Conference: Recent Advances in Harmonic Analysis and Partial Differential Equations

About This Grant

This award supports participation in the international conference "Recent Advances in Harmonic Analysis and Partial Differential Equations", held May 19-22, 2025 at Baylor University, Waco, TX. Partial differential equations (PDE) are fundamentally important in mathematically oriented scientific fields such as physics and engineering. They are foundational in the modern scientific understanding of sound, heat, diffusion, electrostatics, electrodynamics, thermodynamics, statistical mechanics, fluid dynamics, elasticity, general relativity, and quantum mechanics. Similarly, harmonic analysis, historically developed from Fourier analysis, holds fundamental relevance in science, engineering, and the study of wave phenomena in general, beginning with the idea that a signal is composed of a sum of individual oscillatory components. Naturally, PDE and harmonic analysis go hand in hand, forming a powerful building block of modern mathematical analysis. Recent years have witnessed the emergence of tools and techniques at the confluence of harmonic analysis and PDE, providing solutions to longstanding open problems and permitting progress on multiple fronts. The invited speakers for this event are world-class experts who have been at the forefront of many recent breakthroughs and advances in these areas. Bringing them together offers a great opportunity to actively seek a timely cross-fertilization of ideas. For other conference participants, this provides a distinct chance to confer with and directly learn from experts across various fields. The interdisciplinary research fostered by this conference contributes to efforts to enlarge the nation's science personnel base and is expected to catalyze collaboration between mathematicians working at the confluence of harmonic analysis and PDE. Particular attention is directed to early-career researchers. In addition to providing them with a platform for learning from and interacting with leading experts in these fields, the conference will offer graduate students the opportunity to disseminate their research findings via poster presentations. During the last decade we have witnessed an accelerated development of techniques rooted in harmonic analysis which have been motivated by problems arising in PDE. As a consequence, new research venues have been created and deep difficult questions come within reach of these methods. These make the conference a very timely event which has the potential to disseminate and advance the current knowledge in the area of mathematics at the interface between harmonic analysis and PDE. Ideas originating in geometric measure theory have proved crucial in obtaining sharp estimates and regularity results in partial differential equations, the Calderon-Zygmund theory of singular integral operators, complex analysis, and potential theory on Riemannian manifolds, among other fields. Harmonic analysis techniques have also proved to be powerful, resilient, adaptable, and impactful in nonlinear PDE and the spectral theory of linear operators. The list of speakers is comprised of individuals who have pushed the boundaries and established new paradigms in these fields, playing an influential role and having a lasting impact in the area. A website for the conference is available at: https://math.artsandsciences.baylor.edu/harmonic-analysis This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.