Pablo Andújar Guerrero

Postdoctoral Fellow
School of Mathematics
University of Leeds

matpa@leeds.ac.uk

me looking good

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

  • Definable separability and and definable second-countability in o-minimal structures,
    in preparation.
  • Types in distal dp-minimal theories,
    in preparation.
  • One-dimensional definable topological spaces in o-minimal structures, with Margaret E. M. Thomas,
    submitted, arXiv:2310.04510, pdf.
  • Around definable types in p-adically closed fields, with William Johnson,
    submitted, arXiv:2208.05815, pdf.
  • Types, transversals and definable compactness in o-minimal structures,
    submitted, arXiv:2111.03802, pdf.

Publications

  • A shorter proof of the Marker-Steinhorn Theorem,
    Notre Dame Journal of Formal Logic, accepted ( arXiv:2306.09897, pdf).
  • Definable (ω,2)-theorem for families with VC-codensity less than 2,
    The Journal of Symbolic Logic, 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
    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)

Unpublished

  • Cardinality of definable families of sets in o-minimal structures
    (Help!) A reviewier for this manuscript suggested that the main result about counting types should be part of a more general article, which includes proving if true that the result also holds for the p-adics, and for ACVF "using precisely that the value group is an o-minimal structure". The point being that this property could be an interesting dividing line among NIP theories. If you have any ideas around this or would like to get involved email me.
    ,
    submitted, arXiv:2305.12294, pdf.

Ph.D. Thesis

Definable Topological Spaces in O-minimal Structures (pdf)
Purdue University, 2021
Advisor: Margaret E. M. Thomas
  • A different (better?) way of reading arXiv papers.
  • Gabriel Conant's map of the universe.
  • A database of topological spaces called π-Base.