Charlotte Aten's Homepage


I am a mathematics postdoc at the University of Colorado Boulder.

Research Interests

My core interests tend to cycle around combinatorics, universal algebra, and category theory. I study functorial constructions of spaces from quasigroups, representation stability, and categorified invariant theory. I am also a proponent of applied category theory, in particular with respect to machine learning and formal verification.

Curriculum Vitae


Publications and preprints

YearTitleCoauthorsJournalNotes
2024Invariants of structures
2024Higher-dimensional book-spaces
2023Discrete neural nets and polymorphic learningUnder revision at Mathematical Structures in Computer Science
2023A partition formula from idempotents
2022Finite Generation of Families of Structures Equipped with Compatible Group ActionsPhD thesis
2021Orientable triangulable manifolds are essentially quasigroupsSemin YooUnder revision at Topology and its Applications
2021A multi-linear geometric estimateAlex Iosevich
2020Multiplayer rock-paper-scissorsAlgebra Universalis
2018Multiplayer Rock-Paper-Scissorsconference proceedings of Algebras and Lattices in Hawai'i
2017The Topology of Magmassenior thesis
2016Nonnormal Quotientsundergraduate independent study project
2015Tiling sets and spectral sets over finite fieldsREU group at the University of RochesterJournal of Functional Analysis

Textbooks

Category Theory: A Concise Course (with Venanzio Capretta and William DeMeo, 2019)

Code

Github

News

Why this Rochester math professor champions year-round undergraduate research

Video

YouTube channel
Old YouTube channel (No longer in use.)
Universal algebra and lattice theory lectures (Currently on old channel.)

Social media

Mastodon
Mathematics StackExchange (Not currently in use.)
History of Science and Mathmematics StackExchange (Not currently in use.)

