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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2021-03-16  11:00-12:00  Transfer operators and limit laws for typical cocycles Kiho Park  선택 
2024-02-06  17:00-19:00  Tate Homology and Powered Flybys Kevin Ruck  선택 
2022-05-06  16:00-18:00  On an upper bound of the average analytic rank of a family of elliptic curves Keunyoung Jeong  27-325 
2019-09-18  16:00-17:00  Fermat's Last Theorem, 25 years later Kenneth A. Ribet  129-101 
2014-05-21  16:00-17:00  Classification of Calabi-Yau threefolds of type K Kenji Hashimoto  129-310 
2015-12-17  15:00-16:00  Random semigroups in solvable linear groups file Keivan Mallahi-Karai  129-104 
2016-12-12  16:00-17:00  On the chromatic number of structured Cayley graphs Keivan Mallahi-Karai  129-301 
2019-12-10  16:30-18:00  Spectral independence of compact groups Keivan Mallahi-Karai  129-406 
2022-10-04  16:00-17:00  On an extreme value law for the unipotent flow on $\mathrm{SL}_2(\mathbb{R})/\mathrm{SL}_2(\mathbb{Z})$. Keivan Mallahi Karai  선택 
2014-06-11  16:00-17:00  Mirror symmetry and K3 surfaces Kazushi Ueda  129-301 
2016-05-02  17:00-18:00  Stability of heat kernel estimates under Feynman-Kac perturbations for symmetric Markov processes Kazuhiro Kuwae  27-116 
2018-03-19  11:00-12:10  Twisted Donaldson Invariant (3/19-3/22"room 24-112.25-103) KATO Tsuyoshi  25-103 
2018-11-28  14:00-15:30  Geometric structures from dynamical rigidity Kathryn Mann  129-301 
2016-07-12  16:00-18:00  The Teichmüller diameter of the thick part of moduli space Kasra Rafi  129-301 
2016-07-19  16:00-17:00  Global a priori estimates below the natural exponent for quasilinear equations in non-smooth domains file Karthik Adimurthi  129-406 
2019-12-23  15:00-16:00  Uniform L^{infty}, Lipschitz and C^{1,alpha} estimates for quasilinear parabolic equations Karthik Adimurthi  27-116 
2022-07-05  15:00-17:00  Overview of DeGiorgi-Nash-Moser theory Karthik Adimurthi  27-325 
2021-09-29  16:00-18:00  Minimal dynamical systems, C*-algebras, and the classification program Karen Strung  선택 
2022-07-18  11:00-12:00  New multiplicity results for critical p-Laplacian problems (joint work with Carlo Mercuri) Kanishka Perera  27-220