Kurt Vinhage

Email: vinhage@math.utah.edu
Office: JWB309

Welcome to Kurt Vinhage's website! Here you will find important information regarding teaching, current research activities, and a (reasonably) updated CV/Resume. Feel free to look around!

pre-REU 2024


Utah Dynamics Mini-Workshop

Research Interests

Smooth Dynamical Systems, Algebraic and Homogeneous actions, Higher-rank actions, Rigidity Properties, Measurable Invariants of Smooth Systems


Resource Archive

  • Pre-REU 2023
  • Brin Summer School 2023 Notes
  • Fun Math Websites


    Below, find the smooth time change of a linear flow. In the first GIF, the red points move with the linear flow, and the green and blue correspond to slow-downs of varying degeneracies. Notice that the orbits eventually re-align! In the second, you can see this slowdown affects a box in linear flow on a torus.

    Slowdown of vertical flow

    Slowdown of flow on 2-torus

    Below find a fundamental domain of the modular surface, and periodic horocycles on it sampled at 4000 points. In the first animation, they move ``downward'' in the Poincare disc model by applying the geodesic flow, eventually equidistributing. In the second figure, the half space model is used (rotated from standard conventions), and you can see the points distributing the the hyperbolic volume (more dense closer to the bottom).