Curriculum Vitae

Steve Trettel / Department of Math & Statistics, University of San Francisco / strettel@usfca.edu / stevejtrettel.site

Appointments

2022--
University of San Francisco, Assistant Professor of Mathematics
2019--2022
Stanford University, Szegő Assistant Professor of Mathematics
Fall 2019
Brown University, ICERM Institute Postdoc

Research Residencies

Apr--Jun 2026
Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
Jan--Apr 2026
Institut Henri Poincaré, Paris, France — Semester program on [Illustration as a Mathematical Research Technique](https://www.ihp.fr/en/news-research-activities/t1-2026-illustration-mathematical-research-technique).
May 2025
Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
Aug--Dec 2019
ICERM, Providence, Rhode Island — Semester program on [Illustrating Mathematics](https://icerm.brown.edu/programs/sp-f19/).

Education

2013--2019
University of California, Santa Barbara, PhD, Mathematics
Advisor: Darren Long. Thesis: Families of Geometries, Real Algebras and Transitions
2008--2013
University of Minnesota, Twin Cities, B.S. Mathematics
Minors: Philosophy, Astrophysics, Linguistics. Additional Emphasis: Dakhóta Language

Research & Creative Work

Publications

2026
Illustrating Hyperbolic Surfaces with Mesh Embeddings , with Anna Wienhard, Diaaeldin Taha, Erik Loffelholtz, Fabian Lander
accepted, Bridges 2026
2025
Classical Optics for Charged Black Holes
Bridges Math Art Proceedings
2025
Elliptic Curves & The Hopf Fibration , with Nadir Hajouji
Bridges Math Art Proceedings
2024
Degenerations of the Product Geometries in Projective Space that contain Nil , with Tom Shifley
Topology and its Applications
2023
The Heisenberg Plane
Algebraic and Geometric Topology
2023
Modeling Graphs Beyond Hyperbolic: Graph Neural Networks in Symmetric Positive Definite Matrices , with Diaaeldin Taha, Federico Lopez, Max Riestenberg, Michael Strube, Wei Zhao
ECML (European Congress of Machine Learning)
2022
Raymarching Thurston Geometries , with Henry Segerman, Rémi Coulon, Sabetta Matsumoto
Experimental Mathematics
2022
Algebraic Number Starscapes , with Edmund Harriss, Kate Stange
Experimental Mathematics
2021
Vector-valued Distance and Gyrocalculus on the Space of Symmetric Positive Definite Matrices , with Anna Wienhard, Beatrice Pozzetti, Federico Lopez, Michael Strube
NeurIPS (Neural Information Processing Systems)
2021
Symmetric Spaces for Graph Embeddings: A Finsler-Riemannian Approach , with Anna Wienhard, Beatrice Pozzetti, Federico Lopez, Michael Strube
ICML (International Conference on Machine Learning)
2020
Non-Euclidean Virtual Reality III: Nil , with Henry Segerman, Rémi Coulon, Sabetta Matsumoto
Bridges 2020 Conference Proceedings
2020
Non-Euclidean Virtual Reality IV: Sol , with Henry Segerman, Rémi Coulon, Sabetta Matsumoto
Bridges 2020 Conference Proceedings

Preprints & Work in Progress

2026
Certifying Arithmeticity for Two Degree-Six Symplectic Hypergeometric Monodromy Groups , with Anna Wienhard, Diaaeldin Taha, Max Riestenberg
arXiv
2026
Discrete Isometric Embeddings into Riemannian Manifolds via Energy Minimization , with Diaaeldin Taha, Fabian Lander
2026
Surfaces of Revolution in Homogeneous 3-Manifolds , with Fabian Lander
2026
Visualizing Elliptic Curves over Finite Fields , with Nadir Hajouji

