About Me
I am a Ph.D. candidate in mathematics at the University of California, Irvine. My research brings together probability, harmonic analysis, complex analysis, optimization, and machine learning. I work across mathematical theory, algorithm development, and numerical experiments.
I use AI and large language models as conjecture engines: tools for proposing formulas, exploring patterns, and testing possible approaches. I examine their assumptions, search for counterexamples, and use reproducible computations to guide the work. Mathematical conclusions ultimately rest on rigorous proof.
My applied projects include prioritizing drug and vaccine safety reporting signals, complex-valued kernel regression, and mathematical visualization. In ongoing research on portfolio compression and deep hedging, I study how representation and learning errors affect financial risk.
I am interested in collaborations where mathematical reasoning helps make computational methods more reliable and interpretable, with clear assumptions and evidence for their performance.
Education
- Ph.D. in Mathematics — University of California, IrvineIn progress · Expected May 2027
- M.S. in Applied Mathematics — University of California, IrvineDecember 2025
- Chapman UniversityB.S. in Mathematics, B.S. in Physics, B.S. in Computer Science, and B.A. in French · May 2022
Teaching and Mentoring
I have taught Numerical Analysis I and II as instructor of record at UC Irvine and supported courses across the undergraduate mathematics curriculum as a teaching assistant. My mentoring includes undergraduate research in data analysis and dimensionality reduction.
Selected Recognition
- Ronald M. Huntington Outstanding Scholarship AwardChapman University · 2022
- Outstanding Mathematics Student and Outstanding Physics Student HonorsChapman University · 2022
- DataFest — First Place and Best InsightTeam award · Chapman University · 2019
Beyond Research
I speak English, French, Russian, and Hebrew. Outside mathematics and computing, I enjoy weightlifting, building LEGO models, and karaoke.
Contact and Documents
For research, teaching, and industry opportunities, contact nalpay@uci.edu.