I am a professor in low-dimensional topology at the mathematics department of Ruhr-University Bochum, Germany.

Ich bin Professor für niedrig-dimensionale 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.

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).

I currently have a postdoc, Dr. Subhankar Dey. Chen Zhang, currently PhD candidate at MSU, will join my group as a postdoc in September 2024. I expect to hire more postdocs and PhD students soon. Open positions will be advertised here.

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.

Ich betreue momentan einen Postdoktoranden, Dr. Subhankar Dey. Im September wird Chen Zhang, z.Z. Doktorand an der MSU, hinzukommen. Ich gehe davon aus, in naher Zukunft weitere Postdoktoranden und Doktoranden beschäftigen zu können. Offene Stellen werden hier an dieser Stelle bekannt gegeben.

	Curriculum Vitæ
	claudius.zibrowius@DELETEME@rub.de ( PGP) claudius.zibrowius@DELETEME@posteo.net ( PGP)
	Office IB 3/117 Faculty of Mathematics Universitätsstraße 150 Building IB, Postbox 23 44801 Bochum Germany

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

• Rasmussen invariants of Whitehead doubles and other satellites
  

  arXiv:2208.13612, 48 pages, joint with Lukas Lewark
  A supplementary table of invariants can be found here.

• Khovanov multicurves are linear
  

  arXiv:2202.01460, 41 pages, joint with Artem Kotelskiy and Liam Watson

• Khovanov invariants via Fukaya categories: the tangle invariants agree
  

  arXiv:2004.01619, 14 pages, joint with Artem Kotelskiy and Liam Watson, submitted

• 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.

Publications in major scientific journals

Veröffentlichungen in bedeutenden wissenschaftlichen Journalen

• Thin links and Conway spheres
  

  joint with Artem Kotelskiy and Liam Watson
  arXiv:2105.06308, 50 pages, to appear in Compositio Mathematica

• Cosmetic operations and Khovanov multicurves
  

  joint with Artem Kotelskiy, Tye Lidman, Allison Moore, and Liam Watson
  Mathematische Annalen (2023), pp. 28 (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)

• Peculiar modules for 4-ended tangles
  

  Journal of Topology 13.1 (2020), 77–158 (arXiv:1712.05050 | doi:10.1112/topo.12120)

• 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

• Heegaard Floer multicurves of double tangles
  

  arXiv:2212.08501, 31 pages, to appear in the proceedings of Frontiers in Geometry and Topology, a conference in honour of Tom Mrowka's 60th birthday.

• 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

• On a Heegaard Floer theory for tangles (PhD thesis)
  

  arXiv:1610.07494, also available from Cambridge Apollo

• On a Heegaard Floer theory for tangles (Doktorarbeit)
  

  arXiv:1610.07494, auch bei Cambridge Apollo verfügbar

• Khovanov Stable Homotopy (Part III essay)
  

  This is essentially a summary of Lipshitz and Sarkar's construction of a Khovanov homotopy type.

• 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

• (video) Multicurves of double tangles
  

  The low-dimensional workshop of the research semester Singularities and low dimensional topology at the Erdős Center

• (video) Classification of multicurve invariants
  

  ICTP conference Frontiers in Geometry and Topology in honour of Tom Mrowka, August 2022

• (video|slides) Thin links and Conway spheres
  

  The Nearly Carbon Neutral Geometric Topology Conference, June 2021

• (video|slides) L-space knots have no essential Conway spheres
  

  Simons Center Workshop: Floer homology in low-dimensional topology, January 2021

• (video|slides) Thin links and Conway spheres
  

  Regensburg low-dimensional geometry and topology seminar, July 2020

• (video|slides) Khovanov and Heegaard Floer theories through the lens of immersed curves
  

  Trends in Low-Dimensional Topology, May 2020, joint with Artem Kotelskiy

• (video|slides) Conway mutation in link Floer, Khovanov and Bar-Natan homology
  

  geometry/topology seminars at Duke, UGA, and Durham, February/March 2020

• (video) Categories of curved complexes for marked surfaces
  

  Isaac-Newton-Institut, May 2017

Conference organization

• Algebra and Low-Dimensional Topology, Berlin, August 2022
  

  minisymposium at the DMV meeting 2022, organized together with Paul Wedrich

• Perspectives on quantum link homology theories, Regensburg, August 2021
  

  combined SFB student workshop and research conference, organized together with Lukas Lewark

• Topology session of the winter meeting of the Canadian Mathematical Society, Vancouver, December 2018
  

  organized together with Krishanu Sankar

• Perspectives on bordered Heegaard Floer theory, Montréal, May 2018
  

  combined ISM workshop/CIRGET conference, organized together with Liam Watson and Steve Boyer

Computer programs

Computerprogramme

• kht++ (program website|github), a C++ program for computing Khovanov invariants of links and tangles. 2021.

  This program supersedes KhT.py, a python program that I wrote with G. Chhina during an undergraduate summer research project.

• 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.

• 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 four programs are licensed under AGPLv3.

Outreach talks

• (slides) Mathematik zum Anfassen, Nacht.Schafft.Wissen 2022 (Night of Science), Regensburg

Lectures

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)
• Michaelmas '13+'14: Part II Algebraic Topology (Dr Oscar Randal-Williams)
  

Student mentoring

Graduate projects

• Ludovico Morellato (2022): Implementing the Sarkar-Wang nicefication algorithm for Heegaard diagrams

  joint supervision with Lukas Lewark

• 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