Conference: PDE in Moab: Advances in Theory and Application

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The purpose of this award is to fund a research conference on Partial Differential Equations (PDE) to take place on June 3-7, 2024, at the Utah State University (USU) building located in Moab, Utah. The conference, called "PDE in Moab: Advances in Theory and Application" will feature 14 invited talks, along with 9 contributed talks from early career mathematicians, with a total of approximately 40 participants. Funding attached to this grant will be used to support travel and lodging expenses for participants in the conference, with priority for junior participants who do not have access to other sources of travel funding. The conference website is https://pdemoab.byu.eduThis conference aims to explore the tools and methods of partial differential equations (PDE), and their applications in related fields such as geometric measure theory (GMT), harmonic analysis, and free boundary problems. Historically, these areas of mathematics have benefited from many fruitful interconnections. Indeed, pioneering advancements in free boundary problems adapted techniques from regularity theory in both PDE and GMT. Moreover, recent advances in both nonlinear and nonlocal PDE have enlarged the intersection of the aforementioned fields, thereby increasing interactions, collaborations, and the overall advancement of these areas. This conference will bring together experts from the areas of PDE, GMT, harmonic analysis, and free boundary problems to explore and build on recent progress. The list of speakers is comprised of a dynamic group of mathematicians specializing in complementary fields, many of whom already have intersecting interests. It is expected that by bringing these researchers together, there will be further interaction between research areas, leading to the cross-pollination of techniques and novel research results.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.