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.
2018-11-30  12:00-13:00  Optimal investment and consumption with liquid and illiquid assets 최진혁  129-301 
2018-11-28  16:00-18:00  Quantum information and random matrices Motohisa Fukuda  129-301 
2018-11-28  17:00-18:30  An efficient approach for removing look-ahead bias in the least square Monte Carlo algorithm: Leave-one-out 최재혁  27-325 
2018-11-28  14:00-15:30  Geometric structures from dynamical rigidity Kathryn Mann  129-301 
2018-11-26  15:00-16:30  Generically smooth components of the Hilbert scheme of curves via ruled surfaces file Hristo Iliev  27-325 
2018-11-23  18:00-19:00  Stability of periodic traveling waves 정소연  27-325 
2018-11-23  17:00-18:00  Hölder continuity of weak type minimizers for functionals with generalized Orlicz growth 이미경  27-325 
2018-11-21  16:00 -18:00  Four independences in non-commutative probability Takahiro Hasebe  129-301 
2018-11-16  16:00-18:00  The Laplacian on some round Sierpin´ski carpets and Weyl’s asymptotics for its eigenvalues file Naotaka Kajino  27-325 
2018-11-14  16:00-17:30  Aluthge transforms for a commuting n-tuple of operators and common invariant subspaces 김재웅  129-301 
2018-11-13  16:00-17:00  Green's functions and Well-posedness of Compressible Navier-Stokes equation Shih-Hsien Yu  27-220 
2018-11-13  17:00-18:00  A/B Testing - why you should do it and why it could be hard 이종호  129-406 
2018-11-07  16:00-17:30  The kernel of Hankel operators 황인성  129-301 
2018-11-06  17:30-18:30  The Calderon-Zygmund estimates for elliptic equations with singular drift 김현석  27-116 
2018-11-05  11:00-12:00  Vlasov-Poisson-Boltzmann system in convex domains 김찬우  27-220 
2018-11-01  11:00-12:00  Self-Organized Hydrodynamic models for nematic alignment and the application to myxobacteria Hui Yu  27-220 
2018-10-31  16:00-18:00  Geometry of Banach space and norm attaining functions 김선광  129-301 
2018-10-30  16:30-18:00  Continuum limit for discrete nonlinear Schrödinger equations 홍영훈  27-116 
2018-10-30  16:00-17:30  The mapping class groups of Heegaard splittings Sangbum Cho  129-406 
2018-10-30  15:00-16:00  The linear and nonlinear wave equations with critical Lorentz regularity file Javier Ramos  27-116