This is an introductory talk on algebraic theories, which are a categorical way of doing universal algebra. I discuss the history of the topic and give some of the universal algebra background needed to see the motivation for the concept. The talk ends with some comments on the relationship between algebraic theories and monads. This lecture was given in Doug Ravenel's topics course on category theory at the University of Rochester in the Spring 2021 semester.

Slides: https://aten.cool/documents/slides/algebraic_theories.pdf

This is the seventh in a series of talks about universal algebra and lattice theory. I introduce the notion of a complete lattice and (at long last) show that the congruences and subuniverses of an algebra form lattices. I also go over early results of Dedekind on congruence lattices of groups and Funayama and Nakayama on congruence lattices of lattices. The webpage for this series of talks can be found at https://aten.cool/2020ua.html.

This is a talk that I gave for the University of Denver Algebra and Logic Seminar in the fall of 2023. I discuss a formula I found when I was a graduate student which involves the partition numbers. During the summer of 2023 I was reminded of this and posted a preprint to the arXiv (linked below) which I mostly wrote back then. The formula is obtained by using Burnside's Lemma in the context of monoid representations on a finite set.

Title: Monoid representations and partitions

Slides: https://aten.cool/documents/slides/aten_du_algebra_logic_2023.pdf

This is my talk at the University of Colorado Boulder's PALS seminar in the spring of 2022. I discuss the contents of a preprint Semin Yoo and I recently posted on the arXiv, which concerns the manufacture of (pseudo)manifolds from alternating n-quasigroups. I give an overview of our basic constructions and argue that every orientable triangulable manifold can be produced in this manner.

PALS: https://math.colorado.edu/algebralogic/index.html

Tinkerers August 2026

Ben explained more about how his shape recognition robot works, this uses computer vision to see shapes and work out what they are, and react as per programming. This is powered by a Raspberry Pi zero.

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Tinkerers August 2026

More testing of the dragster car, created by Helen. This went Ok, but there were a few issues, however later runs seemed to be better.

#Tinkerers

Tinkerers August 2026

More testing of the dragster car, created by Helen. This went OK, but there were a few issues, however later runs seemed to be better.

#Tinkerers

Tinkerers August 2026

More testing of the dragster car, created by Helen. This went Ok, but there were a few issues, however later runs seemed to be better.

#Tinkerers

Abstract: I will discuss one part of my PhD thesis, in which I provide a categorification of the notion of a mathematical structure originally given by Bourbaki in their set theory textbook. The main result is that any isomorphism-invariant property of a finite structure can be checked by computing the number of isomorphic copies of small substructures it contains. A special case of this theorem is the classical result of Hilbert about elementary symmetric polynomials generating the algebra of all symmetric polynomials. I will also discuss how the logical complexity of a positive formula controls the size of the small substructures one must count.

Slides: https://aten.cool/documents/slides/Aten_New_York_Category_Seminar_2024.pdf

Tinkerers August 2026

More testing of the dragster car, created by Helen. This went Ok, but there were a few issues, however later runs seemed to be better.

#Tinkerers