報告題目：Boson-Fermion Correspondence and Its Applications to Integrable Hierarchies Revisited From The Point of View of Representation Theory and Random Walks
報 告 人：周堅(清華大學)
報告時間：2022年04月15日 10:00-12:00
報告地點：#騰訊會議：694-475-243
加入會議：https://meeting.tencent.com/dm/dbl4pDJLd3zS
報告摘要: We revisit the boson-fermion correspondence and its applications to integrable hierarchies via representation theory of symmetric groups. This makes it natural to consider random walks on various diagrams and graphs related to symmetric groups. Random partitions, hypergeometric tau-functions and weighted Hurwitz numbers are then brought together under a unified probabilistic treatment, rooted in their connections to the fermionic Fock space. Various approaches to the representation theory of symmetric groups all turn out to be useful in this treatment. They include: the new approach of Okounkov and Vershik, the Hopf algebra approach of Zelevinsky, and the lambda-ring approach of Knutson. A connection to the interpolating statistics in the study of fractional quantum Hall effect will also be explained.
報告人簡介：周堅，清華大學數學科學系教授，2005年國家傑出青年基金獲得者、2007年入選長江學者、2009年入選國家“百千萬人才工程”。他的研究領域為黎曼面的模空間與霍奇積分，拓撲場論，微分幾何，弦理論等。周堅教授通過對超弦理論中Vafa學派的工作中出現的一些數學問題的研究，揭示了一些不同的數學分支之間的内在聯系，他與合作者完成的“Marino-Vafa猜想的證明”入選2004年度“中國高校十大科技進展”。
