报告题目：Boson-Fermion Correspondence and Its Applications to Integrable Hierarchies Revisited From The Point of View of Representation Theory and Random Walks

报 告 人：周坚(清华大学)

报告时间：2022年04月15日 10:00-12:00

报告地点：#腾讯会议：694-475-243

加入会议：https://meeting.tencent.com/dm/dbl4pDJLd3zS

报告摘要: 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.

报告人简介：周坚，清华大学数学科学系教授，2005年国家杰出青年基金获得者、2007年入选长江学者、2009年入选国家“百千万人才工程”。他的研究领域为黎曼面的模空间与霍奇积分，拓扑场论，微分几何，弦理论等。周坚教授通过对超弦理论中Vafa学派的工作中出现的一些数学问题的研究，揭示了一些不同的数学分支之间的内在联系，他与合作者完成的“Marino-Vafa猜想的证明”入选2004年度“中国高校十大科技进展”。