报告题目：Rank-based indices for testing independence between tw…

报 告 人：周叶青

时 间：11月11日上午10：00 - 11：00

地 点：6号楼二楼报告厅

简 介：To test independence between two high-dimensional random vectors, we propose three tests based on the rank-based indices derived from Hoeffding’s D, Blum-Kiefer-Rosenblatt’s R and Bergsma-Dassios-Yanagimoto’s τ∗. Under the null hypothesis of independence, we show that the distributions of the proposed test statistics converge to normal ones if the dimensions diverge arbitrarily with the sample size. We further derive an explicit rate of convergence. Thanks to the monotone transformation-invariant property, these distribution-free tests can be readily used to generally distributed random vectors including heavily tailed ones. We further study the local power of the proposed tests and compare their relative efficiencies with two classic distance covariance/correlation based tests in high dimensional settings. We establish explicit relationships between D, R, τ∗ and Pearson’s correlation for bivariate normal random variables. The relationships serve as a basis for power compari...

报告题目：Recent advances on categorical Torelli problems

报 告 人：张诗卓

时 间：2024年11月05日（周二） 上午 10:00 - 11:00

地 点：国交2号楼315会议室

简 介：Let X be a Fano variety(not necessarily smooth) and denote the non-trivial semi-orthogonal component by Ku(X)Ku(X), known as the Kuznetsov component. The categorical Torelli problem asks if Ku(X)Ku(X) determines the isomorphism class of XX. I will briefly talk about the history of this topic, including the known results and popular strategies to prove these results(Hodge theoretic, moduli space theoretic and Chow theoretic). Then, I will survey the recent advances for (weighted) hypersurfaces, a cubic threefold with a geometric involution, del Pezzo threefold of Picard rank one, and a class of nodal prime Fano threefolds. Meanwhile, I will talk about infinitesimal version of categorical Torelli problem. If time permits, I will also speak about categorical Torelli problems for a class of index one prime Fano threefold as the double cover of del Pezzo threefolds. This talk is based on a series of works with Daniele Faenzi,Xun Lin, Zhiyu Liu, Soheyla Feyzbakhsh, Jorgen Renneomo, Xianyu...

报告题目：The magnitude of Nakayama algebras

报 告 人：沈大伟

时 间：2024年10月29日上午10:30—11:30

地 点：腾讯会议：918-261-712

简 介：The magnitude for algebras is a generalization of the Euler characteristic. We investigate the magnitude for Nakayama algebras. Using Ringel’s resolution quiver, the existence and the value of rational magnitude is given. As a result, we show directly that the finite global dimension criteria for Nakayama algebras of Madsen and the first author are equivalent.