Academics

Fundamentals of Programming (MIT 6.1010, former 6.009) Lab Assistant | Spring 2019 - Spring 2020

Eta Kappa Nu (HKN) Tutor for Fundamentals of Programming | Fall 2019

Math Learning Center Tutor | Fall 2019

Mathematics for Computer Science (MIT 6.1200, former 6.042) Teaching Assistant | Spring 2020

Eta Kappa Nu (HKN) Tutor for Mathematics for Computer Science | Spring 2020

Mathematics for Computer Science  (MIT 6.1200, former 6.042) Grader | Spring 2022

Research works

DFS vs BFS for Random Targets in Ordered Trees | 2023 | Stoyan Dimitrov, Luz E. Grisales Gomez, Yan Zhuang

We compare the performance of DFS and BFS given that we are at the root of an unknown ordered tree T with n edges and that we want to find a specific target node x located at a given level l in T.

Digraphs with exactly one Eulerian tour | 2022 | Luz Grisales, Antoine Labelle, Rodrigo Posada, Stoyan Dimitrov

We give two combinatorial proofs to the formula for the umber of diagraphs with exactly one Eulerian tour. This work was the result of a remote collaboration in summer 2020 under the supervision of Stoyan Dimitrov.

Alexander Invariants of 2-knots from triplane diagrams (Unfinished) | 2021 | Ethan Clelland, Calvin Godfrey, Alexandra Emmons, Luz Grisales, and William E. Olsen

This work was done during the UVA Topology REU of 2021. We used the trisection data of a bridge trisected 2-knot to compute Alexander invariants, and also developed an implementation of our results on Sage.

Expository works

Three approaches for counting spanning trees in a K_n that can be applied in a K_{m,n} | 2021 | Luz Grisales

Three popular proofs of Caley's formula and insights on how the strategies used can be borrowed to count the number of spanning trees of a K_{m,n}.

Other works

Solutions to "Bijective proof problems" by Richard Stanley | Stoyan Dimitrov, Luz Grisales, Rodrigo Posada

Compilation of solutions and references to solutions for more than 150 problems in the Richard Stanley’s list of bijective proof problems.

This section is a bit lacking right now, as I built this website not long ago, and I still don't know enough math. I'm hoping that with time it will become a good demonstration of the kind of math that I like :)

18.900: Geometry and Topology in the plane - Lecture Notes Spring 2020

I'm not allowed to share these notes, but I truly loved every single topic in this class, which included scissors congruencies, Pick's theorem, the shoelace formula, the winding numbers, the free homotopy class, the phase space, the linking number, immersed loops, the rotation number, Arnold invariants, algebraic curves, and triangulations.

Fast Fourier Transform - 6.046 Lecture Notes 2015

I personally loved how a concept such as the roots of unity was used to improve the runtime of polynomial multiplication!

Cubic Graphs Induced by Bridge Trisections

The Knot Book | 1994 | Colin Adams

I read this book as part of MIT's Math Department's Directed Reading Program and I was really drawn by all the knot invariants discussed!

Tilings | 2005 | Federico Ardila and Richard Stanley