Charlotte Aten's Homepage
I am a mathematics graduate student at the University of Rochester.
My advisor is Jonathan Pakianathan.
My research interests skew combinatorial and I have an affinity for universal algebra. On the algebro-topological side of combinatorics I like to study graphs/complexes/manifolds manufactured from (quasi)groups and on the analytic side I enjoy applying methods from Fourier analysis over finite fields to problems in additive combinatorics. In either case, representation theory is always relevant.
Orientable smooth manifolds are essentially quasigroups (with Semin Yoo, 2021)
Multiplayer rock-paper-scissors (Algebra Universalis, 2020)
Multiplayer Rock-Paper-Scissors (short paper appearing in the conference proceedings of Algebras and Lattices in Hawaiʻi 2018)
The Topology of Magmas (senior thesis)
Nonnormal Quotients (undergraduate independent study project)
Tiling sets and spectral sets over finite fields (with 2015 REU group at UR)
A multi-linear geometric estimate (Virginia Tech Analysis and Mathematical Physics Seminar 2021 Fall) [Video]
Orientable smooth manifolds are essentially quasigroups (Binghamton University's Graduate Conference in Algebra and Topology 2021) [Video]
My Hawaiʻian Earring (SUMS Math Talk 2021 Spring) [Video and Code]
Algebraic theories (Lecture for MTH 549 Category theory) [Video]
Multiplayer rock-paper-scissors (New York Combinatorics Seminar 2021 Spring) [Video]
Universal algebra gives universal approximation for neural nets (Rochester Combinatorics Seminar 2021 Spring) [Video]
Multiplayer rock-paper-scissors (Panglobal Algebra and Logic Seminar 2021 Spring) [Video]
Multiplayer rock-paper-scissors (Binghamton University's Graduate Conference in Algebra and Topology 2020) [Video]
A High School Algebra Problem (SUMS Math Talk 2020 Spring)
More Multiplayer Rock-Paper-Scissors (University of Rochester Graduate Student Seminar 2019 Fall)
Topological Lattices and Book Spaces (Binghamton University's Graduate Conference in Algebra and Topology 2018)
Classifying Topological Magmas (University of Rochester Graduate Student Seminar 2018 Fall)
Multiplayer Rock-Paper-Scissors (Algebras and Lattices in Hawaiʻi 2018)
Multiplayer Rock-Paper-Scissors (University of Rochester Graduate Student Seminar 2018 Spring)
Universal Algebra and Boolean Semilattices (Binghamton University's Graduate Conference in Algebra and Topology 2017)
A Brief Introduction to Universal Algebra (University of Rochester Graduate Student Seminar 2017 Fall)
The Topology of Magmas (Senior thesis presentation)
Relational Structures as Directed Hypergraphs (Nebraska Conference for Undergraduate Women in Mathematics 2017)
The Topology of Magmas (National Conference on Undergraduate Research 2016)
Topological Algebra: On Viewing Operations as Simplicial Complexes (National Conference for McNair Scholars 2016)
Constructions of Geometric Objects Encoding Algebraic Structures (David T. Kearns Center Research Symposium 2015)
TA for MATH 208 Operations research (2021 Fall)
MATH 165 Linear algebra with differential equations (2021 Summer)
MATH 162 Calculus IIA (2020 Summer)
Other TA and tutoring experience may be found on my CV, which is linked above.
A proof that everything can be described using mathematics: Recall that mathematics is the study of abstract relationships. Suppose towards a contradiction that there is some thing, say A, which is not describable in terms of math. "X is not describable in terms of Y" is a relationship between X and Y. We have then exhibited a relationship between A and math, which is a mathematical descriptor of A, contradicting our assumption that A was not amenable to such descriptions.
Office: The seat on the big couch next to the outlet, 9th floor lounge, Hylan Building