Simultaneously bounded and dense orbits for commuting Cartan actions
Chengyang Wu 吴乘洋 (Peking University)
2025-09-17 14:00— Room 102, SCMS

Abstract: With the goal to attack Uniform Littlewood’s Conjecture proposed in [BFK25], we introduced the concept of ``fiberwise nondivergence’’ for the action of a cone inside the full diagonal subgroup of SL_3(R). Then it is proved in our paper that there exists a dense subset of SL_3(R)/SL_3(Z) in which each point has a fiberwise non-divergent orbit under a cone inside the full diagonal subgroup and an unbounded orbit under every diagonal flow. Our proof also presented the first instance of results concerning simultaneously bounded and dense orbits for commuting actions on noncompact spaces. This is a joint work with Dmitry Kleinbock.

The natural flow on infinite volume locally symmetric spaces
Shi Wang 汪湜 (Shanghai Tech / 上海科技大学)
2025-09-30 14:00— Room 102, SCMS

Abstract: Motivated by the work of Besson-Courois-Gallot, we define a gradient flow using the Patterson-Sullivan theory. We show the flow has certain volume contracting properties if the critical exponent is small enough. This leads to many applications in geometry and topology. Finally, we will mention a related subexponential growth condition on the Patterson-Sullivan measures and how this condition connects to the finiteness of the Bowen-Margulis measure in certain cases. This is joint work with Chris Connell and Ben McReynolds.

Fourier and other aspects on multiplicative chaos
Yanqi Qiu 邱彦奇 (国科大杭州高等研究院)
2025-10-15 14:00— Room 102, SCMS

Abstract: I will review our recent processes on Fourier decay of random measures arising from Kahane’s T-martingale theory, including Mandelbrot Cascades (canonical or microcanonical), Gaussian Multiplicative Chaos, Random Coverings and more abstract ones. If time allows, I shall also mention some more recent work on a class of new critical multiplicative chaos random measures. The talk is based on a series of joint works with Xinxin Chen, Yong Han, Zipeng Wang, and with Zhaofeng Lin, Mingjie Tan, as well as with Yukun Chen, Zhaofeng Lin, and with Ma Heng, Yushu Zheng.

Generalized u-Gibbs measures for C^\infty systems (1)
David Burguet (CNRS & Université de Picardie Jules Verne)
2025-10-28 12:00-2:00— Gu Lecture Hall, SCMS

Abstract: TBA

Generalized u-Gibbs measures for C^\infty systems (2)
David Burguet (CNRS & Université de Picardie Jules Verne)
2025-10-29 13:00-15:00— Gu Lecture Hall, SCMS

Abstract: TBA

Global rigidity for higher rank group actions on manifolds: Zimmer program and Katok-Spatzier conjecture
Disheng Xu 许地生 (Great Bay university / 大湾区大学)
2025-10-29 15:30— Room 102, SCMS

Abstract: Zimmer’s superrigidity theorems on higher rank Lie groups and their lattices launched a program of study aiming to classify actions of semisimple Lie groups and their lattices, known as the Zimmer program. When the group is too large relative to the dimension of the phase space, the Zimmer conjecture predicts that the actions are all virtually trivial. At the other extreme, when the actions exhibit enough regular behavior, the actions should all be of algebraic origin. We make progress in the program by showing smooth conjugacy to a bi-homogeneous model for volume-preserving actions of semisimple Lie groups without compact or rank one factors, under mild assumptions: partial hyperbolicity for “many” of elements and accessibility. We also obtain classification for actions of higher-rank abelian groups under certain hyperbolicity assumptions, i.e. progress to the (generalized) Katok-Spatzier conjecture. Joint work with D. Damjanovic, R. Spatzier and K. Vinhage.

Generalized u-Gibbs measures for C^\infty systems (3)
David Burguet (CNRS & Université de Picardie Jules Verne)
2025-10-30 15:00-17:00— Gu Lecture Hall, SCMS

Abstract: TBA

Escape of mass for higher rank diagonal actions
Wooyeon Kim (Korea Institute For Advanced Study)
2025-11-12 14:00— Room 102, SCMS

Abstract: We discuss the escape of mass for higher-rank diagonal actions on the space of lattices and its applications to the inhomogeneous version of the Littlewood conjecture. We first show that the Hausdorff dimension of the set of points that are A-divergent on average in the (d−1)-dimensional closed horosphere in the space of d-dimensional Euclidean lattices, where A is the group of positive diagonal matrices, is at most (d−1)/2. Using these dimension estimates on mass and entropy escape for higher-rank diagonal actions, we then compute the Hausdorff dimension of the exceptional set for the inhomogeneous uniform version of the Littlewood conjecture.

Spectral theory of free group representations
Jean-Francois Quint (CNRS & Montpellier University)
2025-11-14 09:30-10:30— Room 102, SCMS

Abstract: In this talk, I will define a new family of unitary representations of (virtually) free groups. The interest of these representations lies in the fact that for them, certain spectral invariants may be computed explicitely.

A conditioned local limit theorem via heat kernel approximation
Ion Grama (Universite Bretagne-Sud)
2025-11-14 11:00-12:00— Room 102, SCMS

Abstract: We study a real-valued random walk with centered increments and a finite (2+delta)-moment. Using a previously established approximation of the Gaussian heat kernel for persistence probabilities, we prove a new local limit theorem conditioned by the exit time from the half-line. This result unifies and generalizes existing theorems and provides uniform asymptotics with respect to both the starting and ending points.

Counting rational approximations on grassmannians
René Pfitscher (USTC / 中科大)
2025-11-26 14:00— Room 102, SCMS

Abstract: In the divergence case of Khintchine’s theorem, Schmidt obtained an asymptotic formula for the number of rational approximations of bounded height to almost every real number. We prove a version of this result for intrinsic Diophantine approximation on Grassmannians. The proof relies on an L^{1+\epsilon}-integrability property of a Siegel transform naturally associated with the Grassmannian, together with the effective single and double equidistribution property of translated orbits of maximal compact subgroups, results of independent interest.