Claudius Zibrowius
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I am a professor in low-dimensional topology at the mathematics department of Ruhr-University Bochum, Germany.
Ich bin Professor für niedrigdimensionale Topologie an der mathematischen Fakultät der Ruhr-Universität Bochum.
I study local versions of Heegaard Floer theories and categorifications of quantum invariants, in particular bordered (sutured) Heegaard Floer theory and Bar-Natan's generalizations of Khovanov homology to tangles. An important tool in my work which binds these two types of invariants together is their relationship with Fukaya categories of surfaces.
Ich studiere lokale Varianten von Heegaard-Floer-Theorien sowie Kategorifizierungen von Quanten-Invarianten, insbesondere bordered (sutured) Heegaard-Floer-Homologie und Bar-Natan's Verallgemeinerungen von Khovanov-Homologie für Tangles. Ein wichtiges Element, das diese beiden Arten von Invarianten zusammenführt, ist ihre Verbindung zu Fukaya-Kategorien von Flächen.
→ Check out rational tangles in the Combinatorial Cabinet of Christian Stump.
→ Lernen Sie mehr über Tangles im Kombinatorischen Kabinett von Christian Stump.
My work is supported by an individual research grant (project number 505125645) from the German Research Foundation (DFG) and a Starting Grant (project number 101115822) from the European Research Council (ERC).
Meine Arbeit wird von der Deutschen Forschungsgemeinschaft (DFG) im Rahmen der Einzelförderung (Projektnummer 505125645) sowie einem Starting Grant (Projektnummer 101115822) des Europäischen Forschungsrats (ERC) unterstützt.
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Curriculum Vitæ |
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claudius.zibrowius@DELETEME@rub.de
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PGP)
claudius.zibrowius@DELETEME@posteo.net (
PGP)
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+49 (0)234 32-23324 |
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Office IB 3/117 |
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Ruhr-Universität Bochum Fakultät für Mathematik Prof. Dr. Claudius Zibrowius Gebäude IB, Postfach 23 Universitätsstraße 150 44780 Bochum (for letters) 44801 Bochum (for parcels) Germany |
Current group members
Aktuelle Mitarbeiter
- Luca Marchiori
- Dr. Tomás Mejía-Gómez
- Dr. Roberto Ladu (Floer Postdoc)
Former group members
Ehemalige Mitarbeiter
- Dr. Chen Zhang, Research Assistant Professor, Mathematics Department, Stony Brook
- Dr. Subhankar Dey, Assistant Professor, Department of Mathematics, IIT Palakkad
If you can't say it simply and clearly, keep quiet, and keep working on it till you can.
Karl Popper, 1970, in Wider die großen Worte
Wer's nicht einfach und klar sagen kann, der soll schweigen und weiterarbeiten, bis er's klar sagen kann.
Karl Popper, 1970, in Wider die großen Worte
Preprints
Preprints
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On mutation invariance in Khovanov homology
arXiv:2602.23442, 85 pages, joint with Artem Kotelskiy and Liam Watson
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Khovanov homology and refined bounds for Gordian distances
arXiv:2409.05743, 42 pages, joint with Lukas Lewark and Laura Marino
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Khovanov multicurves are linear
arXiv:2202.01460, 41 pages, joint with Artem Kotelskiy and Liam Watson
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Khovanov invariants via Fukaya categories: the tangle
invariants agree
arXiv:2004.01619, 14 pages, joint with Artem Kotelskiy and Liam Watson, submitted
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Immersed curves in Khovanov homology
arXiv:1910.14584, 95 pages, joint with Artem Kotelskiy and Liam Watson, submitted
I gave a mini-course on selected material from this paper at the 2019 ISM discovery school Current Progress in Low Dimensions in Montréal. My lecture notes are available here along with exercises. See also Jesse Cohen's notes.
In June 2024, Liam Watson gave a similar mini-course at Institute Fourier in Grenoble, which is available to watch on youtube.
