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Short description of portfolio item number 1

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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.

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.

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.

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.

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Presented some initial results from “Primes and Perfect Powers in the Catalan Triangle”.

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Practice qualifying exam presentation.

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Presented the results of our research group formed during the first AIM Latinx Mathematics Research Community Meeting.

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Presented on “A Model for Birdwatching and other Chronological Sampling Activities”. Slides are available here.

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Presented on “Barcode Posets: Combinatorial Properties and Connections”. Slides are available here.

Undergraduate course (TA), *UC Berkeley*, 2017

Linear Algebra. Lead Instructor: Michael Hutchings.

Undergraduate course (TA), *UC Davis*, 2020

Differential Calculus. Lead Instructor: Daniel Martin.

Undergraduate course (TA), *UC Davis*, 2021

Linear Algebra. Lead Instructor: David Marsico.

Undergraduate course (TA), *UC Davis*, 2021

Integral Calculus. Lead Instructor: Ben Morris.

Undergraduate Directed Reading Program, *UC Davis*, 2021

Lead a directed reading program in Mathematical Optimization for two undergraduate students.