动力系统研究中心

数学研究所

学术报告

动力系统研究中心

报告人：Reda Chhaibi (Université Paul Sabatier, Toulouse)
   

题  目：Infinite Curvature on H^3, Pitman's Theorem, and Quantum SL_2
   

时  间：2024.08.05（星期一）13：30-14：30
   

地  点：南楼N913

摘  要：We will start by recalling Pitman's classical Theorem in probability. It states that a simple 

random walk minus twice its running infimum enjoys the Markov property -- miraculously.In the

 continuous diffusive setting, we will explain how this property in law can be interpreted as a 

curvature interpolation in the hyperbolic half-space H^3 = SL_2 / SU_2. Furthermore the continuous 

version is better understood as the semi-classical limits of quantum random walks on the 

Jimbo-Drinfeld quantum group U_q(sl_2).
   

If time permits, we will also present the relevance of Pitman's theorem and its generalizations 

to Random Matrix Theory and Directed Percolation.This talk is based on ongoing work and joint 

work with François Chapon. Chapon, F., Chhaibi, R. Quantum , infinite curvature and Pitman’s 

2M-X theorem. /Probab. Theory Relat. Fields/ *179*, 835–888 (2021). 

https://doi.org/10.1007/s00440-020-01002-8
   

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报告人：Jialun Li (École Polytechnique, Paris)
   

题  目：Density of shapes of periodic tori in the cubic case
   

时  间：2024.08.05（星期一）15：00-16：00
   

地  点：南楼N913

摘  要：Given a compact orbit of diagonal action on $\SL(3,\R)/\SL (3,\Z)$,

 the set of periods of the orbit forms a lattice in the diagonal group, which can be

 identified with $\Z^2$. We refer to this lattice as the shape of the compact orbit, 

which can be identified as a point in $\SL (2,\R)/\SL(2,\Z)$ after re-scaling to

 covolume one.
   

We prove that in $\SL(3,\R)/\SL (3,\Z)$ the shapes of periodic tori are dense in 

$\SL (2,\R)/\SL(2,\Z)$. The dense family of shapes are constructed explicitly 

from a family of cubic orders and their suborders. The talk is based on an 

ongoing joint work with Thi Dang and Nihar Gargava.