Paul Apisa

Paul Apisa is an Assistant Professor in the Department of Mathematics at the University of Wisconsin - Madison, where he conducts research in dynamical systems and geometry. His office is located in Van Vleck Hall, and he can be contacted via email or phone.

Research Focus: Apisa specializes in Teichmüller theory, moduli spaces of Riemann surfaces, and ergodic theory. His investigations include:

• Dynamics on translation and dilation surfaces
• GL(2,R)-orbit closures in moduli spaces
• Invariant subvarieties and their classification
• Lyapunov exponents and monodromy in dynamical systems
• Geometric structures and billiards in polygonal surfaces

Recent Publications: Apisa's 15 most recent works focus on invariant measures, holonomy of affine surfaces, classification of higher-rank invariant subvarieties, and periodic points in genus two surfaces. His research consistently bridges dynamical systems, geometric topology, and moduli theory, with frequent applications to billiards and surface geometry.

Graduate Advising: Currently mentors two PhD students:

• Ruocheng Yang
• Gabriela Brown

Educational Outreach: Contributed lecture series on Teichmüller dynamics at institutions including ICERM, BIRS, and Pacific Dynamics Seminar. Developed comprehensive course notes on dynamical systems and geometric topology.