Modular invariance of (logarithmic) intertwining operators

發(fā)布者:文明辦發(fā)布時間:2023-06-26瀏覽次數(shù):676

主講人:黃一知 美國羅格斯大學(xué)(Rutgers University)教授


時間:2023年6月30日15:30


地點:三號樓301室


舉辦單位:數(shù)理學(xué)院


主講人介紹:黃一知,美國羅格斯大學(xué)(Rutgers University)教授,國際上著名的頂點算子理論和理論物理學(xué)專家,主要研究興趣是建立量子場理論的數(shù)學(xué)基礎(chǔ),及其在代數(shù)學(xué),拓撲學(xué),幾何學(xué),凝聚態(tài)物理和弦理論上的應(yīng)用,他的代表性研究工作包括建立公理化的頂點算子代數(shù)的定義,頂點算子代數(shù)的張量范疇理論的研究,頂點算子代數(shù)框架下一般形式的Verlinde猜想的證明,并以此為基礎(chǔ)證明了大量的重要定理等。黃一知教授出版學(xué)術(shù)專著一部,撰寫和發(fā)表研究論文80余篇,多數(shù)發(fā)表在國際頂尖數(shù)學(xué)雜志上,如《Duke Mathematical Journal》,《Communications in Mathematical Physics》等,他引次數(shù)超過1600次。黃一知教授還是國際知名數(shù)學(xué)雜志《Communications in Contemporary Mathematics》的主編,《New York Journal of Mathematics》的編委等。


內(nèi)容介紹: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 invariance 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.