Hausdorff School: “Uniformity and Stability of Oscillatory Integrals”

Dates:  July 8 - 12, 2024

Venue: Lipschitz-Saal (Endenicher Allee 60, Bonn)

Organizers: Philip Gressman (U. Penn), Dóminique Kemp (UW Madison/IAS/Princeton), Lillian Pierce (Duke University/Bonn Research Chair)

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.

Lecture series by:

• Michael Christ, UC Berkeley
• Philip Gressman, U. Penn
• Ian Petrow, UCL
• James Wright, U. Edinburgh
• Ruixiang Zhang, UC Berkeley

Additional talks by:

• Polona Durcik, Chapman University
• Dóminique Kemp, UW Madison/IAS/Princeton
• Dominique Maldague, MIT
• Hong Wang, UCLA