Професор Драгомир Шарић са Queens College, The City University of New York, ће одржати предавање у четвртак, 11. јула са почетком у 10 часова, у амфитеатру Природно – математичког факултета. Позивамо студенте и наставно особље да присуствују у што већем броју. Наслов предавања и апстракт су у наставку.
Title: When is the geodesic flow ergodic?
Abstract: A Riemann surface X is infinite if its fundamental group is not finitely generated. We consider the geodesic flow on the unit tangent bundle T^1(X) of an infinite Riemann surface X in its conformal hyperbolic metric, i.e., metric of constant curvature -1.
A theorem of Hopf-Tsuji-Sullivan-Ahlfors-Sario-… states that the geodesic flow on T^1(X) is ergodic iff the Poincare series is divergent iff the Brownian motion on X is recurrent iff X has no Green’s function iff the extremal distance from a compact subsurface of X to the ideal boundary of X is infinite.
Any Riemann surface can be constructed by gluing the geodesic pairs of pants (and, if necessary, adding funnels and half-planes). The Fenchel-Nielsen parameters describe the hyperbolic metric on the surface, and we consider whether the geodesic flow is ergodic in terms of these parameters. We find explicit conditions on the Fenchel-Nielsen parameters to guarantee that the geodesic flow is ergodic and also explicit conditions to guarantee that it is not. Somewhat surprisingly, we find an equivalent condition for ergodicity in terms of finite-area holomorphic quadratic differentials on X, adding to the list of equivalencies in the above paragraph.
Some of these results are joint with Ara Basmajian, Hrant Hakobyan and Michael Pandazis.