Abstract: The mini-course is an introductory and self-contained approach to the method of intrinsic scaling, aiming at bringing to light what is really essential in this powerful tool in the analysis of degenerate and singular equations. The theory is presented from scratch for the simplest model case of the degenerate p-Laplace equation, leaving aside
technical renements needed to deal with more general situations. A striking feature of the method is its pervasiveness in terms of the applications and I hope to convince the audience of its strength as a systematic approach to regularity for an important and relevant class of nonlinear partial dierential equations. I will extensively follow my book
14 , with complements and extensions from a variety of sources (listed in the references), mainly
6,7,17

10/16()09:00 11:00 Lecture I.
An impressionist history lesson: from Hilbert's 19th problem to DeGiorgi-Nash-Moser theory; the quasilinear case { contributions from the Russian school; enters DiBenedetto { the method of intrinsic scaling.

10/17()09:00- 11:00 Lecture II.
The building blocks of the theory: local energy and logarithmic estimates. The geometric setting and an alternative.

10/19()09:00 -11:00 Lecture III.
The rst alternative: getting started; expansion in time and the role of the logarithmic estimates; reduction of the oscillation.

10/22()09:00 -11:00 Lecture IV.
Towards the Holder continuity: the second alternative; the recursive argument.

10/23()09:00 -11:00 Lecture V.
The singular case and further generalisations: immiscible uids and chemotaxis; phase transitions.
Subject
Aug 24, 2022  10:00-11:30  Low regularity ill-posedness for elastic waves and ideal compressible MHD in 3D and 2D Xinliang An  선택 
Aug 18, 2022  14:00-17:00  Spectral theory of Hankel and Toeplitz operators 황인성  129-406 
Aug 17, 2022  14:00-17:00  Spectral theory of Hankel and Toeplitz operators 황인성  129-406 
Aug 17, 2022  11:00-12:00  Almost minimizers for the thin obstacle problem with variable coefficients 전성민  27-220 
Aug 16, 2022  14:00-17:00  Spectral theory of Hankel and Toeplitz operators 황인성  129-406 
Aug 16, 2022  10:00-12:00  The generalization error of max-margin classifiers in the overparametrized regime 손영탁  129-101 
Aug 10, 2022  11:00-12:00  Dynamics of self-joinings of hyperbolic manifolds: 2 Dongryul Kim  129-301 
Aug 10, 2022  15:30-18:00  Hyperkahler manifolds in mathematics and physics Arnav Tripathy  129-104 
Aug 09, 2022  11:00-12:00  Dynamics of self-joinings of hyperbolic manifolds: 1 Dongryul Kim  27-325 
Aug 09, 2022  11:00-12:00  Harmonic map flow and its variants of evolving metric 박웅배  129-301 
Aug 08, 2022  10:30-18:00  Pseudoholomorphic Sections 김용환  129-406 
Aug 02, 2022  16:00-18:00  Nikodym sets for spheres and related maximal functions 김종천  27-220 
Aug 02, 2022  16:00-17:00  Harmonic map and its applications to minimal surface 박웅배  129-406 
Aug 01, 2022  10:00-18:00  <QSMS-BK21 Toric Geometry Seminar> Dehn Twist Along an Exact Lagrangian Sphere 김도형  129-406 
Jul 28, 2022  11:00-12:00  The Liouville PDE, Reinforcement Learning, and their applications 이필화  27-220 
Jul 25, 2022  10:00-17:00  Seidel's Long Exact Sequence on Lagrangian Floer Cohomology 김경모  129-406 
Jul 22, 2022  14:00-16:00  Recursive Quantum Approximate Optimization Algorithm 배은옥  선택 
Jul 21, 2022  10:00-11:00  Finding ALL solutions 이경용  129-406 
Jul 19, 2022  10:30-13:00  A quadratic form associated with pseudo-periodic homeomorphisms arising from singularity theory. Pablo Portilla cuadrado  129-406 
Jul 18, 2022  11:00-12:00  New multiplicity results for critical p-Laplacian problems (joint work with Carlo Mercuri) Kanishka Perera  27-220