We are excited to announce the TSVP Thematic Program "Singularities and Partial Differential Equations Representing Natural Phenomena". The program will run from July to August, 2028 (tentative).
This thematic program will follow the 3rd OIST-Oxford-SLMath Summer School which is scheduled to be held from June 26 - July 7, 2028 at the Okinawa Institute of Science and Technology (OIST). Information on upcoming and past summer schools of this series can be found here: https://www.oist.jp/research/research-units/apde/summer-schools .
Title: Singularities and Partial Differential Equations Representing Natural Phenomena
Theme of the Program: Comprehending a full characterization of singularities representing natural phenomena expressed by Partial Differential Equations (PDEs) is a major open problem in Mathematics and Modern Science. This thematic program will foster concentrated scientific activities in the following current research areas in Analysis & PDE:
- Potential Theory of Second-Order Elliptic and Parabolic PDEs
- Nonlinear Hyperbolic Systems of Conservation Laws and the Mathematical Theory of Shock Waves
- Nonlinear Schrödinger Equations
- Nonlinear PDE Systems in Fluid Mechanics
The four areas of research outlined above have on their own an extremely well-established research history, as well as ambitious forward-looking plans. At the same time, however, important underlying common themes are recently emerging with an unusual recurrence. In this program, the organizers plan to enhance these common themes, facilitate a more uniform mathematical language, and ultimately initiate collaborations that otherwise would not have started. This research program will generate significant interdisciplinary activities with other fields of mathematics and other sciences and engineering such as probability theory and stochastic processes, multiscale numerical analysis, fluid mechanics and biomedical engineering.
Program Coordinators
Ugur G. Abdulla (OIST)
Gui-Qiang G. Chen (OxPDE, University of Oxford)
Suncica Canic (University of California, Berkeley)
Donatella Danielli (Arizona State University)
Zoran Grujic (University of Alabama at Birmingham)
Gigliola Staffilani (Massachusetts Institute of Technology)
Tentative Schedule
The program's concept is to bring together experts from four distinct subfields of Analysis & PDE, united by a common goal of full characterization of singularities representing the natural phenomena. The format we are envisioning will repeat the one implemented in the Simons Laufer Mathematical Sciences Institute, formerly MSRI, AxIOM (Accelerated Innovation in Mathematics) program on the same topic, which will be held on May 3 - May 28, 2027. The plan is to create discussion groups comprising members with diverse expertise across the subfields. Some of the leading experts in each subfield will present a two-hour introductory lecture, followed by a one-hour open discussion session, during which an outstanding open problem and subproblems will be formulated. It is expected that the program will have at least four or five main speakers, representing each subfield. This series of talks will outline a certain vision in the intersection of some (if not all) subfields.
To provide participants with the opportunity to become acquainted with the work of early-career scientists in the field and to connect early-career researchers with potential senior mentors, the program will feature individual one-hour talks by junior participants, tentatively with a PhD received within the last 8 years or so. Some PhD students - attendees of the preceding 3rd OIST-Oxford-SLMath Summer Graduate School (June 26-July 7, 2028) - will be invited to join the program.Towards the end of the second week, there will be at least four or five groups formed, working on the formulated open problems. All the early-career participants will be encouraged to join one of the groups of their interest. Groups will continue intensive work for the remainder of the program. We plan to organize one-day workshops on Fridays of the third and fourth weeks, where each group will present a progress report.