报告题目：Shuffle algebras and their integral forms: specializat…

报 告 人：胡越

时 间：2025年4月18日（周五）下午15：00-16：00

地 点：国交2号楼315会议室

简 介：Shuffle algebras were introduced by Feigin-Odesskii, whose benefit is that it provides a combinatorial model for the positive subalgebra of quantum loop algebras in new Drinfeld realization. Enriquez conjectured, and recently proved by Negut-Tsymbaliuk, that the images of this algebra embedding are governed by certain wheel conditions. Another approach to address Enriquez conjecture is by utilizing certain specialization maps. For type A, this was accomplished through works of Feigin, Negut, and Tsymbaliuk. In this talk, we shall generalize the specialization map approach to types B,C,D,G. As a significant application, we also construct a family of PBW bases for the positive subalgebra of quantum loop algebras in these types, as well as their integral forms.

报告题目：Two-stage estimation and bias-corrected empirical like…

报 告 人：Liugen Xue

时 间：2024年4月8日（周二）上午10:00

地 点：国交2号楼315会议室

简 介： In this talk, we study the estimation and empirical likelihood (EL) of the parameters of interest in a partially linear single-index varying-coefficient model. A two-stage method is presented to estimate the regression parameters and the coefficient functions. The asymptotic distributions of the proposed estimators are obtained. Furthermore, a bias-corrected EL ratio for the regression parameters is proposed. It is shown that the ratio is asymptotically standard chi-squared. The result can be directly used to construct the EL confidence regions of the regression parameters. Simulation studies are carried out to evaluate the finite sample behavior of the proposed method. An application example of a real data set is given.

报告题目：Logarithmic Sobolev inequality and ABP method

报 告 人：王国芳

时 间：2025年4月1日（周二）上午10:30-11:30

地 点：国交2号楼315会议室

简 介：The Euclidean Logarithmic Sobolev inequality plays an important role in many fields. By extending the recent work of Brendle, we use the ABP method to give a new proof of it. Moreover we prove an optimal logarithmic Sobolev inequality for noncampact self-shrinkers. The method is robust and can be used to prove various logarithmic Sobolev inequalities. The talk is based on joint work with Chao Xia and Xiqiang Zhang.