(2025/01/01-2025/12/31)
2025/11/07, 10:00 a.m., Tencent Meeting
Chen Zaoli (Cornell University)
Extreme Value Theory of Long-Range Dependent Sequences
In a long-range dependent setting, extreme values of a stationary processes exhibit both macroscopic and microscopic clustering features. Such an extremal clustering is subject to the dependence structure as well as the marginal distribution. In this talk, I will introduce the mechanism of a class of long-range dependent time series and its unique extremal behaviors. The talk is based on the following two articles.
[1] Extremal clustering under moderately long range dependence and moderately heavy tails, Z. Chen and G. Samorodnitsky, Stochastic Processes and Their Applications, 2022.
[2] Moderately Heavy Extreme Values under Extreme Long Range Dependence, Z. Chen, arXiv: 2505.23103.
2025/09/26, 10:00 a.m., Tencent Meeting
Lin Zhuowei (Nankai University, Center for Combinatorics)
The Combinatorics of Flagged Weyl Characters
In this talk, we introduce two aspects of flagged Weyl charcters, which can be restricted to Schubert polynomials. One is about coefficient-wise upper bounds and lower bounds of flagged Weyl charcters. This settles two conjectures proposed by Mészáros-St. Dizier-Tanjaya. The other one is about the principal specialization of Schubert polynomials, which improves the results previously obtained by Weigandt, Gao, and Mészáros-St. Dizier-Tanjaya.
Article1, Article2, and arXiv.
2025/07/04, 10:00 a.m., Tencent Meeting
Yang Zhilin (CAS)
Weak coupling limit of a Brownian particle in the curl of the 2D GFF
We study the weak coupling limit of the following equation in \(\mathbb{R}^2\): \[dX_t^\varepsilon=\frac{\hat{\lambda}}{\sqrt{\log\frac1\varepsilon}}\omega^\varepsilon(X_t^\varepsilon)dt+\nu dB_t,\quad X_0^\varepsilon=0. \] Here \(\omega^\varepsilon=\nabla^{\perp}\rho_\varepsilon*\xi\) with \(\xi\) representing the \(2d\) Gaussian Free Field (GFF) and \(\rho_\varepsilon\) denoting an appropriate identity. \(B_t\) denotes a two-dimensional standard Brownian motion, and \(\hat{\lambda},\;\nu>0\) are two given constants. We use the approach from to show that the second moment of \(X_t^\varepsilon\) under the annealed law converges to \((c(\nu,\hat\lambda)^2+2\nu^2)t\) with a precisely determined constant \(c(\nu,\hat\lambda)>0\), which implies a non-trivial limit of the drift terms as \(\varepsilon\) vanishes. We also prove that in this weak coupling regime, the sequence of solutions converges in distribution to \(\left(\sqrt{\frac{c(\nu,\hat\lambda)^2}{2}+\nu^2}\right)\widetilde{B}_t\) as \(\varepsilon\) vanishes, where \(\widetilde{B}_t\) is a two-dimensional standard Brownian motion.
2025/05/09, 10:00 a.m., Tencent Meeting
Xue Xiaolong (Tsinghua University)
The rigidity of eigenfunctions's gradient estimates
We introduce the rigidity results for eigenfunctions on Riemannian manifolds with nonnegative Ricci curvature. We also obtain the Li-Yau gradient estimate on convex domains and prove similar rigidity results.
Article in Mathematische Zeitschrift.
2025/02/26, 10:00 a.m., Tencent Meeting Password: ETDR
Yilong Zhang (Bonn University)
Green points in the reals
We construct an expansion of a real closed field by a multiplicative subgroup adapting Poizat's theory of green points Its theory is strongly dependent, and every open set definable in a model of this theory is semialgebraic. We prove that the real field with a dense family of logarithmic spirals, proposed by Zilber, satisfies our theory.