This seminar is about the singularity of PDEs in hydrodynamics and quantum mechanics, led by Prof. Huang's group. The relevant informations and sources(including recording videos and documents) will be updated in this post. Contents Our seminar proceed as follows: Ni will mainly introduce the recent works by Merle-Raphaël-Rodnianski-Szeftel, which worked out the Millennium problem in compressible version. Some related topics, like shock waves and other types of singularity, will also considered in our seminar. And Meng and Gu will lecture basic theory of elliptic equations. See references at the end. Schedule and sources We schedule on every Friday, 2:00-5:30 pm, located at Siyuan building S615, AMSS, CAS. No. Schedule Topic Lecturer Notes Records Location 1 24.03.08 Singularity & Stability A. Ni written typed offline S615 2 24.03.08 Laplace's equation 1 Y. Gu typed offline S615 3 24.03.15 Smooth implosion 1 A. Ni written offline S615 4 24.03.15 Moser iteration W. Meng typed offline S615 5 24.03.22 Smooth implosion 2 A. Ni written offline S615 6 24.03.22 Spherical blowup 1 Y. Gu written offline S615 7 24.03.29 Smooth implosion 3 A. Ni written offline S615 8 24.03.29 Perron's method W. Meng written offline S615 9 24.04.05 Smooth implosion 4 A. Ni written offline S615 10 24.04.05 Newtonian Potential W. Meng written offline S615 11 24.04.12 Smooth implosion 5 A. Ni written offline S615 12 24.04.12 Iteration method Y. Gu written offline S615 13 24.04.19 Smooth implosion 6 A. Ni written offline S615 13 24.04.19 Laplace equation 4 W. Meng written offline S615 14 24.04.26 Smooth implosion 7 A. Ni written offline…