Publications in major scientific journals
Veröffentlichungen in bedeutenden wissenschaftlichen Journalen
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Rasmussen invariants of Whitehead doubles and other satellites
joint with Lukas Lewark
Journal für die reine und angewandte Mathematik (Crelle) 816 (2024), 241–296 (arXiv:2208.13612 | doi:10.1515/crelle-2024-0061)
A supplementary table of invariants can be found here. -
Thin links and Conway spheres
joint with Artem Kotelskiy and Liam Watson
Compositio Mathematica 160.7 (2024), 1467–1524 (arXiv:2105.06308 | doi:10.1112/S0010437X24007152) -
Cosmetic operations and Khovanov multicurves
joint with Artem Kotelskiy, Tye Lidman, Allison Moore, and Liam Watson
Mathematische Annalen 389 (2023), 2903–2930 (arXiv:2109.14049 | doi:10.1007/s00208-023-02697-5) -
A mnemonic for the Lipshitz-Ozsváth-Thurston correspondence
joint with Artem Kotelskiy and Liam Watson
Algebraic & Geometric Topology 23.6 (2023), 2519–2543 (arXiv:2005.02792 | doi:10.2140/agt.2023.23.2519) -
L-space knots have no essential Conway spheres
joint with Tye Lidman and Allison Moore
Geometry & Topology 26.5 (2022), 2065–2102 (arXiv:2006.03521 | doi:10.2140/gt.2022.26.2065) -
On symmetries of peculiar modules; or, \(\delta\)-graded link
Floer homology is mutation invariant
Journal of the European Mathematical Society 25.8 (2023), 2949–3006 (arXiv:1909.04267 | doi:10.4171/JEMS/1201)
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Peculiar modules for 4-ended tangles
Journal of Topology 13.1 (2020), 77–158 (arXiv:1712.05050 | doi:10.1112/topo.12120)
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Kauffman states and Heegaard diagrams for tangles
Algebraic & Geometric Topology 19.5 (2019), 2233–2282 (arXiv:1601.04915 | doi:10.2140/agt.2019.19.2233)
Publications in conference proceedings and in other peer-reviewed scientific journals
Veröffentlichungen in Konferenzbänden oder in anderen peer-reviewten Journalen
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Heegaard Floer multicurves of double tangles
in Frontiers in Geometry and Topology (Tom Mrowka's birthday conference proceedings)
Proceedings of Symposia in Pure Mathematics 109 (2024), 253–284 (arXiv:2212.08501 | doi:10.1090/pspum/109/01999) -
Khovanov homology and strong inversions
joint with Artem Kotelskiy and Liam Watson
in Gauge theory and low-dimensional topology: progress and interaction,
Open Book Series 5.1 (2022), 223–244 (arXiv:2104.13592 | doi:10.2140/obs.2022.5.223) -
Rasmussen invariants
joint with Lukas Lewark
Mathematical Research Postcards 1.2 (2021) (pdf)
Theses
Doktor- und Masterarbeit
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On a Heegaard Floer theory for tangles
(PhD thesis)
arXiv:1610.07494, also available from Cambridge Apollo
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On a Heegaard Floer theory for tangles
(Doktorarbeit)
arXiv:1610.07494, auch bei Cambridge Apollo verfügbar
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Khovanov Stable Homotopy
(Part III essay)
This is essentially a summary of Lipshitz and Sarkar's construction of a Khovanov homotopy type.
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Khovanov Stable Homotopy
(Part III essay)
Dies ist hauptsächlich eine Zusammenfassung von Lipshitz and Sarkars Konstruktion eines Khovanov-Homotopie-Typs.
