The Analysis and PDE Seminar will take place on Monday, April 17, in room 740, Evans Hall, from 4:10-5:00 pm.

Title: Control of water waves

Abstract: Water waves are disturbances of the free surface of a liquid. They are, in general, produced by the immersion of a solid body or by impulsive pressures applied on the free surface. The question we discuss in this talk is the following: which waves can be generated by blowing on a localized portion of the free surface. Our main result asserts that one can generate any small amplitude, periodic in x, two-dimensional, gravity-capillary water waves. This is a result from control theory. More precisely, we prove the local exact controllability of the incompressible Euler equation with free surface. This is a joint work with Pietro Baldi and Daniel Han-Kwan.

The Analysis and PDE Seminar will take place on Monday, April 10, in room 740, Evans Hall, from 4:10-5:00 pm.

Title: The Helicoidal Method II

Abstract: The helicoidal method is a new, extremely efficient way, of proving multiple vector valued inequalities in harmonic analysis. About a month ago, we gave a talk at MSRI, in which we explained some consequences of this method, such as the proof of sparse domination results for various multilinear operators, and their multiple vector valued extensions.

The main task of the current talk will be different (hence the II from the title) as we plan to discuss the ideas that led us to the method. One specific application that we also plan to present, is the proof of mixed norm estimates for paraproducts on the bidisk, in the full possible range of Lebesgue spaces, answering completely an open question of Kenig, from the early 90’s. Joint work with Cristina BENEA.