Mini-course: An introduction to the theory of wave and kinetic equations

Thời gian: 09:00:16/07/2024 đến 16:30:17/07/2024

Địa điểm: Vietnam Institute for Advanced Study in Mathematics (VIASM), Hanoi

Organizers:

  • Phan Thanh Nam, LMU Munich, Germany
  • Le Minh Ha, VIASM, Vietnam

Abstract: Phenomena involving interactions of waves happen at different scales and in different media: from gravitational waves to the waves on the surface of the ocean, from our milk and coffee in the morning to infinitesimal particles that behave like wave packets in quantum physics. These phenomena are difficult to study in a rigorous mathematical manner, but maybe because of this challenge mathematicians have developed interdisciplinary approaches that are powerful and beautiful. We will describe some of these approaches and show for example how the need to understand certain multilinear and periodic wave interactions provided also the tools to prove a famous conjecture in number theory, or how classical tools in probability gave the right framework to still have viable theories behind certain deterministic counterexamples. We will also introduce the concept of the kinetic equation for waves. We will start with the deterministic approach of Bourgain, involving the study of long time asymptotics of higher Sobolev norms of solutions of dispersive equations, and we will end with the rigorous derivation of a wave kinetic equation.

Participants: Students and young researchers with basic background on Partial Differential Equations, Sobolev Spaces and Functional Analysis.

Lecturers: 

  • Gigliola Staffilani, Massachusetts Institute of Technology, USA;
  • Minh Binh Tran, Texas A&M University, USA.

Program: click Here 

Language: English

Registration: click Here 

Deadline for registration: 2 July, 2024

Contact: Mrs. Tran Thuy Linh, Email: ttlinh@viasm.edu.vn