Camillo De Lellis, Almgren’s Center Manifold in a Simple Setting, part 1
Channel: IAS | Park City Mathematics Institute | PCMI
Date: 2018-07-09

Camillo De Lellis
Institute for Advanced Study

A world-renowned geometric analyst with broad expertise in the calculus of variations, geometric regularity theory, and fluid dynamics, Camillo De Lellis has been appointed to the Faculty of the School of Mathematics at the Institute for Advanced Study.

Almgren’s Center Manifold in a Simple Setting, lecture part 1.
Lecture notes available at: https://pcmi.ias.edu/sites/pcmi.ias.edu/files/PCMILectures_DeLellis-14.pdf

All lecture notes from PCMI 2018 available at https://pcmi.ias.edu/program-gss/2018ss


In my course I will analyze a toy case, that of a single sheet, where one can prove direct $C^{3,\alpha}$ regularity for a minimal surface without using Schauder's estimates and with elementary considerations, following an early paper by Spadaro and myself (Center manifold: a case study). If time allows I will give some ideas about the center manifold needed in Almgren's theory and its youngest relatives.
Prerequisites: basic knowledge of elliptic partial differential equations (harmonic functions and their properties), of harmonic analysis (maximal functions and related estimates) and elementary geometric measure theory (Hausdorff measures, rectifiable sets, area formula) are enough to understand the toy case in full details.

This 4-lecture course is being presented at the 28th annual PCMI Summer Session taking place July 1–21, 2018, at the Prospector Conference Center in Park City, Utah. The residential, three-week Summer Session is the flagship activity of the IAS/Park City Mathematics Institute (PCMI), an outreach program of the Institute for Advanced Study. The 2018 research theme is Harmonic Analysis.

The PCMI Summer Session is an intensive program that includes several parallel sets of activities aimed at different groups of participants across the entire mathematics community. These activities include a program for mathematics researchers, eight mini-courses for graduate students on topics related to harmonic analysis, two lecture series for undergraduate students, a program for faculty from predominantly undergraduate institutions, a workshop on equity and mathematics education for undergraduate faculty, and a professional development program for K–12 school teachers. All of PCMI’s groups meet simultaneously, pursuing individual courses of study and a meaningful amount of interaction both scientifically and socially.

For more information, visit https://pcmi.ias.edu.