Regularity Theory for Area-Minimizing Currents

Explore the fundamental concepts of regularity theory for area-minimizing currents in this comprehensive lecture by C. De Lellis and E. Spadaro from the University of Zurich and Max Planck Institute for Mathematics. Delve into key topics including the definition of currents, boundaries, mass, and integration. Examine the concept of definable currents and their significance in geometric measure theory. Investigate the Federal Inflaming Theorem and its implications for regularity theory. Gain insights into the optimality and proof of area-minimizing currents, as well as the goals of this mathematical field. This in-depth presentation is part of the School and Workshop on "Geometric Measure Theory and Optimal Transport" held at ICTP Mathematics in 2013.

Introduction
What is a current
Concept of boundary
Definition of boundary
Definition of mass
Integration over
Integratedefinable currents
Upshot
Infinite series
Generalized plateaus
Federal Inflaming Theorem
Regularity theory
Optimality
Proof
Goals