中国科学院数学与系统科学研究院

数学研究所

学术报告

偏微分方程研讨班

报告人：Phan Thanh Nam（Mathematics Institute, LMU Munich）

题  目：Talk 2: Bogoliubov approximation for Bose gases

时  间：2024.9.9（周一）下午2:00-3:00

地  点：思源楼S803

摘 要：In this talk, I will review the basic ingredients of Bogoliubov theory as an effective description of the excitations around the condensate in weakly interacting Bose gases. I will also present some recent rigorous results concerning the ground state energy of interacting Bose gases in different scaling regimes, where the Bogoliubov quasi-free theory and its variants play a prominent role.

题  目：Talk 3: Random phase approximation for Fermi gases 

时  间：2024.9.16（周一）下午2:00-3:00

地  点：思源楼S803

摘 要：I will discuss rigorous bosonization techniques used to describe the ground state energy and excitation spectrum of fermionic systems through an appropriate bosonic quasi-free theory. This approach, in particular, provides a justification for the random phase approximation for a broad class of weakly interacting Fermi gases.

题  目： Correlation estimates for Coulomb systems

时  间：2024.9.23（周一）下午2:00-3:00

地  点：思源楼S803

摘 要：While the Hartree-Fock theory is a popular tool for understanding large Coulomb systems, finding rigorous corrections that account for correlations between particles remains a major challenge in mathematical physics. I will provide an overview of this topic, starting with the Lieb-Oxford inequality and its refinements, and then moving to recent developments on the correlation energy in the mean-field regime.