# Seminars & Events for Analysis Seminar

##### Geometric convolutions and Fourier restriction beyond curves and hypersurfaces

I will present recent results relating to two problems in Fourier analysis, L^p-improving properties of convolutions with singular measures and the Fourier restriction problem, both of which deal with the analysis of operators associated to submanifolds of Euclidean space. In both cases the theory is much more well-developed for curves and hypersurfaces than it is for submanifolds of intermediate dimension. This relative lack of

##### Honeycomb structures, Dirac points and Edge States

``Edge states" are a type of energy-localization along a line-defect, an interface between two different media. Topologically protected edge states are a class of edge states which are stable to strong local distortions of the edge. We present recent results on such states in continuous honeycomb structures. This is joint work with C.L. Fefferman and J.P. Lee-Thorp.

##### On a polynomial Carleson operator along the paraboloid

Since Carleson’s original work, the study of the Carleson operator has been taken in many directions, including new methods of proof, higher dimensions, and versions called polynomial Carleson operators with polynomial rather than linear phase. This talk will describe joint work with Po-Lam Yung (Chinese University of Hong Kong) in a new direction of enquiry, studying a polynomial Carleson operator along the paraboloid.

##### Boundary layer separation for stationary Prandtl

**This is a joint Analysis of Fluids & Related Topics and Analysis seminar. **We give a rigorous proof of the speed at which Boundary layer separation occurs in Prandtl system. In particular this justifies a heuristic rate proposed by Landau and formal asymptotic expansions proposed by Goldstein and Stewartson. The proof is based on the construction of an approximate solution, energy estimates and maximum principle. Joint work with Anne-Laure Dalibard (UPMC).