Arne Mertens Homepage

<rss version="2.0"
	xmlns:content="http://purl.org/rss/1.0/modules/content/"
	xmlns:wfw="http://wellformedweb.org/CommentAPI/"
	xmlns:dc="http://purl.org/dc/elements/1.1/"
	xmlns:media="http://search.yahoo.com/mrss/"
	
	>

<channel>
	<title>Arne Mertens Homepage</title>
	<link>https://arnemertens.com</link>
	<description>Arne Mertens Homepage</description>
	<pubDate>Wed, 08 Nov 2023 14:00:11 +0000</pubDate>
	<generator>https://arnemertens.com</generator>
	<language>en</language>
	
		
	<item>
		<title>Home</title>
				
		<link>https://arnemertens.com/Home</link>

		<pubDate>Thu, 02 Nov 2023 16:50:27 +0000</pubDate>

		<dc:creator>Arne Mertens Homepage</dc:creator>

		<guid isPermaLink="true">https://arnemertens.com/Home</guid>

		<description>Arne MertensHomepage
I am a postdoctoral researcher at the Department of Mathematics of the

University of Antwerp

 (UA), where I work in the research group of Wendy Lowen. I am also currently cosupervising the PhD project of Timothée Bonnefoi.
Previously, I have cosupervised the PhD project of Violeta Borges Marques.
My research interests include homotopy theory and higher structures, as well as homological algebra and deformation theory. In particular I study models for linear&#38;nbsp;∞-categories, with a focus on applications in non-commutative algebraic geometry.
Previous positions:

Oct 2023 - Sep 2025
	Guest lecturerDepartment of MathematicsLocation: University of Antwerp
	Oct 2022 - Sep 2023
	Postdoctoral researcherSupervisor: Wendy LowenLocation: University of AntwerpFunding: ERC Consolidator Grant

“Foundations for Higher and Curved Noncommutative Algebraic Geometry”


	Oct 2018 - Sep 2022
	Predoctoral fellow

Supervisor: Wendy Lowen


Location: University of Antwerp


Funding: Research Foundation - Flanders (FWO), file number [1137921N]
PhD thesis:&#38;nbsp;Templicial objects: simplicial objects in a monoidal category
Background image: Xavier De Graeve</description>
		
	</item>
		
		
	<item>
		<title>Preprints and publications</title>
				
		<link>https://arnemertens.com/Preprints-and-publications</link>

		<pubDate>Thu, 02 Nov 2023 16:50:29 +0000</pubDate>

		<dc:creator>Arne Mertens Homepage</dc:creator>

		<guid isPermaLink="true">https://arnemertens.com/Preprints-and-publications</guid>

		<description>Preprints and publications


Preprints


Templicial nerve of an A-infinity category

 [arXiv]
Joint with Violeta Borges Marques
Nerves of enriched categories via necklaces [arXiv]
Publications


Frobenius Templicial Modules and the dg-Nerve. [pdf]
International Mathematics Research Notices, Volume 2025, Issue 13, 
rnaf178

 (2025)Joint with Wendy Lowen


Discrete vertices in simplicial objects internal to a monoidal category.

 [pdf]
Applied Categorical Structures, Volume 33, 22 (2025).
Deformations of Quasi-categories in Modules.

 [pdf]
Journal of Pure and Applied Algebra, Volume 229, Issue 2, 107866 (2025).

Joint with Violeta Borges Marques and Wendy Lowen


Enriched Quasi-categories and the Templicial Homotopy Coherent Nerve.

 [pdf]
Algebraic and Geometric Topology,&#38;nbsp;25, 1029–1074 
(2025).

Joint with Wendy Lowen


The Category of Necklaces is Reedy Monoidal.

 [pdf]
Theory and Applications of Categories, Volume 41, p.71-85 (2024). 

