Research

Schmidt is nominally a number theorist. He is currently most interested in: natural extensions for continued fractions for various Fuchsian groups (with C. Kraaikamp, and various third co-authors: K. Calta, I. Smeets, H. Nakada, and W. Steiner; with K. Calta; and, with P. Arnoux) and connections between the ergodic theory of billiards and 1-forms on algebraic curves and, with the ergodic theory and arithmetic of generalized continued fractions. Recent results also include joint work with former Ph.D. student A. Yiltekin-Karatas on families of interval maps arising from actions of cocompact triangle groups on the unit circle.

PhD Students

Schmidt's current PhD students are: Peyton Pfeiffer and Mesa Walker. Ayse Yiltekin Karatas finished her dissertation in May 2023, on "One-Parameter Deformations of the Bowen-Series Map Associated to Cocompact Triangle Groups". Worapan Homsomboon finished his dissertation, on dynamical systems on the Sierpinski carpet in the summer of 2022. Other former PhD students: K. Daowsud, H. Do, B. Edwards, T. Hatase, W. Homsomboon, A. Moreira (Bell), J. Schmurr, K. Smith, see linked website (under photo).

Education

Ph.D., Pennsylvania, 1989

College strategic research areas