HSM Special Topic Schools

Because of the ubiquity of Fourier analysis, oscillatory integrals are present in many techniques in both harmonic analysis and analytic number theory. Current state-of-the-art methods in both fields are pushing beyond classical methods because of increased importance of understanding the uniformity and stability of the estimates. In addition, researchers are uncovering unifying ideas that span the (traditionally somewhat separated areas) of oscillatory integrals in the setting of analysis, and character sums in number theory. Recent work on estimating oscillatory integrals have even applied model theory, from logic. This summer school will give participants an introduction on the classical methods for estimating oscillatory integrals and explain current cutting-edge developments. Throughout, the lectures will view these problems through a lens of understanding the uniformity and stability of the estimates.

This summer school will give participants an introduction to contemporary methods for studying maximal operators, with a particular focus on using maximal operators as a tool to understand other phenomena in analysis.

Disordered systems emerge from physical models by incorporating additional random effects. They also appear as models for complex systems in various contexts, such as computer science or biology. Understanding these models rigorously has been a great challenge for several decades, but the mathematical research in disordered systems and related fields has seen tremendous progress in recent years and benefits from a fruitful interplay of techniques from probability theory, mathematical analysis, combinatorics and mathematical physics. The aim of the school is to present to PhD students and young researchers some of the most fascinating developments in disordered systems and related fields in recent years.