Joint with Violeta Borges Marques


</description>
		
	</item>
		
		
	<item>
		<title>Talks, posters and seminars</title>
				
		<link>https://arnemertens.com/Talks-posters-and-seminars</link>

		<pubDate>Thu, 02 Nov 2023 16:50:30 +0000</pubDate>

		<dc:creator>Arne Mertens Homepage</dc:creator>

		<guid isPermaLink="true">https://arnemertens.com/Talks-posters-and-seminars</guid>

		<description>Talks, posters and seminars &#38;nbsp;


Upcoming Talks


Past Talks

March 2023
	Enriched quasi-categories: cartesian vs non-cartesian


Research Seminar on Algebraic TopologyUniversität Hamburg


July 2025
	Lecture series on Algebraic Models for Spaces
Summer School on Non-commutative Algebraic GeometryUniversity of Antwerp


Oct 2024
	The dg-nerve via necklaces [slides]
Tale of GeometriesUniversité libre de Bruxelles


Jun 2024
	Non-cartesian internalisation and enriched quasi-categories [slides]
International category theory conferenceUniversidad de Santiago de Compostela


Apr 2024
	

Quasi-categories in modules as weak dg-categories (pitch presentation) [slides]


Hochschild (Co)Homology and Applications
Mathematisches Forschungsinstitut Oberwolfach


Mar 2024
	

A colax monoidal approach to quasi-categories

 [slides]


Young Homotopy-theorist Online Meeting
International

Feb 2024
	Quasi-categories in vector spaces as a model for weak dg-categories [slides]
Introductory Workshop: Noncommutative Algebraic GeometrySimons Laufer Mathematical Sciences Institute


Jan 2024
	Templicial modules as a model for weak dg-categories [slides]
Research Seminar on Algebraic TopologyUniversität Hamburg


	May 2023
	A colax monoidal approach to weak dg-categories [slides]
Séminaire d’Homotopie et Géométrie AlgébriqueUniversité Toulouse III - Paul Sabatier&#38;nbsp;


	Jul 2022
	

An internalization approach to enriched ∞-categories (online) [slides]
SFB Higher Invariants SeminarUniversität Regensburg


	May 2022
	Two lectures on templicial objects [slides 1, slides 2]
HYDRA mini conference
University of Antwerp

	Oct 2021
	

An elementary introduction to (∞,1)-categories via quasi-categories [slides]
Antwerp Algebra ColloquiumUniversity of Antwerp


	Dec 2020
	

Linear quasi-categories as templicial modules (online) [slides]
Pure Maths SeminarUniversity of East Anglia


	Nov 2020
	

Linear quasi-categories as templicial modules (online) [slides]
FD SeminarInternational


May 2019
	

Hoe kunnen we verschillende wiskundige gebieden verbinden? [slides]
Mathematics Research Day
University of Antwerp


	2019
	

A humble attempt at defining linear quasi-categoriesAntwerp Algebra SeminarUniversity of Antwerp


Poster presentations

	Jul 2023
	Nerves of enriched categories via necklaces [pdf]
International category theory conference
Université Catholique de Louvain


Reading Seminars
	Fall 2023
	Deformations of categories of coherent sheaves via quivers with relations - S. Barmeier and Z. Wang
Reading seminar with Violeta Borges Marques, Lander Hermans, Alessandro Lehmann, Carl Mazzanti and Julie Symons.

	Spring 2023
	Deformation theory: Lecture notes - M. Doubek, M. Markl, P. Zima
Reading seminar with&#38;nbsp;

Violeta Borges Marques, Lander Hermans, Alessandro Lehmann&#38;nbsp;and Julie Symons.


	2020 - 2021
	Algebraic geometry and arithmetic curves - Q. Liu
Reading seminar with Nicolas Daans, Shira Gilat,&#38;nbsp;Lander Hermans, Gonzalo Manzano, Piergiorgio Panero and Marco Zaninelli


	2019 - 2022
	Kerodon - Jacob Lurie
Reading seminar with
Matt Booth, Violeta Borges Marques, Francesco Genovese, Lander Hermans, Alessandro Lehmann,&#38;nbsp;Piergiorgio Panero, Julia Ramos González
</description>
		
	</item>
		
		
	<item>
		<title>Teaching</title>
				
		<link>https://arnemertens.com/Teaching</link>

		<pubDate>Thu, 02 Nov 2023 16:50:30 +0000</pubDate>

		<dc:creator>Arne Mertens Homepage</dc:creator>

		<guid isPermaLink="true">https://arnemertens.com/Teaching</guid>

		<description>TeachingCourses


2025 - 2026
	

Lecturer for Overbruggingsonderwijs
1st Bachelor matheatics and physics, Semester 1, University of Antwerp

Lecturer for Linear Algebra1st Bachelor mathematics, Semester 1, University of AntwerpLecturer for Lie groups for physicists3rd Bachelor physics, Semester 1, University of AntwerpLecturer for Algebraic Topology3rd Bachelor&#38;nbsp; mathematics, Semester 2, University of Antwerp


