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.
Generalized Alekseevsky Conjecture: Let M be a
non-compact homogeneous space with Ricci soliton metric. Then M is
isometric to a simply-connected solvable Lie group with algebraic
Ricci soliton metric.
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).
Upcoming Conferences and Workshops
(see below for funding information)
Lie Group Actions in Riemannian Geometry
June 26-30, 2017
The primary theme of the conference will be curvature properties in
the presence of symmetry, with emphasis on homogeneous Einstein and
Ricci soliton metrics, metrics of positive curvature, and Ricci
Lectures will be held in the morning and late afternoon to allow
time for informal discussions each afternoon. We thus hope to
encourage progress on open problems and the formation of new
For further information, see https://math.dartmouth.edu/~lga/
Through a grant from Dartmouth College, we can provide support for a
limited number of researchers. Priority will be given to
graduate students, recent Ph.D.'s, and others who do not have other
sources of federal support. To apply for funding, please
contact Michael Jablonski at email@example.com.
Graduate students and recent Ph.D.'s should include a brief
statement of interests and a CV. Graduate students
should also have their advisors send a supporting letter. For full
consideration, please apply by April 15. We especially
encourage women and members of underrepresented minorities to apply.