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UID:d1eb6e86f94363a2f9f5d443330d4dcb
CATEGORIES:Lie Group Quantum Mathematics Seminar
CREATED:20240330T194736
SUMMARY:Conformal blocks for C_2-cofinite vertex operator algebras
LOCATION:Hill 705
DESCRIPTION:Vertex operator algebras (VOAs) mathematically characterize 2d conformal fi
 eld theories. For C_2-cofinite and rational VOAs (plus some minor assumptio
 ns), Yi-Zhi Huang proved that their representation categories are rigid mod
 ular tensor categories. For C_2-cofinite (not necessarily rational) VOAs, H
 uang-Lepowsky-Zhang proved that their representation categories are braided
  tensor categories, which mean that the rigidity and modularity are still o
 pen problems. Geometrically, one of the main reasons is that, for C_2-cofin
 ite VOAs, their conformal blocks associated to compact Riemann surfaces of 
 genera 1 were not clear at that time. In 2023, Yi-Zhi Huang proved that suc
 h conformal blocks can be expressed by pseudotraces of genus 0 conformal bl
 ocks (intertwining operators). This result is expected to be used to prove 
 rigidity (and hence modularity).\nIn this talk, I will introduce a systemat
 ic approach towards higher genus conformal blocks for C_2-cofinite VOAs and
  explain the relationship between our work and Yi-Zhi Huang’s results above
 . This is based on an ongoing project (arXiv: 2305.10180) joint with Bin Gu
 i.\n
X-ALT-DESC;FMTTYPE=text/html:<p>Vertex operator algebras (VOAs) mathematically characterize 2d conformal
  field theories. For C_2-cofinite and rational VOAs (plus some minor assump
 tions), Yi-Zhi Huang proved that their representation categories are rigid 
 modular tensor categories. For C_2-cofinite (not necessarily rational) VOAs
 , Huang-Lepowsky-Zhang proved that their representation categories are brai
 ded tensor categories, which mean that the rigidity and modularity are stil
 l open problems. Geometrically, one of the main reasons is that, for C_2-co
 finite VOAs, their conformal blocks associated to compact Riemann surfaces 
 of genera 1 were not clear at that time. In 2023, Yi-Zhi Huang proved that 
 such conformal blocks can be expressed by pseudotraces of genus 0 conformal
  blocks (intertwining operators). This result is expected to be used to pro
 ve rigidity (and hence modularity).</p><p>In this talk, I will introduce a 
 systematic approach towards higher genus conformal blocks for C_2-cofinite 
 VOAs and explain the relationship between our work and Yi-Zhi Huang’s resul
 ts above. This is based on an ongoing project (arXiv: 2305.10180) joint wit
 h Bin Gui.</p>
CONTACT:Hao Zhang, Tsinghua University 
DTSTAMP:20260831T030734
DTSTART;TZID=America/New_York:20240419T121000
DTEND;TZID=America/New_York:20240419T131000
SEQUENCE:0
TRANSP:OPAQUE
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