Pablo Andújar Guerrero

Here's my CV

Last event organized: Combinatorial Problems in Model Theory and Computer Science.

Research Interests

I study model theory, an area of mathematical logic, and its interface with topology and combinatorics.
In particular I am interested in the following topics:

• Definable topology and functional analysis in o-minimal, dp-minimal, and other classes of tame theories.
• Types and combinatorics in NIP theories.

Research Statement

Preprints and Work in Progress

• Domination, cofinal curves, and semi-bounded o-minimal theories, with Pantelis Eleftheriou and Rosario Mennuni,
  in preparation.
• Types in distal dp-minimal theories,
  in preparation.
• Definable separability and second-countability in o-minimal structures ,
  submitted, arXiv:2405.07114, pdf.
• Definable compactness in o-minimal structures ,
  submitted, arXiv:2405.07112, pdf.
• One-dimensional definable topological spaces in o-minimal structures, with Margaret E. M. Thomas,
  submitted, arXiv:2310.04510, pdf.

Publications

• A note on the cardinality of definable families of sets in o-minimal structures ,
  Mathematical Logic Quarterly (2024), doi.org/10.1002/malq.202300030 (open access, arXiv).
• Around definable types in p-adically closed fields, with William Johnson,
  Annals of Pure and Applied Logic, 175 (2024) (arXiv, pdf).
  Until 3 August view and download the published version for free using this link.
• A shorter proof of the Marker-Steinhorn Theorem,
  Notre Dame Journal of Formal Logic, accepted (arXiv, pdf).
• Definable (ω,2)-theorem for families with VC-codensity less than 2,
  The Journal of Symbolic Logic (2023), doi:10.1017/jsl.2023.46 (open access, arXiv, pdf).
• Directed sets and topological spaces definable in o-minimal structures, with Margaret E. M. Thomas and Erik Walsberg,
  Journal of the London Mathematical Society, Second Series, 104 (2021) no. 3, 989-1010 (arXiv, pdf)

Some Talks

• O-minimal tame set-theoretic topology
  Leeds Models and Sets Seminar (slides)
• Types and definable compactness in o-minimality and beyond
  AMS Spring Sectional Meeting 2022 (video, slides)
  Fields Model Theory Seminar (video)
• A brief history of (p,q) theorems
  (Updated short version) 75th British Mathematical Colloquium (slides)
  Fields Postdoc Colloquium (video, slides)
• Types, transversals and definable compactness in o-minimal structures
  ASL North American Annual Meeting
• One-dimensional definable topologies in o-minimal structures
  Universität Konstanz Real Algebraic Geometry and Model Theory conference (RAGMT)

Outreach

• Can you win the chocolate game? - Be Curious Live.

Unpublished

• Types, transversals and definable compactness in o-minimal structures,
  arXiv:2111.03802, pdf.

Ph.D. Thesis

Useful Links

• A different (better?) way of reading arXiv papers.
• Gabriel Conant's map of the universe.
• A database of topological spaces called π-Base.