Area-Minimizing Integral Currents: Singularities and Structure - Lecture

Explore the intricacies of area-minimizing integral currents in this advanced mathematics lecture. Delve into the generalization of area-minimizing oriented surfaces, pioneered by De Giorgi and extended by Federer and Fleming. Examine celebrated examples of singular minimizers and dimension bounds for singular sets in various codimensions. Investigate recent developments, including Liu's result on fractal singular sets and progress towards proving the conjecture of $(m-2)$-rectifiability. Learn about oriented Plateau problems, integral currents, rectifiability, and key theorems in the field. Gain insights into monotonicity formulas and Federal reduction arguments as Camillo de Lellis from the Institute for Advanced Study presents recent joint works with Anna Skorobogatova and Paul Minter.