Art Exhibitions

2026
Elliptic Curves, International Congress of Mathematics
Art Exhibition at the Fields Medal Ceremony, Philadelphia PA. August (to appear)
2026
Warped Realities, International Congress of Mathematics
Art Exhibition at the Fields Medal Ceremony, Philadelphia PA. August (to appear)
2026
27 Lines on a Cubic Surface, Maison Poincaré
Mathematical Art Exhibiton, Paris France April-June
2025
The Geometry of Spacetime, National Museum of Mathematics
"Warped Realities" Exhibition, June--August
2025
Geodesic Woodcuts, National Museum of Mathematics
"Warped Realities" Exhibition, June--August
2025
Singularity, Turtle Bay Exploration Park
West Coast Biennial: Juried Exhibition, Redding CA, January--May
2025
Many Paths to the Beach, South SF Cultural Arts Center
South SF, February in the show 'Finding a Path'
2025
Geodesic Woodcuts, Joint Math Meetings , with Edmund Harriss
Seattle, WA
2025
Singularity, Joint Math Meetings
Seattle, WA
2024
Julia, O'Hanlon Center for the Arts
Selected for Juried show 'Chaos'
2024
Many Paths to the Beach, O'Hanlon Center for the Arts
Selected for 'Chaos'
2024
Thurston Geometries, Queens College NY , with Henry Segerman, Rémi Coulon, Sabetta Matsumoto
Mathematical Art Exhibition
2024
Kleinian Creatures from the 4th Dimension, Epperson Gallery
Selected for Juried Show 'Abstract Dimensions', October 2024
2024
Kleinian Creatures from the 4th Dimension, ARC Gallery SF
Accepted into second-tier of the Gallery show 'Fantasy': work displayed on screen in-gallery, June 2024
2024
Thurston Geometries, Wignall Art Museum , with Henry Segerman, Rémi Coulon, Sabetta Matsumoto
Large-Screen Video Installation
2024
4D Kleinian Limit Set, Joint Mathematics Meeting
2023
Bleu Hyperbolique, CNRS La preuve par l'image Competition
First Prize Award
2023
The Geometry of Knot Complements, Joint Mathematics Meeting
2020
Algebraic Starscapes, Gaukurinn, Reykjavik , with Edmund Harriss, Kate Stange
Exhibition of Algebraic Starscapes prints at Gaukurinn, a cultural centre in Reykjavik, Iceland
2019
Real Projective Triangles, and The Hopf Fibration, Joint Mathematics Meeting

Mathematical Software

Systems

JavaScript / Three.js
Three.js Demos
A TypeScript/three.js framework for mathematical visualization and animation.
JavaScript / GLSL
Shader Sandbox
Running mathematical GLSL shaders locally, as an npm package.
GLSL
Path Tracer
Photorealistic path tracing of signed distance functions in GLSL.
TypeScript / three.js
Homogeneous Spaces
Points, geodesics, and surfaces in 2D and 3D homogeneous spaces.
TypeScript / Three.js
Coxeter Visualizations
Coxeter groups, polytopes, and tilings in hyperbolic space.
TypeScript / Three.js
Limit Sets
Limit sets of matrix groups on projective space and flag varieties.
Python, Javascript
Geometric Optimization
A mesh-physics engine for Riemannian ambient spaces.

Projects

Javascript / GLSL
Cubic Lines
Real-time cubic surfaces and their 27 lines, from six points in the plane.
Javascript
Geodesic Boards
Geodesics on curved surfaces, exported as CNC toolpaths for engraving.
Constant Curvature Surfaces
Constant-curvature surfaces of revolution and their Dini twists.
TypeScript / Three.js
Low-Vertex Flat Tori
Numerically discovering low-complexity flat tori in 3-space.
TypeScript / Three.js
Variety Point Clouds
Sampling algebraic varieties in projective space as point clouds.
JavaScript
Knitted Surfaces
Woven and knitted strand patterns on meshed surfaces.
TypeScript / Three.js
Anosov
Certifying Anosov representations into higher-rank Lie groups.
TypeScript / GLSL
Starscapes
Visualizing the geometry of algebraic numbers.

Teaching

Course Notes

Math 211
Multivariable Calculus (200 pages)
Supplementary notes & interactive demos for a 1-semester course in multivariable and vector calculus.
Math 380
Modern Geometry (510 pages)
First draft of a textbook providing a unique treatment of hyperbolic geometry as part of a continuous 1-parameter family including the sphere and Euclidean plane.
Math 453
Real Analysis (370 pages)
Second draft of a textbook for a 1-semester course in real analysis emphasizing historically important problems and an axiomatic approach to integration.
Graduate Mini Course
Shader Programming (130 pages)
Extensive course notes (including fully worked examples and homework) introducing GPU programming to mathematicians. Taught at CIRM Graduate Winter School.

