My main interests are in Riemannian geometry, with a particular
emphasis on homogeneous spaces G/H and the G-invariant structures
they can admit. Much of my work has been dedicated to the
classification of non-compact homogeneous Einstein and Ricci soliton
metrics, and working towards the following conjecture.
While this conjecture is still open even in the
special case of Einstein metrics, there has been substantial
progress in the past five years which has reignited the belief that
the original Alekseevsky conjecture (and its modern version) is
Further, I am interested in understanding the
existence/non-existence of left-invariant Einstein and Ricci soliton
metrics on homogeneous spaces (especially solvable Lie groups),
geometric evolutions on homogeneous spaces, and applications of
Geometric Invariant Theory to the geometry of Lie groups.
My recent work has been supported by the National Science
Foundation, grant DMS-1612357, the OU Research Council, and the
Simons Foundation (#360562, michael jablonski).