The Mathematics of Interacting Bose Gases

In the week of August 1-5, 2022, the summer school "The mathematics of interacting Bose gases" took place at VIASM. The summer school had about 50 participants, half of those participated onsite at the Laurent Schwartz Lecture Hall. There were two lecture series in every morning given by Prof. Phan Thành Nam from the University of Munich and Prof. Nguyễn Trọng Toán (Toan T. Nguyen) from the Pennsylvania State University, plus an exercise section of 2-3 hours in each afternoon instructed by Dr. Dương Giao Kỵ from An Giang University.


In the first lecture series, Prof. Nam discussed the mathematical formulation of quantum mechanics, and then used this fundamental theory to derive the Gross-Pitaevskii equation for the Bose-Einstein condensate, as well as Bogoliubov's theory for the excitation spectrum. In the second lecture series, Prof. Toan started by analyzing the solution of the Gross-Pitaevskii equation, and more generally nonlinear Schrödinger equations, and then explained the relation to classical mechanics, focusing on the Vlasov-Poisson equation and related phenomena such as Landau damping, plasma echoes, plasma oscillations. The summer school ended with an "Open problem section" addressing some important questions in physics and the corresponding mathematical conjectures.

Prof. Phan Thành Nam, University of Munich, Germany

Prof. Nguyễn Trọng Toán, Pennsylvania State University, USA

Dr. Dương Giao Kỵ, An Giang University

The summer school showed a great diversity of participants: from high-school students, to advanced undergraduate and master/PhD students, to experienced researchers such as Prof. Ngô Quốc Anh, Prof. Trịnh Viết Dược and Dr. Đặng Anh Tuấn from Vietnam National University - Ha Noi, Prof. Tăng Quốc Bảo from University of Graz, Prof. Tô Tất Đạt from Sorbonne Université, Dr. Nguyễn Văn Hoàng from FPT University, Dr. Phan Thành Việt from Duy Tân University, ... Besides students studying in Vietnam, there were also many students from abroad: Vũ Hồ Thảo Thuận - PhD student in Mathematics from Università degli Studi di Milano-Bicocca, Trần Quang Lộc - Master student in Applied Mathematics and Theoretical Physics from the University of Cambridge, Trần Nhân Trung - Master student in Mathematics from Université Claude Bernard Lyon 1, ...

In general, the summer school brought up some important topics in mathematical physics, focusing on beautiful connections between heuristic ideas in physics and rigorous methods in mathematics. Given very positive feedbacks from participants, we hope that similar events will be organized in the near future.