Boris Kruglikov: Lie equations and finite determination of symmetries of geometric structures

Highly symmetric geometric structures play a distinguished role in mathematics and applications. Lie equations describe the symmetries. In this talk I discuss bounds on the size of the symmetry algebras and report some new results about maximal and submaximal symmetric geometric structures (the latter includes the joint results with Dennis The and with Henrik Winther). The examples of the structures I consider include conformal and projective, metric projective and contact projective structures, non-holonomic vector distributions, almost complex structures and some classes of differential equations.