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.
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2023-04-04  16:40-17:10  Continued fractions and coding of geodesics 이슬비  129-101 
2023-04-04  16:00-16:30  Teichmuller space and its generalizations 정홍택  129-101 
2023-03-31  16:00-17:00  Higher rank lattice actions with positive entropy 이호민  27-325 
2023-03-28  14:00-15:30  Higher rank lattice actions with positive entropy Homin Lee  129-301 
2023-03-24  15:00-16:00  Mixed local and nonlocal equations with measure data 송경  27-116 
2023-03-24  16:00-17:00  Regularity results via potential estimates to nonlinear elliptic problems Anna Zatorska-Goldstein  27-116 
2023-03-24  18:00-20:00  Ternary diagonal quadratic forms representing the same integers 주장원  27-325 
2023-03-20  09:30-11:00  Homogeneous dynamics and Laplace eigenfunctions I, II, III 권상훈  129-301 
2023-03-17  16:00-17:00  Well-posedness of some MHD models 배한택  27-220 
2023-03-17  14:00-16:00  Provable separation between QNC0 circuits including non-Clifford gates and NC0 circuits 신정현  선택 
2023-03-14  16:40-17:10  Macroscopic structure of stochastic partial differential equations 이재윤  129-101 
2023-03-14  16:00-16:30  Potential Theory for Markov processes 강재훈  129-101 
2023-03-14  15:30-17:00  On the transport-Stokes system Franck Sueur  129-301 
2023-03-13  09:30-11:00  Homogeneous dynamics and Laplace eigenfunctions I, II, III 권상훈  129-301 
2023-03-10  14:00-17:00  Reinforcement Learning in Continuous Time and Applications Xunyu Zhou  129-104 
2023-03-10  12:00-17:00  (QSMS-BK21 Symplectic Seminar) Mirror Symmetry for Log Calabi-Yau Surfaces 김현빈  129-309 
2023-03-10  14:00-16:00  Introduction to fiber-optic communication system 배성현  선택 
2023-03-09  13:00-14:00  When to Sell an Asset? - A Distribution Builder Approach Stephan Sturm  129-301 
2023-03-06  09:30-11:00  Homogeneous dynamics and Laplace eigenfunctions I, II, III 권상훈  129-301