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.
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 
2015-05-15  11:00-12:00  Boundary layer for compressible flow Tong Yang  27-325 
2015-06-11  15:00-16:00  Jacobi's theta function from a representation theoretic viewpoint 이철희  27-325 
2014-11-04  16:00-17:00  A note on the pointwise convergence for the Schrödinger equation 조주희  27-325 
2015-07-03  16:00-17:00  Nonlocal p-Laplace equations depending on the Lp norm of the gradient file Michel Chipot  27-325 
2015-09-18  16:00-17:00  Zeta regularized determinant over Riemann surfaces 박진성  27-325 
2015-04-10  11:00-12:00  Stable Matching in Large Economies 김진우  27-325 
2015-05-01  11:00-12:00  심방 세동 현상을 이해하기 위한 수학적 모델의 시뮬레이션과 분석 이영선  27-325 
2016-01-08  15:00-16:00  Substitution dynamical systems 손영환  27-325 
2015-05-15  11:00-12:00  Boundary layer for compressible flow Tong Yang  27-325 
2015-05-26  15:00-17:00  Regularity for elliptic and parabolic equations Lihe Wang  27-325