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

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.
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2023-10-24  14:00-15:00  A Data-Scientific Approach to Representation Theory: Case Study of Kronecker Coefficients 이규환  27-220 
2014-04-30  16:00-17:00  Non-factorial quartic double solids 홍규식  27-221 
2014-03-26  16:00-17:00  Log canonical thresholds of complete intersection log del Pezzo surfaces 김인균  27-317 
2014-04-16  16:00-17:00  Economic resolutions and G-constellations 정승조  27-317 
2014-05-07  16:00-17:00  Deformations of compact holomorphic Poisson manifolds 김정훈  27-317 
2014-11-28  11:00-12:00  Koszul-Tate resolution for Batalin-Vikovisky algebras 이동건  27-317 
2019-07-09  14:00-17:00  Introduction to XVA and BSDEs, Funding Value Adjustment file Stephan Sturm  27-317 
2019-07-11  14:00-17:00  Repo markets, credit risk, BSDEs with terminal jumps and projection of BSDEs file Stephan Sturm  27-317 
2021-02-02  12:00-13:00  Measure changes for jump processes and derivative pricing 안신미  27-317 
2022-07-14  16:00-18:00  Renormalization of Dynamical Systems Jonguk Yang  27-317 
2022-11-04  10:00-18:00  <QSMS-BK21 Symplectic Geometry Seminar> Introduction to Floer Homotopy: Kuranishi Structures 김용환  27-317 
2022-12-09  10:00-18:00  < QSMS-BK21 Symplectic Geometry Seminar > Introduction to Floer Homotopy: Formal Groups and Complex Cobordism 김용환  27-317 
2023-01-27  14:00-17:00  Localization in Floer theory and its applications 김준태  27-317 
2023-04-21  14:00-15:00  Selberg's central limit theorem of L -functions near the critical line 이윤복  27-317 
2014-07-07  10:00-12:00  Introduction to Large Deviation Theory I 강완모  27-325 
2014-07-11  10:00-12:00  Introduction to Large Deviation Theory III 강완모  27-325 
2014-06-24  15:00-16:00  Introduction to Hecke operators 이철희  27-325 
2014-06-24  14:00-15:00  What is a Coxeter number? 이철희  27-325 
2015-03-09  15:30-17:30  G-structures associated to Hermitian symmetric spaces 김신영  27-325