Steve Trettel

Steve Trettel is a geometric topologist whose research centers on the broad applications of geometry across mathematics and the sciences. A significant component of his work is mathematical illustration, both as a research technique and as fine art with mathematics as its subject. This work further inspires research in computer graphics itself, including the extension of established physically based rendering algorithms to curved spaces and spacetimes.

• Geometry & topology
• Mathematical illustration
• Geometric machine learning
• AI assisted proof

• 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

• Dean's Award for Excellence in Scholarly and Creative Work, 2025
• Innovation in Teaching with Technology Award, 2023

• Elliptic Curves and the Hopf Fibration, joint with Nadir Hajouji 

• Classical Optics for Charged Black Holes

• 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