Research Experience
Current Research Experience
LLM Distillation
March 2026 - Present
Working on LLM distillation.
Mentors: Professors Chuntian Wang and Jia Zhao
Rectifiability
Feb 2026 - Present
Learning about rectifiability related stuff.
Mentor: Professor Simon Bortz
Combinatorial Perspective of \(q,t\)-Catalan Symmetry
Feb 2025 - Present
Working on a subset of the combinatorial proof of the \(q,t\)-Catalan symmetry.
Mentor: Professor Kyungyong Lee
Past Research Experience
Finite-Size Effects in Epidemic Models
May 2025 - Dec 2025
Co-developed agent-based and mean-field SIHRS models incorporating immunity waning to capture recurrent epidemic waves. Employed a martingale-based early-time-step method to identify non-linear amplification of finite-size effects. Validated theoretical predictions via numerical simulations calibrated to county-level COVID-19 data.
Mentors: Professor Chuntian Wang, Professor Yuanyuan Song, Professor Yuanzhen Shao
Game of Cycles on Maximal Plane Graphs
Feb 2024 - June 2024
Defined "IO Maximal Plane Graphs" and analyzed invariant properties to determine the game outcome. Established that the winning strategy is determined by the parity of the graph's vertices.
Mentor: Professor Malgorzata Marciniak
Method of Brackets and Bessel Function Integrals
June 2023 - Aug 2023
Applied the "Method of Brackets" to provide rigorous proofs for entries involving Bessel functions of the first and second kind from the Gradshteyn and Ryzhik tables.
Mentor: Professor Victor H. Moll
Continued Fractions, \(a\)-Fibonacci Numbers, and Middle \(b\)-Noise
Mar 2023 - Aug 2023
Generalized the continued fractions [1,..., 1, 3, 1,..., 1] to [a,..., a, b, a,..., a] using \(a\)-Fibonacci sequences. Showed that the \(a\)-th metallic ratio limit is invariant under the middle noise term \(b\).
Mentor: Professor Cheng-Han Pan
Publications
A. Gurung, S. Wagle, A. Carr, C. McCann, K. Kodatt, Y. Song, Y. Shao, C. Wang. "An exploration of finite-size effects in the dynamics of epidemic compartmental modelling." Under Review.
A. Gurung and C.-H. Pan. "Continued Fractions, a-Fibonacci numbers, and the middle b-noise," Mathematics Exchange, 18(1), 77–87, 2024.
(with the Polymath Jr. Group). "The integrals in Gradshteyn and Ryzhik. Part 34: Bessel functions," Scientia Series A: Mathematical Sciences, 34, 109–129, 2024.
Conferences & Workshops
March 2026: AMS Southeastern Sectional Meeting, Presenter
May 2024: CUNY Undergraduate Research Day 2024, Presenter
Aug 2024: MathFest 2024, Presenter
Sept-Nov 2024: Preliminary Arizona Winter School 2024: Symmetries of Root Systems, Attendee