Invariants of structures (Charlotte Aten at University of Denver Algebra and Logic Seminar 2022)

This is a talk that I gave for the University of Denver Algebra and Logic Seminar in the fall of 2022. I talked about one part of my thesis, which concerns a categorification of the notion of mathematical structure appearing in Bourbaki's textbook on set theory. You can find a link to my slides below if you'd like to follow along with the video. I'll also include a link to my thesis, which contains more examples.

Title: Invariants of structures
Speaker: Charlotte Aten, University of Denver
Abstract: I will be discussing 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 computed by counting 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.

Slides: https://aten.cool/documents/slides/aten_du_algebra_logic.pdf
Thesis: https://aten.cool/documents/papers/thesis.pdf
Preprint: https://arxiv.org/abs/2402.18063