Teaching Experience

University of San Francisco

Foundations of Geometry (Math 380) — Advanced Undergraduate
Real Analysis (Math 453) — Advanced Undergraduate
Linear Algebra (Math 230) — Intermediate Undergraduate
Calculus III: Multivariate (Math 211) — Intermediate Undergraduate
Calculus II: Integral (Math 110) — Introductory Undergraduate
Calculus I: Differential (Math 109) — Introductory Undergraduate

Stanford University

Intro to Proof (Math 56) — Intermediate Undergraduate
Hyperbolic Geometry (Math 142) — Advanced Undergraduate
Functions of a Real Variable (Math 115) — Intermediate Undergraduate
Groups & Symmetry (Math 109) — Intermediate Undergraduate
Integral Calculus (Math 21) — Introductory Undergraduate
Linear Algebra & Multivariable Calculus (Math 51) — Introductory Undergraduate

University of California, Santa Barbara

Integral Calculus (Math 3B) — Introductory Undergraduate

Talks

Undergraduate Colloquia & Related Talks

Fall 2025
Sonoma State University, Undergraduate Colloquium
Mathematics of Beautiful Graphics
Spring 2025
Penn State, Math Club Public Talk
Why You Can't Tie Your Shoes in the 4th Dimension
Spring 2025
Penn State, Student Colloquium
Mathematics of Beautiful Graphics
Spring 2025
Santa Clara University, Department Colloquium
Classical Physics in Curved Space
Spring 2025
Elon University, Student Lecture
Mathematics of Beautiful Graphics
Fall 2024
San Jose State, Department Colloquium
From Geometry to Machine Learning
Fall 2024
UC Irvine, Undergraduate Colloquium
Modern Geometry and Machine Learning
Spring 2024
University of Arkansas, Undergraduate Colloquium
The Poincaré Conjecture
Spring 2024
University of Arkansas, Department Spring Colloquium
Classical Physics in Curved Space
Spring 2023
Sonoma State University, Undergraduate Colloquium
The Linear Algebra of Color Vision
Spring 2022
ICERM REU, Invited Special Lecture
Geometry and the Poincaré Conjecture
Spring 2022
Santa Clara University, Undergraduate Colloquium
A visual introduction to the algebraic topology of surfaces
Winter 2022
Arizona State University, Graduate Colloquium
What is Hyperbolic Dehn Surgery?
Winter 2022
University of Arkansas, Honors College Lecture
Modern Geometry
Winter 2022
Stanford University, SUMO
The Classification of n-Manifolds
Fall 2021
Humboldt State University, Mathematics Colloquium
What do 3-manifolds look like? Using the geometrization theorem to understand topology.
Spring 2021
Stanford Online High School, Invited Lecturer Series
A history of mathematical optics: from the Greeks to Einstein
Spring 2021
MAA Golden Section, Plenary Speaker
Ray Optics, Geodesics and Curved Space
Spring 2021
Stanford Math Club, Public Talk

Invited Public Lectures

Summer 2026
MAA MathFest, Boston, MA , Invited Address (forthcoming)
The Mathematics of Beautiful Graphics
Spring 2025
UCI Geometry Day, Irvine, CA
Charged Black Holes
Spring 2025
Bay Area Math Olympiad , Keynote
Why you Can't Tie Your Shoes in the 4th Dimension
Spring 2025
Spring Math Day, Elon University
The Poincaré Conjecture
Fall 2023
Notre Dame: Math is For Everyone , Annual Lecture
From Geometry to Machine Learning
Fall 2023
Wonderfest, Castro Valley, CA
Seeing Space(time)
Fall 2023
SF Public Library, San Francisco
Geometry and the Poincaré Conjecture
Summer 2023
Heidelberg Institute for Theoretical Studies, Germany
From Geometry to Machine Learning (In honor of Anna Wienhard)
Spring 2023
Wonderfest, Novato, CA
Geometry from the inside: General Relativity and deep space imagery
Fall 2022
SF Science Fair, Lowell HS
From Magnifying Glasses to Black Holes
Fall 2021
Connecting the Young World International STEM Fair , Plenary Speaker
Geometry and Topology in Modern Mathematics
Fall 2021
76th Harry S. Kieval Lecture, Humboldt State University, CA
Optics from Euclid to Einstein
Winter 2021
National Museum of Mathematics, New York, NY (Virtual)
Life in Curved Space: From Magnifying Glasses to General Relativity
Winter 2021
Gathering for Gardner: Celebration of Mind, Virtual
Visualization in low dimensional topology: differences in dimensions 2, 3 and 4
Fall 2020
Bay Area Mathematical Adventures, San Jose, CA (Virtual)
When the shortest path doesn't look straight: geometry in optics, optimization and relativity

