Square function estimates on curved hypersurfaces play a fundamental role in Harmonic Analysis,  and their application to PDEs. They are connected with Fourier restriction estimates, may be embedded in the same family of estimates as Fourier decoupling, and related to local smoothing inequalities. In this minicourse, we will examine a general model of directional square function estimates, its connection to Kakeya and Nikodym maximal functions, and its application to sharp bounds for polyhedral multipliers. We will also explore the proof of the square function estimate for the three dimensional cone by Guth, Wang and Zhang and its connection to local smoothing.

The course will take place at the Maryam Mirzakhani Seminar Room at the Basque Center for Applied Mathematics (BCAM), Bilbao, Spain. 

The 10 hour course, will be from Monday to Friday, 15:00-17:00.