Conference: Geometric Measure Theory, Harmonic Analysis, and Partial Differential Equations: Recent Advances

Washington University, Saint Louis MO

Investigators

Abstract

This award provides travel support for U.S.-based mathematicians to attend the conference "Geometric Measure Theory, Harmonic Analysis and Partial Differential Equations: Recent Advances", to be held at Macquarie University (Australia), June 23--29, 2024. Support will be prioritized for early-career researchers, members of underrepresented groups in mathematics, and researchers without access to other sources of NSF funding. The aim of the conference is to convene leading international scholars, early career researchers, and PhD students in the fields of harmonic analysis, partial differential equations, and geometric measure theory, to disseminate the most recent advances. Harmonic analysis is a foundational mathematical subject that touches upon many different areas of study. Since its inception, the subject of harmonic analysis has developed in close connection to the theory of partial differential equations. In recent years, substantial interest has focused on the use of harmonic analysis as a tool to address questions arising in other fields such as geometric measure theory and number theory. The participation of advanced graduate students and early-career U.S. researchers in this event will facilitate the development of new research collaborations and will strengthen the U.S. research community in this active field. This conference will bring together experts in harmonic analysis, partial differential equations and geometric measure theory to highlight and disseminate recent research progress. These three subjects have had a symbiotic relationship for a long time. Existence and uniqueness of solutions to partial differential equations can be understood through mapping properties and regularity of Calderón-Zygmund operators, a classical topic in harmonic analysis. Rectifiability of sets in Euclidean spaces can be studied through the properties of harmonic measure on their boundaries, which connects to key subjects and tools in partial differential equations. The goal of this workshop is to foster progress in all three of these areas by leveraging their inherent interconnectedness and by bringing together a collection of leading researchers to discuss recent advances and to chart the directions for future progress. The event website is https://event.mq.edu.au/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.