Caglar Uyanik

Caglar Uyanik serves as Assistant Professor of Mathematics and Director of the Madison Experimental Mathematics Lab (MXM) at the University of Wisconsin-Madison's Department of Mathematics. His research bridges geometric topology, group theory, and dynamical systems with significant contributions to Teichmüller theory and geodesic currents.

His primary research interests include Geometric Topology, Geometric Group Theory, Ergodic Theory, and Dynamics, with specialized focus on mapping class groups, Teichmüller spaces, Out(F_N), geodesic currents, Veech surfaces, and symbolic dynamics. His work explores connections between group actions, hyperbolic geometry, and probabilistic methods in dynamical systems.

Recent publications demonstrate evolving focus from foundational work on North-South dynamics (2014-2019) toward contemporary applications in random walks on Teichmüller space (2023) and singularity analysis of Cannon-Thurston maps (2025). Key thematic threads include geometric structures on moduli spaces, spectral properties of group actions, and distribution phenomena in translation surfaces.

Scientific recognition includes:

• NSF CAREER award supporting research on geometric group theory

Uyanik actively mentors graduate students including PhD recipients Yandi Wu (2024) and current candidates Rongsong Yang and Rachel Heikkinen, plus Master's student Hart Easley. He co-leads the NSF-funded RTG: Geometry, Group Actions and Dynamics while directing MXM which engages undergraduates in experimental mathematics projects. His research receives primary support through NSF Award DMS 2439076 and the RTG grant.

As founder and director of the Madison Experimental Mathematics Lab, he cultivates collaborative research environments where students investigate geometric structures through computational experimentation, particularly focusing on translation surfaces and group actions.