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

Institute Visits

Apr--Jun 2026
Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
Jan--Apr 2026
Institut Henri Poincaré, Paris, France — Illustration as a Mathematical Research Technique
May 2025
Max Planck Institute for Mathematics in the Sciences, Leipzig, Germany
Fall 2019
ICERM, Providence, Rhode Island — Illustrating Mathematics

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

Publications

2025
Illustrating Hyperbolic Surfaces with Mesh Embeddings , with Anna Wienhard, Diaaeldin Taha, Erik Loffelholtz, Fabian Lander
submitted, Bridges 2026
2025
Classical Optics for Charged Black Holes
Bridges Math Art Proceedings
2025
Elliptic Curves & The Hopf Fibration , with Nadir Hajouji
forthcoming, Bridges Math Art Conference Proceedings
2024
Degenerations of the Product Geometries in Projective Space that contain Nil , with Tom Shifley
Topology and its Applications
2023
Visualizing Knot Complements
MAA Focus Cover Article, Oct-Nov 2023
2023
Modeling Graphs Beyond Hyperbolic: Graph Neural Networks in Symmetric Positive Definite Matrices , with Diaaeldin Taha, Federico Lopez, Max Riestenberg, Michael Strube, Wei Zhao
European Congress of Machine Learning (ECML)
2022
Raymarching Thurston Geometries , with Henry Segerman, Rémi Coulon, Sabetta Matsumoto
Experimental Mathematics · project website
2021
Algebraic Number Starscapes , with Edmund Harriss, Kate Stange
Experimental Mathematics · project website
2021
The Heisenberg Plane
Algebraic and Geometric Topology, 2023
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)
2020
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

Art Exhibitions

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 Library Art Gallery
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 'Abstractions', 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
3.Dimensional.Space, Wignall Art Museum , with Henry Segerman, Rémi Coulon, Sabetta Matsumoto
Large-Screen Video Installation
2024
Gyroid, and Connect Sum, MAA Golden Section
2024
4D Kleinian Limit Set, Joint Mathematics Meeting
2023
Bleu Hyperbolique, CNRS La preuve par l'image Competition
First Prize Award
2023
Knots in the 3 Sphere, Joint Mathematics Meeting
2022
The Geometry of Knot Complements, MAA Golden Section
2020
Algebraic Starscapes, Iceland
2019
Real Projective Triangles, and The Hopf Fibration, Joint Mathematics Meeting

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) — Undergraduate Course
Hyperbolic Geometry (Math 142) — Advanced Undergraduate Course
Functions of a Real Variable (Math 115) — Undergraduate Math Major Course
Groups & Symmetry (Math 109) — Undergraduate Math Major Course
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 Course

Undergraduate Colloquia & Related Talks

Spring 2025
Penn State, Math Club Public Talk
Spring 2025
Penn State, Student Colloquium
Spring 2025
Santa Clara University, Department Colloquium
Spring 2025
Elon University, Student Lecture
Fall 2024
San Jose State, Department Colloquium
Fall 2024
UC Irvine, Undergraduate Colloquium
Spring 2024
University of Arkansas, Undergraduate Colloquium
The Poincare 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
Summer At ICERM REU, Brown University, Invited Special Lecture
Geometry and the Poincare 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
U Arkansas, Honors College Lecture
Modern Geometry
Winter 2022
Stanford, 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 Sectional Meeting, Plenary Speaker
Ray Optics, Geodesics and Curved Space
Spring 2019
Cornell University, Undergraduate Math Club
Life in hyperbolic space: how a nonzero curvature tensor would screw up your daily routine.
Winter 2019
University of Virginia, Undergraduate Math Club
1,000 Ways to Die in Hyperbolic Space

Invited Public Lectures

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 Poincare 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 Poincare Conjecture
Summer 2023
Heidelberg Institute for Theoretical Studies, Heidelberg, Germany
From Geometry to Machine Learning (In honor of Prof. Dr. 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
Summer 2019
Santa Barbara Media Arts Show, UC Santa Barbara
Curved and twisted worlds: a Virtual Reality Exploration of 3-manifold topology
Spring 2018
National Junior Science and Humanities Symposium
High dimensions in mathematics, computing and the 'real world'
Summer 2018
Santa Barbara Media Arts Show, UC Santa Barbara
3-dimensional shadows of 4-dimensional objects

