Singularities & PDEs Representing Natural Phenomena

Date: 3 - 28 May 2027

Location: Simons Laufer Mathematical Sciences Institute

Unlock the mysteries of singularities with the mathematical tools that study shock waves, fluid flows, quantum systems, and beyond. This research program brings together world-leading experts to advance breakthrough theories in Analysis and PDEs, from Wiener-type criteria and free boundary problems to nonlinear wave dynamics and machine-learning-guided discovery. Bridging pure mathematics, probability, fluid mechanics, numerical analysis, and biomedical engineering, the program will ignite new collaborations and advance how we understand the mathematics behind natural phenomena.

AxIOM are month-long research programs designed to accelerate innovation and introduce transformative ideas into the mathematical sciences. These focused programs are meant to create a dynamic environment for intensive collaboration, where researchers converge to push boundaries, explore bold ideas, and catalyze breakthroughs. Each program centers on a timely theme, from foundational mathematical challenges to fast-moving intersections with fields like artificial intelligence, data science, biology, physics, and medicine. Some programs will amplify the momentum of recent “hot topic” workshops, or build on the outcomes of semester-long programs, while others will chart new territory—engaging with emerging technologies or revisiting classical problems through a modern lens. These one-month intensives, taking place throughout Spring, are uniquely structured to ignite progress on cutting-edge problems, foster cross-disciplinary collaboration and knowledge exchange, translate recent mathematical advances into real-world impact, and seed new research directions and long-term collaborations.

Professor Alexander Kiselev (Duke University) has been appointed as a Clay Senior Scholar to participate in this program.

CMI Enhancement and Partnership Program