Special Year Research Seminar

The talk will consists of a long historical introduction to  the topic of deviation
of ergodic averages for locally Hamiltonian flows on compact surafces  as well as
some current results obtained in collaboration with Corinna Ulcigrai  and Minsung Kim.
New developments include a better understanding of the asymptotic of  so-called error term
(in non-degenerate regime) and the appearance of new exponents in the  deviation spectrum
(in degenerate regime).