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.
Aug 16, 2017  10:00-11:00  The Vlasov-Poisson-Boltzmann System for the Whole Range of Cutoff Soft Potentials Qinghua Xiao  27-325 
Aug 29, 2017  16:00-17:00  Statistics of high-dimensional lattices 김승기  27-325 
Jun 06, 2017  16:00-17:00  Mathematical and numerical approaches to dynamic contact of nonlinear springs Jeongho Ahn  27-325 
Jun 16, 2017  14:00-16:30  An Introduction to algebra and representation theory in Sage Travis Scrimshaw  27-325 
Feb 02, 2018  15:00-18:00  Coalgebraic principles of quantum field theory (two lectures) Jae-suk Park  27-325 
Mar 07, 2018  14:00-15:00  Nonlinear Dirichlet problems: old and new file Lucio Boccardo  27-325 
Mar 09, 2018  16:00-17:00  Regularizing effect of the lower order terms in some nonlinear Dirichlet problems file Lucio Boccardo  27-325 
Aug 07, 2017  16:00-18:00  Mirror of Atiyah flop in symplectic geometry Hansol Hong  27-325 
May 28, 2018  13:30-15:30  Perversely categorified Lagrangian correspondences Lino Amorim  27-325 
Aug 29, 2017  15:00-16:00  MOD p LOCAL-GLOBAL COMPATIBILITY FOR GLn(Qp) IN THE ORDINARY CASE 박철  27-325 
May 29, 2018  09:00-10:00  Backward SDEs and their applications to stochastic optimization and SPDE 남기훈  27-325 
Jul 13, 2018  16:00-17:30  Diffeomorphism groups of critical regularity Thomas Koberda  27-325 
Jul 27, 2018  15:00-17:00  Regularity for multi-phase variational problems 오제한  27-325 
Oct 10, 2018  16:30-17:30  Fundamental concepts in option pricing: Comparison of binomial tree model, partial differential equation approach, and the martingale method 최건호  27-325 
Oct 16, 2018  09:00-11:00  An introduction to intrinsic scaling Lecuture 1 Jose Miguel Urbano  27-325 
Oct 19, 2018  09:00-11:00  An introduction to intrinsic scaling Lecutre III Jose Miguel Urbano  27-325 
Oct 22, 2018  09:00-11:00  An introduction to intrinsic scaling Lecutre IV Jose Miguel Urbano  27-325 
Oct 23, 2018  09:00-11:00  An introduction to intrinsic scaling Lecutre V Jose Miguel Urbano  27-325 
Oct 17, 2018  11:00-12:00  Exotic quasi-Fuchsian groups 이계선  27-325 
Oct 20, 2017  16:00-18:30  Dynamics on the surfaces 백형렬  27-325