University of Washington
Applied Mathematics, Ph.D.
Applied Mathematics, Ph.D.
Kieran Vlahakis
EDUCATION
California Institute of Technology (Caltech)
Applied and Computational Mathematics B.S. (GPA: 4.1)
Applied and Computational Mathematics B.S. (GPA: 4.1)
- Acknowledged in Nakatsukasa and Trefethen (2026) and Horning and Trefethen (2025)
- Gee Family Poster Competition Winner — Waves Resonances and Eigenstates in Periodic Structures
- Bonnie-Cashin Prize for most outstanding admission essays
RESEARCH
Independent Research – Numerical Analysis
Oxford University, Prof. Nick Trefethen
Oxford University, Prof. Nick Trefethen
- Derived closed-form expressions for Cauchy transforms of Gauss-Jacobi weight using hypergeometric series
- Identified key conditions for exact barycentric rational quadrature interpolants and proved existence
- Generated equispaced quadratures through Lawson-iterated least-squares solutions of rational interpolants
J. Weldon Green Research Fellow – Scientific Computing
Caltech, Prof. Oscar Bruno
Caltech, Prof. Oscar Bruno
- Implemented a partial differential equation (PDE) solver based on the rectangular-polar method (RPM)
- Extended the RPM solver to support both Laplace and Helmholtz equations
- Optimized program to reconstruct and graph the PDE's solutions ~50% faster
Researcher – Computer Vision
Caltech, Dr. Ashish Mahabal
Caltech, Dr. Ashish Mahabal
- Assessed contrast tuning effects on zero-shot segmentation performance
- Benchmarked coordinate vs. unprompted prompting modes to identify optimal use
- Tuned hyperparameters to double segmentation accuracy in real-world settings
TEACHING
Head Teaching Assistant (Head TA) – Linear Algebra
Caltech, ACM 104 (160+ students)
Caltech, ACM 104 (160+ students)
- Directed a team of 12 — coordinating all instructional logistics (grading workflows, weekly operations, etc.)
- Delivered weekly office hours, prepared lecture support materials, and led course review lectures
- Aggregate teaching evaluation score: 4.25/5.0
Head Teaching Assistant (Head TA) – Numerical Methods
Caltech, ACM 11 (80+ students)
Caltech, ACM 11 (80+ students)
- Directed a team of 5 — aligning weekly responsibilities and ensuring consistent execution of tasks
- Delivered weekly office hours, graded weekly assignments, and provided in-lecture support for instructor
- Aggregate teaching evaluation score: 4.80/5.0
WORK EXPERIENCE
Operations Coordinator
Satcom Technologies Ltd
Satcom Technologies Ltd
- Prepared and processed documents for the National Institute for Scientific and Industrial Research
- Managed inventory for over $50,000 worth of equipment
- Coordinated transport for staff and equipment to field sites under tight deadlines
EXTRACURRICULAR ACTIVITIES
Student–Faculty Conference Co-chair
Caltech, Applied and Computational Mathematics
Caltech, Applied and Computational Mathematics
- Liaised between faculty and students to align degree objectives with student needs
- Analyzed peer program data to identify structural differences in ACM degree
- Presented findings to faculty and peers, proposing actionable improvements
SKILLS
Programming Languages: Python, MATLAB, Java, C, R, LaTeX
Technologies and Tools: PyTorch, TensorFlow, Keras, Microsoft Suite, Jupyter Notebook, Google Colab, Dropbox, Data Analysis