) field theories form a fascinating c
 lass of quantum field theories. These theories combine features of topolog
 ical quantum field theories (TQFT) and conformal field theories (CFT).\n 
 \nDue to the mixed holomorphic-topological nature of such theories\, they 
 create interactions between TQFT data (e.g.\, algbras\, monoidal categorie
 s\, etc) and CFT data (e.g.\, chiral algebras and chiral categories). This
  leads to exciting new mathematical structures\, and connections to integr
 able systems\, quantum topology and many other areas of mathematics. Recen
 tly. much progress has been made on the representation-theoretic aspects o
 f HT theories. Examples include:\n \n1. (Shifted) Poisson vertex algebras
  and their quantizations are constructed from local operators in HT theori
 es.\n \n2. Dimensional reduction of 4d HT theories lead to integrable sys
 tems and solutions of quantum Yang-Baxter equations.\n \n3. 4d N=2 theori
 es are linked to representation theory of K-theoretic Coulomb branches\, c
 luster algebra categorifications\, wall crossings and elliptic stable enve
 lops.\n \n4. New examples of chiral algebras and their dualities are deri
 ved from boundary conditions and dualities of 3d HT theories.\n \nMoreove
 r\, many interesting TQFTs are given by deformations of holomorphic-topolo
 gical theories. Examples include topological twists of 3d N=4 and 4d N=2 t
 heories. These theories have attracted considerable attention in recent ye
 ars for their connections to 3d mirror symmetry and the Langlands program.
  Some of these TQFTs only admit Lagrangian descriptions as HT QFTs\, and t
 herefore studying HT theories offers a possible approach for understanding
  these non-Lagrangian TQFTs.\n \nThis conference will focus on the repres
 entation-theoretic aspects of HT theories\, particularly:\n \n1. Chiral a
 lgebras arising from observables of HT QFT.\n \n2. Quantum algebras\, inc
 luding Yangians and quantum affine algebras\, and their relation to HT the
 ories.\n \n3. Chiral categories and OPE of line operators in HT theories.
 \n \n4. Deformation of HT theories and their relation to chiral algebra d
 eformations.\n \n5. Relation between various HT theories under dimensiona
 l-reduction.\n \nWe aim to bring together leading mathematicians and phys
 icists\, to inform each other about the recent progress made in this area.
 \n::  ::  ::\n \nFinancial support provided in part by The Fields Insti
 tute for Research in Mathematical Sciences. \n \n\n \n::  ::  ::\nCon
 ference Speakers\n\n\n\nMina Aganagic (University of California\, Berkeley
 )\n\n\nChristopher Beem (University of Oxford)\n\n\nTudor Dimofte (Univers
 ity of Edinburgh)\n\n\nSergei Gukov (California institute of Technology)\n
 \n\nHans Jockers (Johannes Gutenberg University Mainz)\n\n\nAhsan Khan (Ha
 rvard University)\n\n\nSatoshi Nawata (Fudan University)\n\n\nAndrew Neitz
 ke (Yale University)\n\n\nTony Pantev (University of Pennsylvania)\n\n\nHa
 rold Williams (University of Southern California)\n\n\nBrian Williams (Bos
 ton University)\n\n\n\n \nWorkshop OrganizersDavide GaiottoWenjun NiuBen 
 Webster\n\nhttps://events.perimeterinstitute.ca/event/1214/
LOCATION:PI/4-405 - Bob Room (Perimeter Institute for Theoretical Physics)
URL:https://events.perimeterinstitute.ca/event/1214/
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