Mathematics

Schmidt is currently most interested in: natural extensions for continued fractions for various Fuchsian groups (with C. Kraaikamp, and various third co-authors:  I. Smeets,  H. Nakada, and W. Steiner;  with K. Calta; and, most recently with P. Arnoux) and connections between the ergodic theory of billards and 1-forms on algebraic curves and, with the ergodic theory and arithmetic of generalized continued fractions. Recent results include diophantine approximation results for flow directions on translation surfaces (with Y. Bugeaud and P. Hubert, and more recently again with P. Hubert);  a new proof with A. Fisher of a beautiful result of Moeckel.