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.