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.
2023-06-30  15:00-17:00  On Scaled-Hypercomplex Numbers Il Woo Cho  129-309 
2023-06-12  16:00-17:00  Arithmetic geometry and perfect powers Kenneth Ribet  129-101 
2023-06-02  16:00-17:00  A refined Tamagawa number conjecture for modular forms 김찬호  27-325 
2023-06-01  10:00-11:30  On well-posedness of singular vortex patches 조민준  27-325 
2023-05-31  17:00-18:30  Various mapping cones of positive maps arising from quantum information theory 계승혁  129-301 
2023-05-30  16:00-18:00  A pointwise convergence problem for orthonormal systems Neal Bez  27-116 
2023-05-30  17:00-18:00  수학과 보험산업 신민식  선택 
2023-05-29  15:30-17:30  Commuting pairs of bounded linear operators acting on a Hilbert space— Spectral and joint invariant subspace properties Jasang Yoon  129-309 
2023-05-26  15:00-17:00  Commuting pairs of bounded linear operators acting on a Hilbert space—Operator Transforms Jasang Yoon  129-309 
2023-05-26  16:00-17:00  Enriched inflection points and secant planes for linear series on algebraic curves 한창호  27-116 
2023-05-26  16:00-17:00  Entropy, large deviations, and applications 김태형  선택 
2023-05-26  10:00-17:00  1. Product structures on the relative symplectic cohomology / 2. Symplectic homology of affine varieties 1. 이원준 / 2. 배중현  129-104 
2023-05-26  14:00-16:00  Computational Quantum Chemistry on NISQ Devices 최민진  선택 
2023-05-25  13:00-15:00  Commuting pairs of bounded linear operators acting on a Hilbert space—Structure properties Jasang Yoon  129-309 
2023-05-25  14:00-16:00  Symplectic field theory and codimension-2 stable Hamiltonian submanifolds Richard Siefring  27-220 
2023-05-25  15:00-16:00  Recent topics for the regularity of local and nonlocal elliptic equations 이호식  27-325 
2023-05-25  16:00-17:00  Global maximal regularity for equations with variable exponents and degenerate weights in nonsmooth domains Rui Yang  27-325 
2023-05-25  16:00-17:00  Entropy, large deviations, and applications 김태형  선택 
2023-05-17  16:00-18:00  Affinizations, R-matrices and reflection functors 박의용  129-309 
2023-05-16  16:40-17:10  The river of regular quadratic polynomials 김민규  129-101