#categorytheory — Public Fediverse posts

In the mountains, I love exploring nature and climbing any little hidden corner.

My academic interests include mathematics (#mathematics) and mathematical logic ( #mathematicallogic #logic), particularly model theory ( #modeltheory), category theory ( #categorytheory), higher-order logic and metalogic ( #metalogic), as well as the philosophy of mathematics and logic ( #philosophyofmathematics #philosophyoflogic), epistemology and ontology of them.

#introduction

I've been on a longer hiatus from livestreaming than I originally intended, but you can see me give a seminar talk this evening at the The New York City Category Theory Seminar:

https://www.sci.brooklyn.cuny.edu/~noson/Seminar/index.html

I'll be talking about the invariant theory part of my thesis (https://arxiv.org/abs/2402.18063) at 7PM, New York time. I'll discuss how I found that every (positive) property of finite structures can be checked by counting small* substructures.

*Terms and conditions may apply. Small is constrained by the logical complexity of a property and may not conform to mundane notions of smallness in bad cases.

#CategoryTheory #combinatorics #logic #Bourbaki #algebra #AbstractAlgebra

I have a new(ish) preprint on the arXiv! You can find "Invariants of structures" at https://arxiv.org/abs/2402.18063. This is a somewhat embellished version of one half of my PhD thesis. A talk which I gave about this subject in the fall of 2022 is available at https://www.youtube.com/watch?v=5TeGZZ_mepc.

In this new version, I have finally added an explicit description of something I've been telling people for years: My main result shows that any first-order property of finite structures can be computed by counting small substructures. Perhaps surprisingly, this comes as a result of synthesizing a categorical treatment of Bourbaki's notion of mathematical structure with Hilbert's classical result on symmetric polynomials.

#CategoryTheory #combinatorics #algebra #AbstractAlgebra #logic #Bourbaki

Just posted this talk (https://youtu.be/5TeGZZ_mepc) I gave on the categorified invariant theory part of my PhD thesis last fall! You can also find my thesis itself online now at https://aten.cool/documents/thesis.pdf if you'd like to see more.

Part of the reason I waited so long to post this is because I kind of flubbed the last example after the main part of the talk due to having not looked at this stuff for a while before giving the lecture. I thought I'd cut that last part out once I had more time, but enough time has passed and it no longer bothers me.

I actually wrote most of this part of my thesis in 2020, so I waited a long time to advertise this work.

#math #thesis #algebra #AbstractAlgebra #CategoryTheory #Bourbaki #combinatorics

#introduction

Part of the Migration. Moved from @[email protected]

Interested in #topology (for fun and #TDA )
#GraphicalLinearAlgebra and similar notations like string diagrams and #ExistentialGraphs
#CurryHowardIsomorphism
#Semantics for humans and computers
#topoi
#CategoryTheory
#WordEmbeddings (in #NLP )
#language
#logic
#SFF
#History of science, math, societies
etc.

Trans rights are human rights; blm; workers solidarity; native rights; and all the various other ways of not being vile to people