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.
2017-08-16  10:00-11:00  The Vlasov-Poisson-Boltzmann System for the Whole Range of Cutoff Soft Potentials Qinghua Xiao  27-325 
2017-08-29  15:00-16:00  MOD p LOCAL-GLOBAL COMPATIBILITY FOR GLn(Qp) IN THE ORDINARY CASE 박철  27-325 
2017-08-29  16:00-17:00  Statistics of high-dimensional lattices 김승기  27-325 
2017-10-20  16:00-18:30  Dynamics on the surfaces 백형렬  27-325 
2017-11-20  16:00-18:00  Dynamics on the surfaces 백형렬  27-325 
2017-12-18  11:00-13:00  Universal sums of generalized polygonal numbers Ben Kane  27-325 
2017-12-29  13:00-17:00  A Series of Invited Talks 김유찬외 3인  27-325 
2018-01-25  10:00-12:00  Regularity of subelliptic equations Lihe Wang  27-325 
2018-02-02  15:00-18:00  Coalgebraic principles of quantum field theory (two lectures) Jae-suk Park  27-325 
2018-03-07  14:00-15:00  Nonlinear Dirichlet problems: old and new file Lucio Boccardo  27-325 
2018-03-09  16:00-17:00  Regularizing effect of the lower order terms in some nonlinear Dirichlet problems file Lucio Boccardo  27-325 
2018-10-01  17:15-18:15  Interacting particle systems from the viewpoint of configuration space analysis TORBEN FATTLER  27-325 
2018-10-10  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 
2018-10-16  09:00-11:00  An introduction to intrinsic scaling Lecuture 1 Jose Miguel Urbano  27-325 
2018-10-17  09:00-11:00  An introduction to intrinsic scaling Lecture II Jose Miguel Urbano  27-325 
2018-10-19  09:00-11:00  An introduction to intrinsic scaling Lecutre III Jose Miguel Urbano  27-325 
2018-10-22  09:00-11:00  An introduction to intrinsic scaling Lecutre IV Jose Miguel Urbano  27-325 
2018-10-23  09:00-11:00  An introduction to intrinsic scaling Lecutre V Jose Miguel Urbano  27-325 
2018-05-29  09:00-10:00  Backward SDEs and their applications to stochastic optimization and SPDE 남기훈  27-325 
2018-05-28  13:30-15:30  Perversely categorified Lagrangian correspondences Lino Amorim  27-325