2024 - 2025
	Lecturer for Overbruggingsonderwijs1st Bachelor matheatics and physics, Semester 1, University of Antwerp
Lecturer for Linear Algebra1st Bachelor mathematics, Semester 1, University of AntwerpLecturer for Lie groups for physicists3rd Bachelor physics, Semester 1, University of AntwerpLecturer for Algebraic Topology3rd Bachelor&#38;nbsp; mathematics, Semester 2, University of Antwerp


2023 - 2024
	Lecturer for Algebra II - Rings
2nd Bachelor mathematics, Semester 1, University of AntwerpLecturer for Lie groups for physicists
3rd Bachelor physics, Semester 1, University of Antwerp


2022 - 2023
	Lecturer for Rings and Modules

2nd Bachelor in mathematics, Semester 1, University of Antwerp


2021 - 2022
	Teaching assistant for Rings and Modules
2nd

Bachelor in mathematics, Semester 1, University of Antwerp


2020 - 2021
	Teaching assistant for Rings and Modules


2nd and 3rd Bachelor in mathematics, Semester 1, University of Antwerp


Teaching assistant for Mathematics for Biology1st Bachelor in biology, Semester 2, University of Antwerp


2019 - 2020
	

Teaching assistant for Rings and Modules
3rd Bachelor in mathematics,

Semester 1, University of Antwerp


Lecturer for two lessons titled “A Quick Introduction to Category Theory” as part of a series on Linear Algebraic Groups in the course Algebras with InvolutionsMaster in Mathematics, Semester 1


Teaching assistant for Mathematics for Biology1st Bachelor in biology, Semester 2, University of Antwerp


	2018 - 2019
	Teaching assistant for&#38;nbsp;Rings and Modules
3rd Bachelor in mathematics, Semester 1, University of Antwerp

Teaching assistant for Mathematics for Biology1st Bachelor in biology, Semester 2, University of Antwerp


Supervision of bachelor theses

2024 - 2025
	The Dold-Kan CorrespondenceLaxmi Briedjlal

The Banach-Tarski Paradox
Sara Van Oevelen

Deformatietheorie
Stef Verpoorten
	2022 - 2023
	The Banach-Tarski Paradox
Emiel Geudens

</description>
		
	</item>
		
		
	<item>
		<title>Other academic activities</title>
				
		<link>https://arnemertens.com/Other-academic-activities</link>

		<pubDate>Mon, 06 Nov 2023 16:46:05 +0000</pubDate>

		<dc:creator>Arne Mertens Homepage</dc:creator>

		<guid isPermaLink="true">https://arnemertens.com/Other-academic-activities</guid>

		<description>Other academic activities


Organising
	Current, from Jun 2023
	Co-organiser of the Antwerp Algebra Colloquium
University of Antwerp


July 2025
	Co-organiser of the Summer School on Non-commutative Algebraic GeometryUniversity of Antwerp


Mar 2023
	Co-organiser of the Mathematics Research Day
University of Antwerp

	Sep 2023
	Local co-organiser of the Non-commutative Shapes Conference in Honour of Michel Van den Bergh
University of Antwerp

	May 2022
	Co-organiser of the HYDRA mini conference
University of Antwerp


Research Visits


Feb 2024
	Three week visit at the Simons Laufer Mathematical Sciences Institute in Berkeley, United States, where I collaborated with Julian Holstein and Yuri Berest.
	May 2023
	One week visit at the Université Paul Sabatier in Toulouse, where I collaborated with Violeta Borges Marques and&#38;nbsp; Elena Dimitriadis Bermejo, hosted by Bertrand Toën.


