q-Series and Partition Congruences

活动时间： 03月30日15时00分       

地            点  ： 数信学院D-203室

讲座内容：

The theory of q-series has been developed for morethan two hundred years. It has popped up in work in classical analysis, Liealgebras, physics, number theory, and combinatorics. In this talk, we mainlyfocus on Ramanujan's theta functions and q-series and their connections withpartition congruences. Especially, in view of the modular equations of fifthand seventh order, we establish many congruences for a certain kind ofpartition functions. Furthermore, with the aid of dissection identities ofRamanujan's theta functions, we derive some congruence properties of l-regularpartition functions and broken k-diamond partition functions. Finally, wediscuss congruences for some partition functions related to mock thetafunctions.

主讲人介绍：

谷珊珊，南开大学组合数学中心教授、博士生导师。2002年毕业于河北师范大学，2007年获得南开大学博士学位。主要研究方向为代数组合学，尤其在q-级数恒等式的证明与推广、分拆同余等方面取得了一系列成果，主要结果发表在Advances in Mathematics，Mathematics of Computation，Journal of Combinatorial Theory.Series A等。首次建立的关于分拆等式的循环方法被广泛应用到分拆同余的研究中，相关论文被Advances in Applied Mathematics评为该杂志“最高频次引用论文”，被Web of Science评为“高被引论文”。

发布时间：2018-03-27 10:15:42