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.
Dec 17, 2015  15:00-16:00  Random semigroups in solvable linear groups file Keivan Mallahi-Karai  129-104 
Dec 12, 2016  16:00-17:00  On the chromatic number of structured Cayley graphs Keivan Mallahi-Karai  129-301 
Dec 10, 2019  16:30-18:00  Spectral independence of compact groups Keivan Mallahi-Karai  129-406 
Jun 11, 2014  16:00-17:00  Mirror symmetry and K3 surfaces Kazushi Ueda  129-301 
May 02, 2016  17:00-18:00  Stability of heat kernel estimates under Feynman-Kac perturbations for symmetric Markov processes Kazuhiro Kuwae  27-116 
Mar 19, 2018  11:00-12:10  Twisted Donaldson Invariant (3/19-3/22"room 24-112.25-103) KATO Tsuyoshi  25-103 
Nov 28, 2018  14:00-15:30  Geometric structures from dynamical rigidity Kathryn Mann  129-301 
Jul 12, 2016  16:00-18:00  The Teichmüller diameter of the thick part of moduli space Kasra Rafi  129-301 
Jul 19, 2016  16:00-17:00  Global a priori estimates below the natural exponent for quasilinear equations in non-smooth domains file Karthik Adimurthi  129-406 
Dec 23, 2019  15:00-16:00  Uniform L^{infty}, Lipschitz and C^{1,alpha} estimates for quasilinear parabolic equations Karthik Adimurthi  27-116 
Jul 05, 2022  15:00-17:00  Overview of DeGiorgi-Nash-Moser theory Karthik Adimurthi  27-325 
Sep 29, 2021  16:00-18:00  Minimal dynamical systems, C*-algebras, and the classification program Karen Strung  선택 
Jul 18, 2022  11:00-12:00  New multiplicity results for critical p-Laplacian problems (joint work with Carlo Mercuri) Kanishka Perera  27-220 
Dec 23, 2021  16:00-17:00  Weighted estimates for maximal product of spherical averages file Kalachand Shuin  선택 
Dec 24, 2021  16:00-17:00  Weighted estimates for bilinear Bochner-Riesz means at the critical index file Kalachand Shuin  선택 
Dec 24, 2021  17:00-18:00  Bilinear Bochner-Riesz means and square function file Kalachand Shuin  선택 
May 17, 2022  16:00-16:30  Bilinear Bochner-Riesz means and square function file Kalachand shuin  129-101 
Apr 05, 2019  16:00-18:00  Dynamics of continued fractions and conjecture of Mazur-Rubin Jungwon Lee  27-325 
Dec 14, 2018  11:00-12:00  Ergodicity and nodal counting of eigenfunctions on 3-manifolds Junehyuk Jung  27-220 
Jun 16, 2016  16:00-17:30  Fractals and fractal wavelets Judith Packer  129-301