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portfolio
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publications
SEAR: A Polynomial- Time MultiRobot Path Planning Algorithm with Expected Constant-Factor Optimality Guarantee
Published in 2018 IEEE/RSJ International Conference on Intelligent Robots and Systems (Conference Paper) with S. Han and J. Yu., 2018
We study the labeled multi-robot path planning problem in continuous 2D and 3D domains in the absence of obstacles where robots must not collide with each other.
Primes and Perfect Powers in the Catalan Triangle
Published in Journal of Integer Sequences with N. Benjamin, G. Fickes, E. Fiorini, E. Jovinelly, and T.W.H. Wong, 2019
The Catalan triangle is an infinite lower-triangular matrix that generalizes the Catalan numbers. The entries of the Catalan triangle, denoted by \(c_{n,k}\), count the number of shortest lattice paths from \((0, 0)\) to \((n, k)\) that do not go above the main diagonal. This paper studies the occurrence of primes and perfect powers in the Catalan triangle.
A Model for Birdwatching and other Chronological Sampling Activities
Published in Arxiv Pre-Print, scheduled to appear in American Mathematical Monthly with J. De Loera, D. Oliveros, and A. Torres, 2022
We study the intersections of time dependent events using an original random interval graph model.
Combinatorial Methods for Barcode Analysis
Published in Arxiv Pre-Print, under review, 2022
We study a new partial order on the space of barcodes closely related to the permutahedron. The resulting poset has connections to continuous metrics on barcodes such as the bottleneck and Wasserstein distances.
talks
Young Mathematicians Conference 2016
Published:
Presented some initial results from “Primes and Perfect Powers in the Catalan Triangle”.
UC Davis Graduate Student Research Seminar
Published:
Practice qualifying exam presentation.
AIM Latinx Mathematician Research Community Meeting
Published:
Presented the results of our research group formed during the first AIM Latinx Mathematics Research Community Meeting.
Algebraic Statistics 2022
Published:
Presented on “A Model for Birdwatching and other Chronological Sampling Activities”. Slides are available here.
Society for Industrial and Applied Math Conference on Discrete Mathematics 2022 (SIAM-DM22)
Published:
Presented on “Barcode Posets: Combinatorial Properties and Connections”. Slides are available here.
teaching
Math 54 – Fall 2017
Undergraduate course (TA), UC Berkeley, 2017
Linear Algebra. Lead Instructor: Michael Hutchings.
Math 21A – Fall 2020
Undergraduate course (TA), UC Davis, 2020
Differential Calculus. Lead Instructor: Daniel Martin.
Math 22A – Winter 2021
Undergraduate course (TA), UC Davis, 2021
Linear Algebra. Lead Instructor: David Marsico.
Math 21B – Spring 2021
Undergraduate course (TA), UC Davis, 2021
Integral Calculus. Lead Instructor: Ben Morris.
Undergraduate Directed Reading Program – Spring 2021
Undergraduate Directed Reading Program, UC Davis, 2021
Lead a directed reading program in Mathematical Optimization for two undergraduate students.