»ã±¨±êÌâ (Title)£º£¨¶ÔÊý£©²ø½áËã×ÓµÄÄ£²»±äÐÔ£¨Modular invariance of (logarithmic) intertwining operators£©

»ã±¨ÈË (Speaker)£º »ÆÒ»Öª ½ÌÊÚ£¨ÃÀ¹úRutgers´óѧ)

»ã±¨¹¦·ò (Time)£º2023Äê6ÔÂ27ÈÕ (Öܶþ) 16:00-17£º00

»ã±¨µØÖ· (Place)£ºÐ£±¾²¿F309

Ô¼ÇëÈË(Inviter)£ºÕźìÁ« ½ÌÊÚ

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»ã±¨ÌáÒª£º I will discuss a proof of a conjecture of almost twenty years on the modular invariance of (logarithmic) intertwining operators. Let V be a C_2-cofinite vertex operator algebra without nonzero elements of negative weights. The conjecture states that the vector space spanned by pseudo-q-traces shifted by -c/24 of products of (logarithmic) intertwining operators among grading-restricted generalized V-modules

is a module for the modular group SL(2, Z). In 2015, Fiordalisi proved that such pseudo-q-traces are absolutely convergent and have the genus-one associativity property and some other properties. Recently, I have proved this conjecture completely. This modular invariace result gives a construction of C_2-cofinite genus-one logarithmic conformal field theories. We expect that it will play an important role in the study of problems and conjectures on C_2-cofinite logarithmic conformal field theories. The talk will start with the meaning of modular transformations and the definition of vertex operator algebras.