Kevin Dinh Tuan Dao

Summary of Education

PhD in Mathematics, University of Wisconsin–Madison
Fall 2022–present · Expected May 2028

• NSF Graduate Research Fellow since Fall 2023. Tenure years are 2023-2024, 2026-2027, 2027-2028.
• Passed qualifying examinations in algebra and algebraic topology in Summer 2022.
• Research interests include algebraic geometry, neuroalgebraic geometry, and the mathematical foundations of machine learning.

Master of Arts in Mathematics, University of Wisconsin–Madison
Foundations for Research program · September 2022–December 2023

Bachelor of Science in Mathematics, University of California, San Diego
September 2020–June 2022

• Summa cum laude · GPA: 3.967/4.000.
• Errett A. Bishop Memorial Scholarship, Fall 2021.
• Coursework included numerical analysis, applied linear algebra, graduate real analysis, functional analysis, combinatorics, and ordinary differential equations.

Additional Studies Prior to Graduate School
Coastline Community College, Fall 2018–Summer 2020, excluding Fall 2019
University of Minnesota, Twin Cities, Fall 2019
California High School Proficiency Examination, Summer 2018
Los Amigos High School, Fountain Valley, Fall 2016–Spring 2018

Work Experience

Graduate Teaching Appointments — University of Wisconsin–Madison

September 2022–present

• Served as an instructor of record, teaching assistant, and grader across undergraduate and graduate mathematics courses.
• Served as instructor of record for four sections totaling approximately 200 students in Preparatory Algebra, College Algebra, and Multivariable Calculus between Fall 2024 and Spring 2026 at the University of Wisconsin–Madison.
• Designed lectures, assessments, and review materials and provided office-hour instruction.
• Collaborated with faculty and instructional teams to develop and grade midterm and final examinations.
• Explained technical concepts to audiences with varied mathematical backgrounds across preparatory algebra, calculus, linear algebra, differential equations, and discrete mathematics.

Independent Mathematics Tutor

September 2018–present

• Provide individualized instruction from high school mathematics through undergraduate real analysis and abstract algebra.
• Tutored more than 20 students since September 2018.
• Additional tutoring-center experience includes developing SAT preparation materials and supporting students in Prealgebra, Honors Precalculus, AP Calculus AB, and AP Calculus BC.

Mathematical Research

Vector Bundles on the Universal Vector Extension of an Elliptic Curve

PhD thesis research · In progress

• Study vector bundles on the universal vector extension of an elliptic curve using algebraic geometry, moduli theory, and the Laumon–Rothstein transform.
• Investigate the relationship between D-modules on an elliptic curve and O-modules on its universal vector extension.

Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects

Joint work with Jose Israel Rodriguez · Preprint, 2026
arXiv preprint · CoLoRAI 2026 workshop paper and poster record · Research code

• Constructed counterexamples to the conjecture that every minimal filling architecture of a polynomial neural network has unimodal hidden-layer widths.
• Developed a frontier search using symbolic and finite-field Jacobian-rank computations.
• For quadratic activation with two inputs and one output, identified 13 minimal filling architectures at depth 7 and 82 at depth 8, including 21 nonunimodal examples across the two depths.
• Certified counterexamples using recursive dimension bounds and exhaustive checks of width-reduced subarchitectures.
• Developed a CUDA-accelerated version of the frontier search that achieved a 10× speedup over the SageMath implementation.

Explicit Equations for Surfaces of General Type

Undergraduate project with Jack J. Garzella · Summer 2021

Studied explicit equations for algebraic surfaces using homotopy continuation and Julia.

Research Presentations

• “Minimal Filling Architectures of Polynomial Neural Networks: Counterexamples, Frontier Search, and Defects.” Poster at the 2nd Workshop on Connecting Low-rank Representations in AI: From Practice to Theory (CoLoRAI), ICML 2026, Seoul, South Korea, July 2026.
• “Neuroalgebraic Geometry: Defects, Unimodal MFAs, and Architecture Selection.” Invited talk at the BRL–AGSTA One-Day Workshop, DGIST, Daegu, South Korea, July 2026.

Seminar Talks

Earlier presentations include “Cohen–Macaulay Rings” at the UC San Diego RTG Directed Reading Program in Spring 2021 and “Localization of Commutative Rings” at the University of Minnesota Directed Reading Program in Fall 2019.

Projects and Professional Development

Pricing Quanto Options

Erdős Institute bootcamp group project in quantitative finance · Summer 2026
Project repository

• Implemented closed-form and Monte Carlo pricing for European quanto calls and puts and checked numerical agreement across parameter settings.
• Simulated static and dynamic delta hedging and evaluated hedging errors through profit-and-loss bias and dispersion.
• Reconciled independent implementations across a five-person team by tracing differences in model assumptions, discounting conventions, hedge timing, and simulation design.
• Estimated volatility and asset–exchange-rate dependence from Nikkei 225 and foreign-exchange data using exponentially weighted moving averages (EWMA), generalized autoregressive conditional heteroskedasticity (GARCH), and dynamic conditional correlation (DCC), then evaluated calibrated hedging performance.

NYC Rat Sightings Forecasting

Erdős Institute Data Science Bootcamp group project · Spring 2026
Project repository

• Joined historical NYC 311 rat-sighting reports with weather data, engineered calendar features, and developed 14-day forecasts of daily sightings at citywide and borough levels.
• Compared SARIMAX, Prophet, NeuralProphet, XGBoost, Holt–Winters, ridge regression, and ensembles using 26-fold walk-forward cross-validation and RMSE.
• Evaluated selected models on a one-year holdout set.
• Developed reproducible Python notebooks for cleaning data, engineering features, tuning models, evaluating forecasts, and generating updated two-week predictions.

Advanced Reading Courses and Seminars

Teaching History

All university teaching appointments listed below were at the University of Wisconsin–Madison.

Instructor of Record

Teaching Assistant

Graduate Course Grader

Technical Skills

• Programming: Python, SQL, R, Julia.
• Libraries and Frameworks: NumPy, pandas, scikit-learn, PyTorch, XGBoost, Numba.

Service and Outreach

Co-organizer, Graduate Algebraic Geometry Seminar

University of Wisconsin–Madison · Spring 2024–present

• Co-organize a weekly seminar with approximately 30 talks per academic year.
• Recruit and schedule speakers, coordinate logistics, and maintain the seminar program and webpage.
• Work with graduate-student speakers to scope technical talks for audiences with varied mathematical backgrounds.

Organizer, Graduate Reading Seminars

• Seminar Topics in Algebraic Geometry, Fall 2024–Fall 2025. Topics included geometric invariant theory, D-modules, derived categories, abelian varieties, the geometric Satake correspondence, moduli of principal bundles, algebraic stacks, and moduli spaces.
• The Arithmetic of Abelian Varieties Seminar, Summer 2023.

Directed Reading Program Organizer and Mentor

University of Wisconsin–Madison · Mentoring since Fall 2022

• Helped organize the Directed Reading Program in Fall 2022 and Fall 2023, pairing graduate mentors with undergraduate students for advanced reading projects.
• Mentored at least 10 undergraduates through semester-long projects in commutative algebra, algebraic geometry, representation theory, and complex analysis.
• Set weekly reading milestones, reviewed written proofs, and coached students in presenting advanced mathematics clearly.

Travel and Conferences Attended