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, and with former Ph.D. student Mesa Walker proving the distinctness of two pseudo-Anosov maps, answering a question in the literature for some 40 years.

PhD Students

Schmidt has one current PhD student, Peyton Pfeiffer. Mesa Walker finished her dissertation in May 2024 "On the distinctness of two pseudo-Anosov maps". 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

Research areas