Email kikuta(
Algebraic geometry, Group theory
Keywords Autoequivalence group, Derived category, K3 surface

I'm interested in autoequivalence groups of derived categories of algebraic varieties, especially K3 surfaces. The objects of derived categories are complexes of coherent sheaves on algebraic varieties, and the morphisms are given by using morphisms between complexes. Derived categories contain much information of algebraic varieties. Auto-equivalence groups are just like auto-morphism groups of algebraic varieties. The pull-back of automorphisms gives the natural embedding of auto-morphism groups into auto-equivalence groups. Autoequivalence groups of derived categories are interesting objects in also group-theory.

To understand autoequivalence groups, it is not enough to study only the action on the cohomology groups. Then, via homological mirror symmetry originating the string theory in physics, we compare autoequivalence groups and (symplectic) mapping class groups of symplectic manifolds. Rich research history of mapping class groups gives rich ideas to study autoequivalence groups. Actually, motivating the analogue with mapping class groups, I have been studying autoequivalence groups from group-theoretic/ metric geometric/ dynamical viewpoints. But there's still a lot to work on this topic. My main project is to study autoequivalence groups of K3 surfaces by any method in mathematics.