Research
Over this past year, I've become interested in symplectic geometry and topology. I am happily surprised by how one can use old math like calculus to reinvent the wheel (like in the film Hidden Figures)! Symplectic geometry uses topology, (complex) analysis, algebraic geometry, differential geometry to solve problems motivated from theoretical physics.
I'm interested in Morse theory with a view towards Floer theory. I am curious about obstruction bundle gluing, pseudo-holomorphic curves, and Lagrangian Floer homology.
Talks
■ Morse Homology, Informal Student Symplectic Geometry Seminar, Nov 15, 2023. (virtual talk)
■ An Introduction to k-Typed Parking Functions!, UMN Student Combinatorics and Algebra Seminar, Dec 1, 2022. (talk)
■ An Exploration To Determine Polynomials For Specific Finite Groups
Arithmetic and Topology over Global Fields Workshop, University of Wisconsin-Madison, October 7-9, 2022. (Poster)
■ An Exploration To Determine Polynomials For Specific Finite Groups
BRIDGES Conference, University of Utah, June 7-10, 2022. (Poster)
■ Enumerating k-Typed Parking Functions and Their Properties
UW-Madison Math Club, April 22, 2022.
■ Enumerating k-Typed Parking Functions and Their Properties (with Aalliyah Celestine and Jacob van der Leeuw)
JMM MSRI Special Session: MSRI Undergraduate Program, (Invited) April 8, 2022, (Slides)
■ k-Typed Parking Functions
SUMS 2022 Math and Puzzles Conference, Brown University, March 19, 2022, (Slides)
■ Counting 2-Typed Parking Functions
SACNAS National Diversity in STEM Conference, Oct 25-29, 2021, (Poster)
■ Counting 2-Typed Parking Functions
2021 Baylor McNair Research Conference, Aug 19, 2021, (Slides)
■ Counting 2-Typed Parking Functions
2021 UW-Madison McNair Summer Research Experience Symposium, Aug 6, 2021, (Slides)
■ k-Type Parking Functions (with Aalliyah Celestine and Jacob van der Leeuw)
2021 MSRI-UP REU Presentations, June 23, 2021, (Recording) (Slides)
Publications
Exact k-Typed Parking Functions. (In preparation)
Aalliyah Celestine, Rebecca Garcia, Pamela E. Harris, Lina Liu, Casandra Monroe, Dwight J. Carlos Martínez Mori and Jacob van der Leeuw, Anderson Williams II.
Conferences Attended
2024 JMM, San Fransisco, CA (in-person)
2023 JMM, Boston, MA (in-person)
2022 Arithmetic and Topology over Global Fields Workshop, University of Wisconsin-Madison (in-person, presented)
2022 BRIDGES Conference, University of Utah (in-person, presented)
2022 Undergraduate Research Symposium, University of Wisconsin--Madison (virtual, presented)
2022 SUMS Math and Puzzles Conference (virtual, presented)
2021 Baylor McNair Research Conference (virtual, presented)
2021 SIAM Conference on Applied Algebraic Geometry (AG21) (virtual, attended)
2021 University of Wisconsin–Madison McNair Summer Research Experience Symposium (virtual, presented)
2021 Mathematical Sciences Research Institute–Undergraduate Program Presentation (virtual, presented)
2019 Undergraduate Symposium, University of Wisconsin–Madison, Madison, WI (presented)
Collaborators
Tomás Aguilar-Fraga
Yasmin Aguillon
Parneet Gill
Imhotep Hogan
Jakeyl Johnson
Kobe Lawson-Chavanu
Aaron Ortiz
Lauren Quesada
Daniel Alofamoni Quiñonez
Camelle Tieu
Dirk Tolson III
Pamela Vargas
Other Writing
People Over Math: A Co-created Principle for Successful Research Communities. Faculty authors: Rebecca Garcia, Pamela E. Harris, and Dwight Anderson Williams II, Graduate student authors: J. Carlos Martínez Mori and Casandra Monroe, Undergraduate student authors: Tomás Aguilar-Fraga, Yasmin Aguillon, Daniel Alofamoni Quiñonez, Dylan Alvarenga, Aalliyah Celestine, Parneet Gill, Imhotep Hogan, Jakeyl Johnson, Kobe Lawson-Chavanu, Lina Liu, Aaron Ortiz, Lauren Quesada, Cynthia Marie Rivera Sánchez, Christopher Soto, Camelle Tieu, Dirk Tolson III, Jacob van der Leeuw, and Pamela Vargas. MAA Focus. June/July 2022.
Undergraduate Thesis: An Exploration To Determine Polynomials For Specific Finite Groups.
Mentor: Jose I. Rodriguez
Students Speak: How Making Math Friends help make a Competitive Environment Collaborative. MAA MATH VALUES. July 2022 and to appear in a high school textbook titled Engage in March 2024.