Seminars
Current Organizers: Dongchen Li, Jialun Li, Ronggang Shi, Ruxi Shi
Upcoming seminars
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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, SCMSAbstract: TBA
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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, SCMSAbstract: TBA
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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, SCMSAbstract: 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.
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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, SCMSAbstract: TBA
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Wooyeon Kim (Korea Institute For Advanced Study)
2025-11-12 14:00— Room 102, SCMSAbstract: TBA
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Dmitry Turaev (Imperial College London)
2025-12-10 16:00-17:00— Gu Lecture Hall, SCMSAbstract: TBA
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Chen Gong (西湖大学)
2025-12-24 14:00— Room 102, SCMSAbstract: TBA
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Jit Wu Yap (MIT)
2025-12-24 15:30— Room 102, SCMSAbstract: TBA
2025
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Simultaneously bounded and dense orbits for commuting Cartan actions
Chengyang Wu 吴乘洋 (Peking University)
2025-09-17 14:00— Room 102, SCMSAbstract: 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.
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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, SCMSAbstract: 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.
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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, SCMSAbstract: 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.