Jens Hemelaer

I am a postdoc at University of Antwerp (FWO) in the research group Fundamental Mathematics. I study topos theory and its applications to concrete problems in number theory, algebra or (noncommutative) geometry.

My PhD thesis “Topos-theoretic methods in noncommutative geometry” (pdf here) was written under supervision of Lieven Le Bruyn.

Blog: jhemelae.github.io.
Contact details are on my university webpage.

Talks

• “Toposes of presheaves on a monoid and their points”, NYC Category Theory Seminar (December 2021) (slides, video).
• “Are precohesive geometric morphisms locally connected?”, Open House on Category Theory 2021 (November 2021) (slides).
• “Toposes of presheaves on monoids as generalized topological spaces”, Toposes online (June 2021) (slides, video).
• “Duality for noncommutative frames”, 8ECM (June 2021) (slides).
• “Toposes in arithmetic noncommutative geometry”, Global Noncommutative Geometry Seminar (February 2021) (video).
• “How do retracts depend on the endomorphism monoid?”, York Semigroup, University of York (January 2021).
• “Monoids from the point of view of topos theory”, Algebra Colloquium, University of Augsburg (November 2020).
• “Topos-theoretic properties of the category of sets with a monoid action”, Junior Mathematician Research Archive (September 2020) (video).
• “The geometry of monoids via topos theory”, Università degli studi dell’Insubria, Como (January 2020).
• “An arithmetic topos for integer matrices and other monoids”, at the conference “Riemann-Roch in characteristic one and related topics”, Johns Hopkins University, Baltimore (October 2019) (video).

Papers/preprints

• Jens Hemelaer,
  Localization of monoids and topos theory,
  arXiv:2303.06781.
• Jens Hemelaer,
  Some toposes over which essential implies locally connected,
  Cahiers de Topologie et Géométrie Différentielle Catégoriques (2022), arXiv:2204.02749.
• Jens Hemelaer and Morgan Rogers,
  Geometric morphisms between toposes of monoid actions: factorization systems,
  arXiv:2203.09133.
• Jens Hemelaer and Morgan Rogers,
  Solution to a problem of FitzGerald,
  Semigroup Forum (2021), arXiv:2011.12129.
• Jens Hemelaer and Morgan Rogers,
  An essential, hyperconnected, local geometric morphism that is not locally connected,
  Applied Categorical Structures (2021), arXiv:2009.12241.
• Jens Hemelaer and Morgan Rogers,
  Monoid Properties as Invariants of Toposes of Monoid Actions,
  Applied Categorical Structures (2021), arXiv:2004.10513.
• Karin Cvetko-Vah, Jens Hemelaer and Lieven Le Bruyn,
  Duality for noncommutative frames,
  Topology and its Applications (2020), arXiv:1911.12625.
• Karin Cvetko-Vah, Jens Hemelaer and Jonathan Leech,
  Noncommutative Frames Revisited,
  Ars Mathematica Contemporanea (2020), arXiv:1911.12355.
• Jens Hemelaer,
  A topological groupoid representing the topos of presheaves on a monoid,
  Applied Categorical Structures (2020), arXiv:1906.02690.
• Jens Hemelaer,
  Grothendieck topologies on posets,
  arXiv:1811.10039.
• Jens Hemelaer,
  An arithmetic topos for integer matrices,
  Journal of Number Theory (2019), arXiv:1806.01887 (video).
• Jens Hemelaer,
  Azumaya toposes,
  arXiv:1707.03814.
• Karin Cvetko-Vah, Jens Hemelaer and Lieven Le Bruyn,
  What is a noncommutative topos?,
  Journal of Algebra and Its Applications (2018), arXiv:1705.02831.
• Jens Hemelaer and Lieven Le Bruyn,
  Azumaya geometry and representation stacks,
  arXiv:1606.07885.