Talks

NumberYearTitleEventLocationVideoCode
442024Higher-dimensional book-spacesPanglobal Algebra and Logic SeminarUniversity of Colorado BoulderVideo
432024A multi-linear geometric estimateIBS-DIMAG Workshop on Combinatorics and Geometric Measure TheoryInstitute for Basic Science, Daejeon, South Korea
422024Quasigroups, manifolds, and the completion of partial Latin hypercubesRocky Mountain Algebraic Combinatorics SeminarColorado State University in Fort Collins
412024Discrete neural nets and graph polymorphisms for learningJoint Mathematics MeetingsSan Francisco, California
402023A categorical semantics for neural networksThe New York City Category Theory SeminarThe City University of New YorkVideo
392023A categorical semantics for neural networksLogic and Semantics SeminarUniversity of Cambridge
382023Monoid representations and partitionsAlgebra and Logic SeminarUniversity of DenverVideo
372023Discrete neural nets and polymorphic learning (Part 2)Machine Learning SeminarUniversity of DenverCode
362023Discrete neural nets and polymorphic learning (Part 1)Machine Learning SeminarUniversity of Denver
352023Discrete neural nets and polymorphic learningPanglobal Algebra and Logic SeminarUniversity of Colorado BoulderVideo
342023Discrete neural nets and polymorphic learningOnline Machine Learning SeminarUniversity of Nottingham
332023On the construction of manifolds from n-ary quasigroupsLOOPS'23Bedlewo, Poland
322023On the construction of manifolds from n-ary quasigroupsCombinatorics SeminarUniversity of Rochester
312023Categorical models of linear logicAlgebraic Logic SeminarUniversity of Denver
302023Exploring Dialectica Categorical ConstructionsJoint Mathematics MeetingsBoston, Massachusetts
292022Perceptrons and the Fundmental Theorem of Statistical LearningMachine Learning SeminarUniversity of Denver
282022PAC LearningMachine Learning SeminarUniversity of Denver
272022Invariants of StructuresAlgebra and Logic SeminarUniversity of DenverVideo
262022Finite Generation of Families of Structures Equipped with Compatible Group ActionsPhD thesis defenseUniversity of Rochester
252022Distributive lattices in rock-paper-scissorsJoint Mathematics Meetings
242022Orientable smooth manifolds are essentially quasigroupsPanglobal Algebra and Logic SeminarUniversity of Colorado BoulderVideo
232021A multi-linear geometric estimateVirginia Tech Analysis and Mathematical Physics SeminarVirgina TechVideo
222021Orientable smooth manifolds are essentially quasigroupsBinghamton University's Graduate Conference in Algebra and TopologyBinghamton UniversityVideo
212021My Hawai'ian EarringSUMS Math TalkUniversity of RochesterVideoCode
202021Algebraic theoriesLecture for MTH 549 Category TheoryUniversity of RochesterVideo
192021Multiplayer rock-paper-scissorsNew York Combinatorics SeminarThe City University of New YorkVideo
182021Universal algebra gives universal approximation for neural netsRochester Combinatorics SeminarUniversity of RochesterVideo
172021Multiplayer rock-paper-scissorsPanglobal Algebra and Logic SeminarUniversity of Colorado BoulderVideo
162020Multiplayer rock-paper-scissorsBinghamton University's Graduate Conference in Algebra and TopologyBinghamton UniversityVideo
152020A High School Algebra ProblemSUMS Math TalkUniversity of Rochester
142019More Multiplayer Rock-Paper-ScissorsGraduate Student SeminarUniversity of Rochester
132018Topological Lattices and Book SpacesBinghamton University's Graduate Conference in Algebra and TopologyBinghamton University
122018Classifying Topological MagmasGraduate Student SeminarUniversity of Rochester
112018Multiplayer Rock-Paper-ScissorsAlgebras and Lattices in Hawai'iUniversity of Hawai'i at Manoa
102018Multiplayer Rock-Paper-ScissorsGraduate Student SeminarUniversity of Rochester
92017Universal Algebra and Boolean SemilatticesBinghamton University's Graduate Conference in Algebra and TopologyBinghamton University
82017A Brief Introduction to Universal AlgebraGraduate Student SeminarUniversity of Rochester
72017The Topology of MagmasSenior thesis presentationUniversity of Rochester
62017Relational Structures as Directed Hypergraphs (poster presentation)Nebraska Conference for Undergraduate Women in MathematicsUniversity of Nebraska-Lincoln
52016The Topology of MagmasNational Conference on Undergraduate ResearchUniversity of North Carolina at Asheville
42016Topological Algebra: On Viewing Operations as Simplicial ComplexesNational Conference for McNair ScholarsUniversity of Maryland
32015Constructions of Geometric Objects Encoding Algebraic StructuresDavid T. Kearns Center Research SymposiumUniversity of Rochester
22014Division by Zero: Development of a Relevant Algebra with Historical ContextScholars' DayMonroe Community College
12013An Introduction to Hyperspace with a Construction of the 4-CubeMath Awareness MonthMonroe Community College

Teaching

Math 2130 Linear Algebra for Non-Math Majors (2024 Fall)
Math 1952 Calculus II (2024 Spring)
Math 1150 Elementary School Mathematics from the Year 2100 (2024 Winter)
Math 2060 Elements of Linear Algebra (2023 Fall)
Math 1951 Calculus I (2023 Fall)
Math 1953 Calculus III (2023 Spring)
Math 1150 Social Choice Theory: The Mathematics of Voting and Social Welfare (2023 Winter)
Math 2060 Elements of Linear Algebra (2022 Fall)
Math 1951 Calculus I (2022 Fall)
Math 165 Linear algebra with differential equations (2021 Summer)
Math 162 Calculus IIA (2020 Summer)
Other teaching experience may be found in my CV.

History

I did my graduate studies at the University of Rochester, where my PhD advisor was Jonathan Pakianathan. This chart shows my detailed mathematical lineage, as determined by The Mathematics Genealogy Project. My first postdoctoral position was at the University of Denver, where I worked with Michael Kinyon.

Art

Fractals
Automata

Humor

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.

Support

Want to see more content like this? Consider supporting me via one of the links below, so I can focus more on what I do best.
BuyMeACoffee.com
Ko-fi

Contact

charlotte.aten@colorado.edu