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.
2023-12-15  10:30-11:20  Cut jump discontinuity and regularity of compressible Navier-Stokes flows new 권재룡  27-325 
2023-12-11  16:00-17:00  Probabilistic discrete operators on $mathbb{Z}^d$ Daesung Kim  129-104 
2023-12-05  16:40-17:10  Why do we study minimal submanifolds? 이재훈  129-101 
2023-12-05  16:00-16:30  Free boundary minimal surfaces in a ball and eigenvalue problems 서동휘  129-101 
2023-11-29  17:00-18:30  ISOMETRIC EMBEDDABILITY OF S^m_q INTO S^n_p Samya Kumar Ray  129-301 
2023-11-28  16:00-17:00  L^(d+2)/2 bound for Nikodym maximal function 박민석  27-116 
2023-11-28  17:00-18:00  Mixed Norm $l^2$ Decoupling for Paraboloids 김유현  선택 
2023-11-22  15:30-17:30  Blow up dynamics of nonlinear dispersive equations 권순식  27-325 
2023-11-21  16:00-17:00  The modified scattering for Dirac equations of scattering-critical nonlinearity 양창훈  27-116 
2023-11-21  17:00-18:00  Local smoothing estimates for the wave equation in higher dimensions 이정진  27-116 
2023-11-20  16:00-17:00  Deep function approximation for financial mathematics 허정규  선택 
2023-11-14  17:00-18:00  Universality in random matrix theory 서성미  129-301 
2023-11-14  11:00-12:00  Primitive lattice points, primitive Siegel transform, and its integral formulas on S-arithmetic spaces 한지영  129-301 
2023-11-14  15:00-16:00  Extreme value theorem of continued fractions and geodesic flows 이슬비  129-104 
2023-11-14  14:30-15:30  Refinements of Strichartz inequalities via decoupling and applications to nonlinear equations Robert Schippa  27-116 
2023-11-09  16:00-16:30  Some special solutions of incompressible Euler equations 임덕우  129-101 
2023-11-09  16:40-17:10  On wellposedness of $\alpha$-SQG equations 김준하  129-101 
2023-11-08  14:00-16:00  Predicting Agricultural Commodity Prices Using Deep Learning Networks with Multiple Time Series Data 민영호  선택 
2023-11-07  17:00-18:00  L^2 Fourier restriction for α-Salem measure 이성철  27-116 
2023-11-07  15:00-16:30  Volume bounds for hyperbolic 3-polyhedra and knots Andrei Vesnin  129-309