Regularity in (degenerate) variational problems, and beyond

In this talk, I will introduce my research and interests. The primary focus will be on the regularity theory of variational problems (possibly with degeneracy), which are connected to geometric measure theory in various ways. A significant part of the talk will be about variational problems under the quasi-convexity assumption. In particular, I will discuss quasi-convex variational problems involving constant rank operators, with one example being differential forms, and explain how to deal with the degeneracy of such operators. In addition, the unique continuation problem on locally flat domains will be briefly mentioned.