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.
Jun 09, 2022  09:00-11:00  The geometry of shock formation for Euler SHKOLLER, Steve  선택 
Jun 24, 2022  14:40-16:40  Quantum amplitude amplification operators 배준우  선택 
Jun 10, 2022  14:00-16:00  Quantum enhanced multiple-phase estimation with multi-mode N00N states 임향택  선택 
Jun 17, 2022  22:00-23:00  Deep Learning Based Choice Model for Market Segmentation Seung-Wook Kim  선택 
Jul 06, 2022  10:00-12:00  An Improved Regularity Criterion and Absence of Splash-like Singularities for g-SQG Patches 전준기  선택 
Jul 15, 2022  14:00-16:00  Gate operations and telecorrection of hybrid qubits employing cat code 이재학  선택 
Aug 24, 2022  10:00-11:30  Low regularity ill-posedness for elastic waves and ideal compressible MHD in 3D and 2D Xinliang An  선택 
Aug 30, 2022  16:00-18:00  Nonlinear parabolic equation in Orlicz-Musielak spaces - existence theory Miroslav Bulicek  선택 
Aug 23, 2022  10:00-12:00  Well-posedness of logarithmic spiral vortex sheets Wojciech Ozanski  선택 
Oct 04, 2022  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 
Sep 08, 2022  16:00-17:00  Cutoff thermalization in total variation distance for Langevin dynamics Gerardo Barrera  선택 
Sep 21, 2022  18:00-19:00  An overview on noncommutative maximal inequalities Guixiang Hong  선택 
Sep 27, 2022  15:00-16:00  Categories of Whittaker Modules over Lie superalgebras and Categorification of Fock Spaces Shun-Jen Cheng  선택 
Sep 28, 2022  16:00-18:00  A universal framework for entanglement detection of invariant quantum states 박상준  선택 
Oct 05, 2022  16:00-18:00  A universal framework for entanglement detection of invariant quantum states 박상준  선택 
Oct 12, 2022  11:00-12:00  Derivation of the Vlasov equation from quantum many-body Fermionic systems with singular interaction file Jacky Chong  선택 
Apr 21, 2023  11:00-12:00  Grassmannians and Polygon spaces 김유식  선택 
Oct 18, 2022  10:00-12:00  Remarks on the long-time dynamics of 2D Euler Theodore Drivas  선택 
Oct 25, 2022  10:00-11:00  Rational liftings and gRSK Travis Scrimshaw  선택 
Oct 25, 2022  11:00-12:00  Crystal Invariant Theory Travis Scrimshaw  선택