Andrew W. Swan

Andrew Swan,
Department of Mathematics and Physics,
University of Ljubljana,
Slovenia

Email: wakelin.swan@gmail.com

Orcid: 0000-0002-7190-4870

Mastodon: @aws@mathstodon.xyz

I am currently working as a postdoc at the University of Ljubljana.

My research interests include realizability, constructive mathematics, constructive set theory, partial combinatory algebras, type theory, homotopy type theory, cubical sets, nominal sets.

Lecture Notes

Research

Recent preprints

• Double negation stable h-propositions in cubical sets
• Definable and Non-definable Notions of Structure
• Separating Path and Identity Types in Presheaf Models of Univalent Type Theory
• Identity Types in Algebraic Model Structures and Cubical Sets
• On Dividing by Two in Constructive Mathematics
• Lifting Problems in Grothendieck Fibrations
• W-Types with Reductions and the Small Object Argument
• Some Brouwerian Counterexamples Regarding Nominal Sets in Constructive Set Theory

Papers

• On the Nielsen-Schreier Theorem in Homotopy Type Theory, Logical Methods in Computer Science, Volume 18, Issue 1, 2022
• A class of higher inductive types in Zermelo-Fraenkel set theory, Mathematical Logic Quarterly, Volume 68, Issue 1, 2022
• On Church's Thesis in Cubical Assemblies (joint with Taichi Uemura), Mathematical Structures in Computer Science, 2022
• Lifschitz Realizability as a Topological Construction (joint with Michael Rathjen), Journal of Symbolic Logic, Volume 85, Issue 4, 2021 (arXiv link)
• Every metric space is separable in function realizability (joint with Andrej Bauer), Logical Methods in Computer Science, Volume 15, Issue 2, 2019
• An Algebraic Weak Factorisation System on 01-Substitution Sets: A Constructive Proof, Journal of Logic and Analysis, Volume 8, 2016
• CZF does not have the Existence Property, Annals of Pure and Applied Logic, Volume 165, Issue 5, May 2014, Pages 1115-1147 (arXiv link)
• Automorphisms of Partial Combinatory Algebras and Realizability Models of Constructive Set Theory(thesis)