Talks (only those available online)
Vorträge
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(video)
Multicurves of double tangles
The low-dimensional workshop of the research semester Singularities and low dimensional topology at the Erdős Center
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(video)
Classification of multicurve invariants
ICTP conference Frontiers in Geometry and Topology in honour of Tom Mrowka, August 2022
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(video|slides)
Thin links and Conway spheres
The Nearly Carbon Neutral Geometric Topology Conference, June 2021
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(video|slides)
L-space knots have no essential Conway spheres
Simons Center Workshop: Floer homology in low-dimensional topology, January 2021
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(video|slides)
Thin links and Conway spheres
Regensburg low-dimensional geometry and topology seminar, July 2020
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(video|slides)
Khovanov and Heegaard Floer theories through the lens of
immersed curves
Trends in Low-Dimensional Topology, May 2020, joint with Artem Kotelskiy
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(video|slides)
Conway mutation in link Floer, Khovanov and Bar-Natan homology
geometry/topology seminars at Duke, UGA, and Durham, February/March 2020
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(video)
Categories of curved complexes for marked surfaces
Isaac-Newton-Institut, May 2017
Outreach talks
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(slides) Mathematik zum Anfassen, 115. MNU-Bundeskongress, RUB, Bochum
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(slides) Mathematik zum Anfassen, Nacht.Schafft.Wissen 2022 (Night of Science), Regensburg
Conference organization
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Categorification in Low Dimensional Topology,
Bochum, Juli 2025
student workshop and research conference, organized together with Paul Wedrich
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Algebra and Low-Dimensional Topology,
Berlin, August 2022
minisymposium at the DMV meeting 2022, organized together with Paul Wedrich
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Perspectives on quantum link homology theories,
Regensburg, August 2021
combined SFB student workshop and research conference, organized together with Lukas Lewark
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Topology session of the winter meeting of the Canadian Mathematical Society, Vancouver, December 2018
organized together with Krishanu Sankar
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Perspectives on bordered Heegaard Floer theory, Montréal, May 2018
combined ISM workshop/CIRGET conference, organized together with Liam Watson and Steve Boyer
student workshop and research conference, organized together with Paul Wedrich
minisymposium at the DMV meeting 2022, organized together with Paul Wedrich
combined SFB student workshop and research conference, organized together with Lukas Lewark
organized together with Krishanu Sankar
combined ISM workshop/CIRGET conference, organized together with Liam Watson and Steve Boyer
Computer programs
Computerprogramme
- A web-calendar for my maths department, written in javascript. 2025.
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kht++ (program website|github), a C++ program for computing Khovanov
invariants of links and tangles. 2021-2025.
This program supersedes KhT.py, a python program that I wrote with G. Chhina during an undergraduate summer research project.
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BSFH.m, a Mathematica package for computing
Zarev's bordered sutured Floer invariants. 2017–2019.
A manual can be found in appendix D of my thesis. An updated version which also handles more than two glueing surfaces and
\(\alpha\)- and\(\beta\)- arcs simultaneously is available upon request. -
PQM.m, a Mathematica package for computing the invariant \(\operatorname{HFT}\) for Conway tangles. 2018.
A manual can be found here.
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APT.m, a Mathematica package for computing the decategorified
polynomial tangle invariants \(\nabla_T^s\) from my
thesis. 2017.
A manual can be found in appendix C of my thesis.
All programs are licensed under AGPLv3.
