The general setting of my current research is that of
homotopy algebra. I have been working with my student M. Daily on the
study of finite dimensional L-infinity algebras. Questions raised here
also lead to related questions about A-infinity algebras. I am also
interested in formulating familiar topics in Lie theory, such as representation
theory, for L-infinity algebras.
M. Markl in Prague and I are continuing our work on symmetric
brace algebras that involves generalizations of pre-Lie algebras and BV algebras.
I also have my ongoing collaboration with R. Fulp and
J. Stasheff regarding the theory of L-infinity algebras that arise in the
context of Poisson sigma models; this project is oriented towards the
application of homological algebra to mathematical physics.
M. Daily M. Markl