Sep 12 
Gaétan Leclerc Sorbonne Universite 
Fourier dimension and dynamical fractals.
Abstract: Consider the triadic Cantor set equipped with the "uniform" Cantor law. It happens that its cumulative distribution function, the devil’s staircase, is Hölder regular, and its best exponent of regularity is ln(2)/ ln(3), which is exactly the Hausdorff dimension of the Cantor set. Moreover, one can show that the Fourier transform of the Cantor law decay like ξ^{− ln 2/ ln 3} "on average". This is no coincidence, and hint for a deeper link between Fractal Geometry and Fourier Analysis. In this talk we will detail and explore this link through the notion of Fourier Dimension. We will introduce the Fourier dimension, compute it on some easy examples, quote some natural questions that arise, and then discuss a (partial) state of the art on the topic.

Sep 19 
Chengyang Shao U Chicago 
Advances in Spherical Capillary Water Waves System.
Abstract: The speaker aims to report some advances in the study of irrotational oscillation of a water droplet under zero gravity. The governing physical laws, resembling the wellstudied capillary water waves equation, are converted to a quasilinear dispersive paradifferential system defined on the 2sphere. Regarding this conversion, a coordinateindependent, global paradifferential calculus defined on compact Lie groups and homogeneous spaces is developed as a toolbox. After discussing Cauchy theory under this novel formalism, the speaker will propose several unsolved problems concerning existence of periodic solutions, normal form reduction and generic lifespan estimates. It is pointed out that all of these problems are closely related to certain Diophantine equations.

Sep 26 
Felipe Hernandez MIT 
The semiclassical limit of noisy quantum systems
Abstract: Although the laws of physics are quantum mechanical, the world we live in and observe is well described by classical physics. One mathematical justification for this is Egorov’s theorem which shows that the quantum and classical descriptions match as the semiclassical parameter ℏ tends to 0. However, the Ehrenfest timescale for which Egorov’s theorem holds may only be seconds or minutes for realistic systems. In this talk we consider quantum systems that are weakly coupled to a noisy external environment, as modelled by the Lindblad equation. The semiclassical limit of this Lindblad equation is a FokkerPlanck equation which includes the effects of friction and diffusion. In this talk I will show that even for very weak diffusion, the agreement between the Lindblad and FokkerPlanck equations persists for times much longer than the Ehrenfest time. This is joint work with Daniel Ranard and Jess Riedel.

Oct 3 Room 4231 
Benjamin Dodson Johns Hopkins 
Global wellposedness and scattering for the conformal nonlinear wave equation in higher dimensions with radial data.
Abstract: In this talk, we prove global wellposedness and scattering for the conformally invariant, radially symmetric nonlinear wave equation in the defocusing case. This result is sharp in the radial case. We spend the first half of the talk discussing the broader context of the nonlinear wave equation. We also explain why the result is sharp.

Oct 10 
Indigineous Peoples Day 

Oct 17 


Oct 24 
Jacek Jendrej CNRS and Université Sorbonne Paris Nord 
TBA 
Oct 31 
Gregory Berkolaiko Texas A&M 
TBA 
Nov 7 


Nov 14 
Giovanni Forni University of Maryland 
TBA 
Nov 21 


Nov 28 
Lei Yang Institute for Advanced Study 

Dec 5 


Dec 12 

