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.