Speaker: Pan Yan,
Abstract: Let $E/F$ be a quadratic extension of local nonarchimedean fields of characteristic zero and let $D$ be a quaternion algebra over $F$ containing $E$. Let $G=\mathrm{GL}_n(D)$, $H=\mathrm{GL}_n(E)$, and let $\chi$ be a character of $E^\times$. In this talk, we will talk about recent work towards a conjecture of Prasad and Takloo-Bighash, which predicts when an irreducible admissible representation $\pi$ of $G$ is $(H,\chi)$-distinguished in terms of the local epsilon factor of $\pi$. Our main approach is a relative trace formula proposed by Hang Xue and Wei Zhang. This is joint work with Hang Xue.
Room: 216, East 32 Building.
Time: May 28, 14:00-15:00.
Speaker: Li Cai (蔡立), 首都师范大学
Abstract: In both local and global settings, we establish explicit relations between Ichino triple product period and Waldspurger toric periods for CM forms via the theta lifting and the see-saw principle. This is a joint work with Yangyu Fan and Yong Jiang.
Room: 216, East 32 Building.
Time: Aug 26, 16:00-17:00.
Speaker:Wei Xiong, 熊玮，湖南大学
Abstract: Shimura在上个世纪70年代建立了半整权模形式的系统理论并得到了从半整权模形式到整权模形式的一个对应, 随后Waldspurger为了推广Shimura对应而建立了Theta提升理论并得到了 关于半整权模形式的傅里叶系数的若干结果, 随后Tunnell利用Waldspurger的结果得到了一个特殊值公式并用来研究同余数. 在这个报告中, 我们将回顾下之前这些结果并讨论我们 为了推广Tunnell公式而得到的关于Theta提升的一些结果(与田野教授和何伟博士合作获得).
Room: 216, East 32 Building.
Time: Oct 9, 16:30-17:30.
Speaker: 王好武（武汉大学）
Abstract: Singular automorphic products are modular forms of minimal weight that have infinite product expansions at cusps. In this talk we will discuss some relations between such functions and Lie algebras in two cases. We first introduce an one-to-one correspondence between Jacobi forms and affine Lie algebras. We then explain some new relations between modular forms on O(n,2), Borcherds--Kac--Moody Lie algebras, vertex operator algberas, motivated by the famous moonstrous moonshine conjecture and Borcherds' celebrated proof.
Time: Oct 17, 15:30-16:30.