Note: There will be no lecture on October 1 and December 3, 2026.
Description：
This course introduces analytical tools for PDE models arising in mathematical physics, probability, and materials science. The emphasis is on recurring techniques in research, including semigroups and heat kernels, spectral analysis, fixed point theory, perturbation methods, and asymptotic analysis. Both linear and nonlinear equations will be considered, through examples such as many-body Schrödinger equations from quantum mechanics and quantum information science, Kolmogorov-type equations from probability and engineering, and the Ginzburg–Landau equation from condensed matter theory.
Prerequisite：
Basic real and functional analysis; introductory PDE at the graduate or advanced undergraduate level. Prior knowledge of physics and probability is useful but not required.
Reference：
M. Reed and B. Simon, Methods of Modern Mathematical Physics, Vols. I–II and IV.
S. J. Gustafson and I. M. Sigal, Mathematical Concepts of Quantum Mechanics.
P. D. Hislop and I. M. Sigal, Introduction to Spectral Theory.
Additional lecture notes and research papers.
Target Audience: Undergraduate students, Graduate students
Teaching Language: English
Registration: https://www.wjx.top/vm/rNYF86V.aspx#