Outreach

Sep 2024
	Turtles all the Way Down: over zelfreferentie en paradoxen
Talk at MathFest


	Sep 2023
	Assistant at MathFest

	Winter 2023
	Tour guide at the Imaginary Exhibition


	2019 - 2023
	Co-organiser and presenter at Wiskunde In-Zicht


	2019 - 2023
	Assistance at the Vlaamse Wiskunde Olympiade


Upcoming conferences

July 2025
	International category theory conference
Masaryk University


Past Conferences


Jun 2024
	International category theory conferenceUniversidad de Santiago de Compostela


Apr 2024
	

Hochschild (Co)Homology and ApplicationsMathematisches Forschungsinstitut Oberwolfach


Feb 2024
	Introductory Workshop: Noncommutative Algebraic GeometrySimons Laufer Mathematical Sciences Institute


	Oct 2023
	CATS7 in Honour of Bertrand Toën

Centre International de Rencontres Mathématiques


Sep 2023
	Non-commutative Shapes Conference in Honour of Michel Van den BerghUniversity of Antwerp


	Sep 2023
	Hopf Days in Brussels
Université Libre de Bruxelles


	Jul 2023
	International Category Theory Conference

Université Catholique de Louvain

	Dec 2022
	Journées Homotopiques in Honour of Clemens Berger

Université Côte d’Azur, Nice

	Jun 2022
	Barcelona Conference on Higher Structures

Universitat de Barcelona

	Dec 2021
	Virtual Workshop on Higher Topos Theory II
Online

	Aug - Sep 2021
	International Category Theory Conference
Online

	Jun 2021
	Toposes Online
Online

	Spring 2021
	Introduction to Homological Mirror Symmetry by Michel Van den Bergh
Online

	Nov 2020
	Virtual Workshop on Higher Topos Theory
Online

	Summer 2020
	Differential Graded Categories and Applications by Bernhard Keller
Online

	Aug 2020


	Workshop on ∞-categories and their applications
Online

	Mar 2020
	Higher Homotopy Algebras in Topology 2

Trinity College Dublin

	Jul 2019
	International Category Theory Conference

University of Edinburgh

	Jun 2019
	Summer School on Higher Topos Theory and Univalent Foundations

University of Leeds

	Oct 2018
	CATS5

Museu Nacional de Historia Natural e da Ciênca, Lisbon
</description>
		
	</item>
		
		
	<item>
		<title>Contact</title>
				
		<link>https://arnemertens.com/Contact</link>

		<pubDate>Thu, 02 Nov 2023 17:32:50 +0000</pubDate>

		<dc:creator>Arne Mertens Homepage</dc:creator>

		<guid isPermaLink="true">https://arnemertens.com/Contact</guid>

		<description>Contact


	Arne Mertens (he/him)Departement Wiskunde - Faculteit WetenschappenUniversiteit Antwerpen
Postal address:Middelheimlaan 12020 AntwerpenBelgië

Email address:arne dot mertens at uantwerpen dot be


UAntwerp website
ORCID&#38;nbsp;
	&#60;img width="2135" height="2313" width_o="2135" height_o="2313" data-src="https://freight.cargo.site/t/original/i/bd053c7e7db3fde7e966302abb951c43b95dad69d5d2a11fd3dcb1a2a18c3219/IMG_9804c.jpg" data-mid="203092627" border="0" data-scale="100" src="https://freight.cargo.site/w/1000/i/bd053c7e7db3fde7e966302abb951c43b95dad69d5d2a11fd3dcb1a2a18c3219/IMG_9804c.jpg" /&#62;
</description>
		
	</item>
		
		
	<item>
		<title>Cats</title>
				
		<link>https://arnemertens.com/Cats</link>

		<pubDate>Wed, 08 Nov 2023 14:00:11 +0000</pubDate>

		<dc:creator>Arne Mertens Homepage</dc:creator>

		<guid isPermaLink="true">https://arnemertens.com/Cats</guid>

		<description>Cats

&#60;img width="2592" height="1936" width_o="2592" height_o="1936" data-src="https://freight.cargo.site/t/original/i/547cccadb91e4eb8d81889ca9d628f81124cc019ec2289ea4aaaecd333a3d145/IMG_0265.JPG" data-mid="196248844" border="0"  src="https://freight.cargo.site/w/1000/i/547cccadb91e4eb8d81889ca9d628f81124cc019ec2289ea4aaaecd333a3d145/IMG_0265.JPG" /&#62;
&#60;img width="1936" height="2592" width_o="1936" height_o="2592" data-src="https://freight.cargo.site/t/original/i/45a8a50ade63baa649e7f31323cce16653a62e85c493cff3566fe9541f48d890/IMG_0142.JPG" data-mid="196248841" border="0"  src="https://freight.cargo.site/w/1000/i/45a8a50ade63baa649e7f31323cce16653a62e85c493cff3566fe9541f48d890/IMG_0142.JPG" /&#62;
</description>
		
	</item>
		
	</channel>
</rss>