Steve Trettel

Steve Trettel is a geometric topologist, interested in 3-manifolds, interdisciplinary applications of modern geometry, and mathematical illustration.  Steve was born and raised in Minnesota, and received his BS in Mathematics at the University of Minnesota before moving to UC Santa Barbara for his PhD.  Before joining the University of San Francisco, Steve was a Szego Assistant Professor at Stanford University, and a Postdoc at Brown University's Institute for Computational and Experimental Mathematics (ICERM).

• Geometric Topology, particularly trying to understand and classify geometric structures on manifolds
• Riemannian Geometry, particularly interdisciplinary applications of modern geometry across physics and computer science.
• Computer Graphics, particularly extending ray-tracing algorithms and techniques to curved space(time).
• Machine Learning, particularly utilizing the mathematics of curved spaces to more efficiently work with graph embeddings.

• UC Santa Barbara, PhD in Mathematics, 2019
• University of Minnesota, BS in Mathematics, 2013

• Szego Assistant Professor, Stanford University
• Institute Postdoc, ICERM at Brown University

• Algebraic Number Starscapes, coauthored with Edmund Harriss and Kate Stange

• Symmetric Spaces for Graph Embeddings, A Finsler-Riemannian Approach, coauthored with Federico Lopez, Beatrice Pozzetti, Michael Stube, and Anna Wienhard

• Ray-marching Thurston Geometries, coauthored with Remi Coulon, Sabetta Matsumoto and Henry Segerman

• The Heisenberg Plane