Mathematical analysis of the Bose gas

Thời gian: 14h-16h, thứ 6 ngày 11 tháng 9 năm 2026

Địa điểm: Phòng 507 nhà A6

Tóm tắt: We discuss the emergence of Gibbs measures in three dimensions as a rigorous semiclassical limit of the quantum Gibbs state of an interacting Bose gas at temperatures just above the critical temperature for Bose--Einstein condensation. We first focus on regular interaction potentials, which lead to a Hartree measure with a nonlocal nonlinear term. This part is established using variational techniques and novel correlation inequalities. We then discuss the connection between the Hartree measure and the $\Phi^4_3$ theory, where additional ingredients from stochastic quantization are needed. The talks are based on joint work with Mathieu Lewin and Nicolas Rougerie on nonlocal interactions, and on recent work with Rongchan Zhu and Xiangchan Zhu on local interactions.