Abstract:

I will describe joint work in progress with Aaron Brown, Federico Rodriguez-Hertz and Simion Filip. Our aim is to find some analogue,in the context of smooth dynamics,of Ratner's theoremson unipotent flows. This would be a (partial) generalization of the results of Benoist-Quint and my work with Elon Lindenstrauss in the homogeneous setting, the results of Brown and Rodriguez-Hertz in dimension 2, and my results with Maryam Mirzakhani in the setting of Teichmuller dynamics.

Bio:

Prof. Alex Eskin is currently the Arthur Holly Compton Distinguished Service Professor at the University of Chicago. He is a world leading expert in the field of Dynamical System. He received his PhD in 1993 from Princeton University. Prof.Eskin receives many awards and honors that includes invited speaker at 1998 and 2010 ICM, Clay Research Award (2007), Simons Investigator Award (2014), member of AAAS (2011) and National Academy of Science (2015), Breakthrough Prize (2020).