AbstractI 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 d...
AbstractIn this talk, we introduce some recent results on properties of solutions to fractional and higher order systems. For instance, the classification of solutions to conformally invariant systems with mixed order and exponentially increasing or nonlocal nonlinearity, and the uniform a priori estimates for positive solutions to the n-th order superlinear Lane-Emden system in bounded domains...