Lectures and Seminars
Ruhr-Universität Bochum
- Summer Term '26: Research Seminar on Multicurves (joint with MPIM Bonn)
- Summer Term '26: Seminar on low-dimensional topology
- Winter Term '25: Algebraische Topologie (Skript|Übungsblätter)
- Summer Term '25: Topologie (Vorlesungszusammenfassungen|Übungsblätter)
- Winter Term '24: Reading group Bordered knot Floer homology
Durham University
- Michaelmas Term '23: Algebraic Topology I
Universität Regensburg
- Winter Term '21: Elementargeometrie für Lehramt
University of British Columbia
- Spring Term '20: 101:201 Integral Calculus with Applications to Physical Sciences and Engineering
- Winter Term '19: 100:101 Differential Calculus with Applications to Physical Sciences and Engineering
- Spring Term '19: 101:207 Integral Calculus with Applications to Physical Sciences and Engineering
- Winter Term '18: 100:102 Differential Calculus with Applications to Physical Sciences and Engineering
Université de Sherbrooke
- Hiver '18: MAT623/MAT813 Topologie algébrique
Tripos supervisions (University of Cambridge)
- Lent '17: Part Ib Geometry (Dr Alexei Kovalev)
- Michaelmas '15+'16: Part II Algebraic Topology (Dr Henry Wilton)
- Lent '15: Part III Homotopy Theory (Dr Oscar Randal-Williams)
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Michaelmas '13+'14: Part II Algebraic Topology (Dr Oscar Randal-Williams)
Student mentoring
Graduate projects
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Ludovico Morellato (2022): Implementing the Sarkar-Wang nicefication algorithm for Heegaard diagrams
joint supervision with Lukas Lewark
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Benedikt Aubeck (2021): Determining the Seifert genus via the Heegaard Floer tangle invariant HFT
joint supervision with Lukas Lewark
Undergraduate projects
- Gurkeerat Chhina (2019): Computing immersed curves in Khovanov homology
- Johnny Nicholson (2016): Comparing generalisations of the Alexander polynomial to tangles
Music
Musik
I currently sing in the following choirs:
- Philharmonic Choir Bochum directed by Mateo Peñaloza Cecconi
- Chamber Choir Probsteimusic Bochum directed by Prof. Christopher Brauckmann
Ich singe momentan in folgenden Chören:
- Philharmonischer Chor Bochum unter der Leitung von Mateo Peñaloza Cecconi
- Kammerchor der Probsteimusik Bochum unter der Leitung von Prof. Christopher Brauckmann
Genocide in Gaza
Völkermord in Gaza
- I have signed the German and European version of the Uppsala Declaration.
- I stand in solidarity with the Tribunal against Germany; check out the recordings of the panel discussions on the complicity of German media and repression at German universities.
- I support this call by over 160 mathematicians to their colleagues to cease all scientific collaboration with Israeli institutions that do not explicitly condemn the genocide in Gaza and the illegal colonization of Palestine.
- In November 2024, I left the German Protestant Church, despite (or rather because of) being a believer in Christ. My reasons for this are explained in this letter (mostly German), entitled My resignation from the church — silence is complicity, to the pastor who baptized me.
- I support this open letter addressed to the federal government of Germany, demanding that Germany must stop supporting the annihilation of palestinians.
- In May 2024, I supported this public statement by university lecturers in Berlin. I was asked to justify my support.
- Instructions for making your website prettier in these dark times: click here
- Ich habe die deutsche Version der Uppsala Erklärung unterzeichnet.
- Ich stehe in Solidarität mit dem Tribunal gegen die Bundesrepublik; Ich empfehle insbesondere die Aufzeichnungen der Paneldiskussionen zu Medienhetze und Repressionen an deutschen Universitäten.
- Ich unterstütze diesen Aufruf von über 160 Mathematikern an ihre Kollegen, jegliche wissenschaftliche Zusammenarbeit mit israelischen Institutionen einzustellen, die nicht explizit den Völkermord in Gaza und die illegale Kolonisierung Palästinas verurteilen.
- Im November 2024 bin ich aus der Evangelischen Kirche Deutschlands ausgetreten, obwohl (bzw. gerade weil) ich gläubiger Christ bin. Meine Gründe dafür erläutere ich in diesem Brief an den Pfarrer, der mich getauft hat.
- Ich unterstütze diesen Offenen Brief an die deutsche Bundesregierung, der fordert, das Deutschland umgehend aufhören muss, die Vernichtung von Palästinenser:innen zu unterstützen.
- Im Mai 2024 habe ich das Statement von Lehrenden an Berliner Hochschulen unterstützt. Ich wurde aufgefordert, dies zu rechtfertigen
- Anleitung um eine Webseite schöner zu machen in dieser dunklen Zeit: hier klicken (auf englisch)
Raspberry Pi
I have written a guide about how to run a website on a raspberry pi. You can read it here.
Ich habe eine Anleitung darüber geschrieben wie man eine Webseite auf einem Raspberry Pi betreibt. Man kann die Anleitung hier lesen.