Office: Martin O-229
Phone: (864) 656-1284
Fax: (864) 656-5230

Martin Schmoll

Associate Professor
Professional Research Interests
I consider physical models and study those using a variety of mathematical methods. Those methods are rooted in dynamical systems theory, 
measure theory, geometry and topology. In my research I have also used complex analysis, Teichmueller theory, ergodic theory and algebraic geometry.   

Systems I have studied include the billiard in a polygon and more recently the dynamics in doubly periodic, planar Eaton lens patterns. A new direction in my research is based on recent developments in optimal transportation. I try to apply that theory to questions related to ergodic optimization and the study of Ground states for dynamical systems with multi-dimensional potentials. 

For potential students: While particular approaches to billiard theory require a broad mathematical background, some of my research needs less. Depending on students interest I supervise topics ranging from optimal transportation, probabilistic dynamics, dynamical systems and differential geometry that can be conquered by self study upon continuing our standard coursework. Interest in physics or other applications of mathematics is helpful. We have a quite substantial local community that meets once a year at the NSF funded Carolina Dynamics Symposium, short CDS. 
Other Professional Activities
Managing P.I. of the Carolina Dynamics Symposium funded by the NSF (DMS-1600746 Carolina Dynamics Symposium 2016-2018)Information about the group and registration is possible at our webpage We are a growing group and core members of the CD group are faculty at UNC Chapel Hill, UNC Charlotte, Wake Forest, College of Charleston, WCU, Agnes Scott and Davidson College. 
Selected Publications
  • (w. Chris Johnson -- former Student) Pseudo-Anosov eigenfoliations on Panov planes. E.R.A.M.S. 21, 89-108, (2014). 
  • (w. Chris Johnson) Hyperelliptic translation surfaces and folded tori. Topology Appl. 161, 73-94 (2014).
  • (w. Krzysztof Frączek) Directional localization of light rays in a periodic array of retro-reflector lenses. Nonlinearity 27, No. 7, 1689-1707 (2014). 
  • (w. Omri Sarig) Adic flows, transversal flows, and horocycle flows. De Gruyter Proceedings in Mathematics, 241-259 (2014)
Last Updated: 12/21/16