Select Invited Research Talks

Summer 2026
BIRS Oaxaca, Invited Talk: Frontiers in Surface Topology
Spring 2026
Institut Henri Poincaré, Invited Talk: Conference · video
Summer 2025
ICERM, Brown University, Invited Talk: Conference · video
Summer 2025
U. Eindhoven, Invited Talk: Conference
Spring 2025
Penn State, Research Seminar
Spring 2025
Vanderbilt, Department Colloquium
Fall 2024
UC Irvine, Geometry Seminar
Fall 2024
California Community Colleges, Conference Keynote
Fall 2024
Brown University, Geometry Seminar
Spring 2024
University of Arkansas, Topology Seminar
Spring 2024
Spring Topology and Dynamics Conference, Geometric Topology Session
Spring 2024
Surfaces at the Frontier Conference, Plenary Speaker
Winter 2024
Joint Math Meetings, joint talk with Edmund Harriss
Fall 2022
UC Santa Cruz, Colloquium
Winter 2022
Arizona State University, Colloquium
Fall 2021
UC Santa Barbara, Computational Neuroscience Seminar
Summer 2021
Nearly Carbon Neutral Geometry & Topology Conference, Contributed Talk
Spring 2021
Cornell Topology Festival, Introductory Speaker · video
Spring 2021
McGill University, Geometric Group Theory Seminar
Winter 2021
University of Florida, Topology and Dynamics Seminar
Winter 2021
University of Arkansas, Mathematics Colloquium
Summer 2020
Weizmann Institute, Topology Seminar
Spring 2020
Stanford University, Topology Seminar
Spring 2020
UC Davis, Topology Seminar
Winter 2020
Arizona State University, Geometry and Topology Seminar
Fall 2019
UT Austin, Topology Seminar
Fall 2019
Brown University, Topology Seminar
Fall 2019
ICERM, Brown University, Topology & Geometry Workshop · video
Summer 2019
Heidelberg University, Geometry & Dynamics Research Station

Service

Department & University

2024--Present
Academic Integrity Committee , University of San Francisco
2025
Brought USF Students to MAA Math Conference
2025
Math Dept. Working Group: Rethink Placement
2025
USF Putnam Exam Coordinator
2023--2024
Helped Organize USF student trips to two math conferences
JMM and MAA Golden Section
2023
Strategic Enrollment and Student Life: Math Liaison
2023
Calculus Recitation Pilot
On committee organizing Calculus Recitations at USF
2021
Stanford Postdoc Teaching Workshop
Gave presentations on teaching a wide variety of course types, recorded lectures from live classes for future training material
2020
Department Technology Coordinator , Stanford Mathematics Department
Selected and deployed tools to move mathematics courses online during the pandemic, supporting instructors individually

Mathematical Community

Other

Fellowships & Awards

2025
Dean's Award for Excellence in Scholarship , University of San Francisco
2023
Innovation in Teaching with Technology Award , University of San Francisco
One full time, and one part time faculty member
2018--2019
Bertelsen Dissertation Fellowship , UC Santa Barbara
1-year fellowship. Very competitive, awardee can be from any discipline
2018
Outstanding Teaching Award , UC Santa Barbara Mathematics Department
Annual departmental award recognizing a graduate student's teaching

Languages

English — Native Speaker
Dakhóta Iyápi — 2nd language learner
Deutsch — 2nd language learner