Conference: Theory and Applications of Elliptic Partial Differential Equations

This award supports participation in the workshop "Theory and Applications of Elliptic Partial Differential Equations", held June 23-27, 2025 at University of California-Irvine. The workshop consists of three short courses given by experts in elliptic Partial Differential Equations (PDE). Elliptic PDE play an important role in problems from physics, biology, and geometry, and the field has seen exciting advances in recent years. The overall goals of the courses are to bring graduate students up to speed in the most active areas of elliptic PDE, to promote a sense of community within the field, and to set the course for possible future research directions. At a technical level, the courses will discuss recent advances made on free boundary problems, quasilinear and fully nonlinear geometric PDE, stochastic PDE, aggregation-diffusion equations, and steady solutions in fluid dynamics. Examples include delicate regularity results for free boundaries generated by many interacting membranes that appear, for example, in geometry and elasticity, and radial symmetry results for steady states of aggregation-diffusion equations arising in chemotaxis. The workshop gives students a chance to forge new research directions and to make connections with fellow students as well as more established mathematicians. The participants also have an opportunity to give short talks and poster presentations on their research, which serves as training in scientific communication and as a catalyst for networking. Products such as sets of lecture notes and lecture videos will be made accessible to the broader mathematical community. A website for the workshop is available at: https://ucipde2025.github.io/2025-PDE-Summer-School-Website/ 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.