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BEGIN:VEVENT
UID:78ed3afbe49b3e4b713d799aaf8a7d28
CATEGORIES:Lie Group Quantum Mathematics Seminar
CREATED:20230410T101642
SUMMARY:Modular invariance of logarithmic intertwining operators
LOCATION:Hill 705
DESCRIPTION:<p><strong style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (W
 est European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Hel
 vetica Neue', sans-serif; font-size: 15px; letter-spacing: normal; orphans:
  2; text-align: start; text-indent: 0px; text-transform: none; white-space:
  normal; widows: 2; word-spacing: 0px; background-color: #ffffff;">Abstract
 &nbsp;</strong>I will discuss a proof of the conjecture of almost twenty ye
 ars&nbsp;on the modular invariance of (logarithmic) intertwining operators.
 <br style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web (West Eur
 opean)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'Helvetica 
 Neue', sans-serif; font-size: 15px; font-weight: 400; letter-spacing: norma
 l; orphans: 2; text-align: start; text-indent: 0px; text-transform: none; w
 hite-space: normal; widows: 2; word-spacing: 0px; background-color: #ffffff
 ;" aria-hidden="true">Let V be a C_2-cofinite vertex operator algebra of po
 sitive energy.The conjecture states that the vector space spanned by pseudo
 -q-traces<br style="color: #242424; font-family: 'Segoe UI', 'Segoe UI Web 
 (West European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Roboto, 'H
 elvetica Neue', sans-serif; font-size: 15px; font-weight: 400; letter-spaci
 ng: normal; orphans: 2; text-align: start; text-indent: 0px; text-transform
 : none; white-space: normal; widows: 2; word-spacing: 0px; background-color
 : #ffffff;" aria-hidden="true">shifted by -c/24 of products of (logarithmic
 ) intertwining operators&nbsp;among grading-restricted generalized V-module
 s is a module for<br style="color: #242424; font-family: 'Segoe UI', 'Segoe
  UI Web (West European)', 'Segoe UI', -apple-system, BlinkMacSystemFont, Ro
 boto, 'Helvetica Neue', sans-serif; font-size: 15px; font-weight: 400; lett
 er-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; text-t
 ransform: none; white-space: normal; widows: 2; word-spacing: 0px; backgrou
 nd-color: #ffffff;" aria-hidden="true">the modular group SL(2, Z). In 2015,
  Fiordalisi proved that such&nbsp;pseudo-q-traces are absolutely convergent
  and have the genus-one<br style="color: #242424; font-family: 'Segoe UI', 
 'Segoe UI Web (West European)', 'Segoe UI', -apple-system, BlinkMacSystemFo
 nt, Roboto, 'Helvetica Neue', sans-serif; font-size: 15px; font-weight: 400
 ; letter-spacing: normal; orphans: 2; text-align: start; text-indent: 0px; 
 text-transform: none; white-space: normal; widows: 2; word-spacing: 0px; ba
 ckground-color: #ffffff;" aria-hidden="true">associativity property and som
 e other properties. Recently, I have&nbsp;proved this conjecture completely
 . This modular invariace gives<br style="color: #242424; font-family: 'Sego
 e UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-system, BlinkMacS
 ystemFont, Roboto, 'Helvetica Neue', sans-serif; font-size: 15px; font-weig
 ht: 400; letter-spacing: normal; orphans: 2; text-align: start; text-indent
 : 0px; text-transform: none; white-space: normal; widows: 2; word-spacing: 
 0px; background-color: #ffffff;" aria-hidden="true">a construction of C_2-c
 ofinite genus-one logarithmic conformal field&nbsp;theories. It might play 
 an important role in the future proofs of the<br style="color: #242424; fon
 t-family: 'Segoe UI', 'Segoe UI Web (West European)', 'Segoe UI', -apple-sy
 stem, BlinkMacSystemFont, Roboto, 'Helvetica Neue', sans-serif; font-size: 
 15px; font-weight: 400; letter-spacing: normal; orphans: 2; text-align: sta
 rt; text-indent: 0px; text-transform: none; white-space: normal; widows: 2;
  word-spacing: 0px; background-color: #ffffff;" aria-hidden="true">conjectu
 res on the corresponding braided tensor categories, especially&nbsp;their r
 igidity and modularity.</p>
CONTACT:  Speaker Yi-Zhi Huang, Rutgers University
DTSTAMP:20260828T093747
DTSTART;TZID=America/New_York:20230428T121000
DTEND;TZID=America/New_York:20230428T131000
SEQUENCE:0
TRANSP:OPAQUE
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