Kevin Iván Piterman

kevin Postdoctoral researcher at Vrije Universiteit Brussel
Supported by a fellowship of FWO (Fonds Wetenschappelijk Onderzoek)
kevin # piterman at vub # be, and replace # by a [dot]


Here is my CV (as of September 2024).

Research interests: combinatorial structures in algebra and topology, finite topological spaces, finite group theory, combinatorial methods in geometric group theory.

Algebra and Analysis research group at the Vrije Universiteit Brussel.
Research group on Discrete Mathematics and Combinatorics at the Philipps-Universität Marburg.
Research group on Algebraic Topology at the University of Buenos Aires.

Dissertations

  1. English version of my PhD thesis (2019).
  2. Spanish version of my Licentiate (Master) thesis (2016).

Preprints

  1. (with B. Brück) Connectivity of partial basis complexes of freely decomposable groups.
    Preprint (2024). arXiv:2410.17121.
  2. Spherical p-group complexes arising from finite groups of Lie type.
    Preprint (2024). arXiv:2403.07489.
  3. (with V. Welker) Posets arising from decompositions of objects in a monoidal category.
    Preprint (2024). arXiv:2401.09280.
  4. (with I. Sadofschi Costa) Group actions on contractible 2-complexes II.
    Preprint (2021). arXiv:2102.11459.

Publications

  1. (with B. Brück and V. Welker) The common basis complex and the partial decomposition poset.
    Int. Math. Res. Not. IMRN 2024, no. 18, 12746--12760. Article.
  2. (with S.D. Smith) Some results on Quillen's Conjecture via equivalent-poset techniques.
    J. Comb. Algebra. In press (2024). Article.
  3. (with V. Welker) Homotopy properties of the complex of frames of a unitary space.
    J. London Math. Soc. 110 (2024), e12978. Article.
  4. On the frame complex of symplectic spaces.
    J. Algebra 642 (2024), 65--94. Article.
  5. Maximal subgroups of exceptional groups and Quillen's dimension.
    Algebra Number Theory 18 (2023), no. 7, 1375--1401. Article.
  6. (with L. Vendramin) Algebra with GAP.
    Oberwolfach preprint (2023). Manuscript.
  7. (with S.D. Smith) Eliminating components in Quillen's Conjecture.
    J. Algebra 607 (2022), part A, 681--732. Article.
  8. An approach to Quillen's conjecture via centralisers of simple groups.
    Forum Math. Sigma 9 (2021), Paper No. e48, 23 pp. Article.
  9. (with I. Sadofschi Costa and A. Viruel) Acylic 2-dimensional complexes and Quillen's conjecture.
    Publ. Mat. 65 (2021), no. 1, 129--140. Article.
  10. (with E.G. Minian) The fundamental group of the p-subgroup complex.
    J. London Math. Soc. (2) 103 (2021), pp. 449-469. Article.
  11. A stronger reformulation of Webb's conjecture in terms of finite topological spaces.
    J. Algebra 527 (2019), pp. 280-305. Article.
  12. (with E.G. Minian) The homotopy types of the posets of p-subgroups of a finite group.
    Adv. Math. 328 (2018), pp. 1217-1233. Article.

Other publications

  1. Appendix of Group actions on contractible 2-complexes I by I. Sadofschi Costa. Preprint (2021). arXiv:2102.11458.
  2. (with E.G. Minian) Notas de topología diferencial. Cursos y seminarios de matemática, Serie B, Fascículo 12. Departamento de Matemática, FCEyN, UBA (2017). Link.

Software

  1. Posets - Finite posets and finite topological spaces.
    With X. Fernández and I. Sadofschi Costa.
    GAP package (2019). Available at https://github.com/isadofschi/posets.
  2. FASTPASC - From Algebraic Structures To Posets And Simplicial Complexes.
    GAP package (2024). Available at https://github.com/kpiterman/FASTPASC.

Last selected talks

  1. A categorical approach to study posets of decompositions into subobjects.
    University of Copenhagen. March, 2024. Slides.
  2. Fixed points on contractible spaces.
    Oberwolfach workshop. December, 2023. Slides.
  3. Advances on Quillen's conjecture.
    "Northern Group Theory conference in honour of Bernd Fischer", Bielefeld. September, 2023. Slides.
  4. Posets associated to vector spaces with non-degenerate forms.
    KTH seminar, Stockholm. April, 2023. Slides.
  5. The frame complex of a vector space with a Hermitian form.
    "II Encuentro RSME-UMA", Ronda. December, 2022. Slides.
  6. On the homotopy type of p-subgroup posets.
    "Simple groups, representations and applications", Isaac Newton Institute (Cambridge). July, 2022. Slides.

Coauthor homepages

  1. Jonathan Barmak
  2. Ximena Fernández
  3. Gabriel Minian
  4. Stephen D. Smith
  5. Leandro Vendramin
  6. Antonio Viruel
  7. Volkmar Welker