UNIVERSITY OF NOTRE DAME DU LAC
We plan to study the following three branches in the years to come.
1. Systematic study of stationary-harmonic multiple-valued functions;
2. Frequency and branch sets of multiple-valued functions;
3. Regularity of integral varifolds.
These branches are not separated from each other. The proposer and his co-authors have made progress as well as identied connections for them. The solutions of those problems will definitely contribute to the understanding of long standing problems in geometric analysis, for example, the boundary regularity of area minimizing integral currentsin general codimension and the singularity estimate of integral varifolds under natural assumptions on the mean curvature or the second fundamental form.