Select Invited Research Talks

Summer 2025
ICERM, Brown University, Invited Talk: Conference
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, Session: 3D Fabricated Materials for Ed. (with Edmund Harriss)
Fall 2022
UC Santa Cruz, Colloquium
Winter 2022
Arizona State University, Colloquium
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, Topology & Geometry Workshop
Summer 2019
Heidelberg University, Geometry & Dynamics Research Station
Spring 2019
UC Irvine, Topology Seminar
Spring 2019
Stanford University, Geometric Topology Seminar
Winter 2019
University of Virginia, Geometry Seminar
Winter 2019
Cornell University, Topology Seminar
Fall 2018
University of Minnesota, Topology Seminar

Service & Outreach

2024--Present
Academic Integrity Committee
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
2021
Topology beyond the Chalkboard: Speaker
NCNGTC Virtual Conference. Mini-course on creating teaching/outreach animations, session on writing outreach talks
2020
Department Technology Coordinator , Stanford Mathematics Department
Selected electronic tools to help move mathematics courses online during the pandemic, arranged for approval through the university, worked individually with instructors on remote teaching needs
2018--2019
Directed Reading Program: Co-Founder , University of California, Santa Barbara
Co-founded and organized a DRP pairing undergraduate students with graduate mentors. Successfully applied for and received a grant for its continuation
2018--2019
Directed Reading Program: Mentor , University of California, Santa Barbara
2018--2019
SIMS: Tutor , University of California, Santa Barbara
Program pairing graduate students with undergraduates from underrepresented communities
2015--2018
National Science Fair: Speaker, Judge
Jr. Science & Humanities Symposium. Judge in mathematics category. Organizer of STEM outings, panel discussions. Invited speaker
2016--2019
Graduate Topology Seminar: Organizer , University of California, Santa Barbara
Organized schedule, invited speakers, gave talks

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
Annual award given to one full time faculty member, and one part-time faculty member
2018--2019
Bertelsen Dissertation Fellowship , UC Santa Barbara
1-year fellowship. Awardee can be of any academic field, requires departmental nomination
2018
Outstanding Teaching Award , UC Santa Barbara Mathematics Department
Annual departmental award recognizing a graduate student's teaching
2018
Excellence in Teaching Nominee , UC Academic Senate
Nominations across all faculty and instructors directly by students to the Academic Senate
2015--2016
UC Regents Fellowship
Fellowship from the UC Regents, awardees chosen from across all disciplines
2013--2014
UC Regents Fellowship
2013
Excellence in Mathematics Award , University of Minnesota, Twin Cities
Annual award to the two top graduating seniors in the mathematics department
2008--2012
University of Minnesota Gold Scholarship , University of Minnesota, Twin Cities
4-year merit based tuition scholarship
2008
Intel Scholarship , International Science and Engineering Fair (ISEF)
1st place award. Project in Engineering
2008
Department of Defense Scholarship , National Science Fair (JSHS)
1st place award, Junior Science and Humanities Symposium, project in Mathematics
2006
Department of Defense Scholarship , National Science Fair (JSHS)
1st place award, Junior Science and Humanities Symposium, project in Physics

Mathematical Software

Open Source Projects

2019--Present
Raymarcher for the Thurston Geometries
GPU accelerated calculation of the geodesic flow in homogeneous 3-manifolds and physically based shading to compute accurate 'inside views' of manifolds relevant to geometrization
2020--Present
JS System for Mathematical Illustration
Collection of numerical integrators, 3D modeling tools, GPU accelerated computation systems for producing mathematical illustrations, both for research and for class
2020--Present
Path Tracer for Mathematical Illustration
Physically Based Renderer for producing photo-realistic images of mathematical objects (algebraic varieties, limit sets of hyperbolic groups, etc)
2021
GPU-Accelerated Numerical PDEs
Framework for computing and visualizing the results of highly parallelizable numerics in real time (e.g. mean curvature flow on surfaces, 2D Schrodinger equation)
2021
GPU-Accelerated Parametric Surfaces
Framework for computing real-time visualizations of functions defined on parametric surfaces (e.g. surfaces colored by mean curvature, domain coloring on Riemann surfaces)

Selected Specific Programs

Program
Geodesics and Spheres in Sol , for Rich Schwartz
Animation
Finding Lines on a Cubic , for Benson Farb, Jesse Wolfson
Animation
Braid Monodromy , for Benson Farb, Jesse Wolfson
Figures
Cubic Surfaces , for Stephen McKean
Animation
Approaching ∂(Teichmüller Space) , for Katie Mann
Program
Phase of Complex Polynomials , for Jon McCammond, Michael Dougherty

Languages

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