I am a professor (permanent W2) at the Department of Mathematics at the University of Hamburg, a member of the management committee of the Collaborative Research Center Higher Structures, moduli spaces and integrability, and a PI in the Cluster of Excellence Quantum Universe.

I am the departmental coordinator for the Erasmus+ programme and an equal opportunity representative at the department.

My research interests are in low-dimensional topology and representation theory. In particular, I am interested in topological field theories (TFTs) and higher structures related to knot homology theories, and the exploration of their deep connections to (higher) representation theory and mathematical physics. I also enjoy applying topological and combinatorial tools to solve problems in representation theory.

My CV.

Hirzebruch Research Instructor

MPIM and University of Bonn

MSRI Postdoctoral Fellow

Mathematical Sciences Research Institute

Hirzebruch Research Instructor

MPIM and University of Bonn

Postdoctoral Fellow

The Australian National University

Research Associate

Imperial College London


University of Cambridge
10/2015, Advisor: Jake Rasmussen

Master of Advanced Study

University of Cambridge

Bachelor of Science

Universität Wien


  • Dr. Jesse Cohen started as a Quantum Universe postdoctoral researcher in 2023. Jesse's research focuses on homological invariants of knots and 3-manifolds, from bordered Heegaard Floer homology to Khovanov homology.
  • Leon Goertz started as a doctoral student in 2023. Leon is interested in higher categories that arise in categorification and low-dimensional topology.
  • Isabela Recio started as a doctoral student in 2024. Isabela is interested in TFTs related to link homology theories and Soergel bimodules.
  • Karim Ritter von Merkl started as a doctoral student in 2023. Karim is interested in computational and structural aspects of colored link homology theories.

Our research seminar on Quantum Topology and Categorification (QTcat) is run jointly with Dr. David Reutter's Emmy Noether Research Group Topological quantum field theory beyond three dimensions.


All my research papers are available on the mathematics arXiv. They are also listed by Google Scholar, ORCiD and ResearchGate. Preprints and published or accepted articles appear in order of first arXiv posting on the following list.

27) Bordered invariants from Khovanov homology

To every compact oriented surface that is composed entirely out of 2-dimensional 0- and 1-handles, we construct a dg category using structures arising in Khovanov homology. These dg categories form part of the 2-dimensional layer (a.k.a. modular functor) of a categorified version of the sl(2) Turaev-Viro topological field theory. As a byproduct, we obtain a unified perspective on several hitherto disparate constructions in categorified quantum topology, including the Rozansky-Willis invariants, Asaeda-Przytycki--Sikora homologies for links in thickened surfaces, categorified Jones-Wenzl projectors and associated spin networks, and dg horizontal traces.

With Matthew Hogancamp and David Rose.

26) Invariants of surfaces in smooth 4-manifolds from link homology

We construct analogs of Khovanov-Jacobsson classes and the Rasmussen invariant for links in the boundary of any smooth oriented 4-manifold. The main tools are skein lasagna modules based on equivariant and deformed versions of gl(N) link homology, for which we prove non-vanishing and decomposition results.

With Scott Morrison and Kevin Walker.

25) A braided (infinity,2)-category of Soergel bimodules

The Hecke algebras for all symmetric groups taken together form a braided monoidal category that controls all quantum link invariants of type A and, by extension, the standard canon of topological quantum field theories in dimension 3 and 4. Here we provide the first categorification of this Hecke braided monoidal category, which takes the form of an E2-monoidal (infinity,2)-category whose hom-(infinity,1)-categories are k-linear, stable, idempotent-complete, and equipped with Z-actions. This categorification is designed to control homotopy-coherent link homology theories and to-be-constructed topological quantum field theories in dimension 4 and 5. Our construction is based on chain complexes of Soergel bimodules, with monoidal structure given by parabolic induction and braiding implemented by Rouquier complexes, all modelled homotopy-coherently. This is part of a framework which allows to transfer the toolkit of the categorification literature into the realm of infinity-categories and higher algebra. Along the way, we develop families of factorization systems for (infinity,n)-categories, enriched infinity-categories, and infinity-operads, which may be of independent interest. As a service aimed at readers less familiar with homotopy-coherent mathematics, we include a brief introduction to the necessary infinity-categorical technology in the form of an appendix.

With Yu Leon Liu, Aaron Mazel-Gee, David Reutter, and Catharina Stroppel.

  • arXiv 2024
  • 24) A Kirby color for Khovanov homology

    We construct a Kirby color in the setting of Khovanov homology: an ind-object of the annular Bar-Natan category that is equipped with a natural handle slide isomorphism. Using functoriality and cabling properties of Khovanov homology, we define a Kirby-colored Khovanov homology that is invariant under the handle slide Kirby move, up to isomorphism. Via the Manolescu--Neithalath 2-handle formula, Kirby-colored Khovanov homology agrees with the gl(2) skein lasagna module, hence is an invariant of 4-dimensional 2-handlebodies.

    With Matthew Hogancamp and David Rose.

    Journal of the European Mathematical Society (accepted, 2023)

    23) Skein lasagna modules and handle decompositions

    The skein lasagna module is an extension of Khovanov-Rozansky homology to the setting of a four-manifold and a link in its boundary. This invariant plays the role of the Hilbert space of an associated fully extended (4+epsilon)-dimensional TQFT. We give a general procedure for expressing the skein lasagna module in terms of a handle decomposition for the four-manifold. We use this to calculate a few examples, and show that the skein lasagna module can sometimes be locally infinite dimensional.

    With Ciprian Manolescu and Kevin Walker.

    Advances in Mathematics 425 (2023) Paper No. 109071

    22) Link splitting deformation of colored Khovanov-Rozansky homology

    We introduce a multi-parameter deformation of the triply-graded Khovanov-Rozansky homology of links colored by one-column Young diagrams, generalizing the "y-ified" link homology of Gorsky-Hogancamp and work of Cautis--Lauda--Sussan. For each link component, the natural set of deformation parameters corresponds to interpolation coordinates on the Hilbert scheme of the plane. We extend our deformed link homology theory to braids by introducing a monoidal dg 2-category of curved complexes of type A singular Soergel bimodules. Using this framework, we promote to the curved setting the categorical colored skein relation from arXiv:2107.08117 and also the notion of splitting map for the colored full twists on two strands. As applications, we compute the invariants of colored Hopf links in terms of ideals generated by Haiman determinants and use these results to establish general link splitting properties for our deformed, colored, triply-graded link homology. Informed by this, we formulate several conjectures that have implications for the relation between (colored) Khovanov--Rozansky homology and Hilbert schemes.

    With Matthew Hogancamp and David Rose.

    Proceedings of the London Mathematical Society (accepted, 2023)

    21) A skein relation for singular Soergel bimodules

    We study the skein relation that governs the HOMFLYPT invariant of links colored by one-column Young diagrams. Our main result is a categorification of this colored skein relation. This takes the form of a homotopy equivalence between two one-sided twisted complexes constructed from Rickard complexes of singular Soergel bimodules associated to braided webs. Along the way, we prove a conjecture of Beliakova-Habiro relating the colored 2-strand full twist complex with the categorical ribbon element for quantum sl(2).

    With Matthew Hogancamp and David Rose.

    20) SL2 tilting modules in the mixed case

    Using the non-semisimple Temperley-Lieb calculus, we study the additive and monoidal structure of the category of tilting modules for SL2 in the mixed case. This simultaneously generalizes the semisimple situation, the case of the complex quantum group at a root of unity, and the algebraic group case in positive characteristic. We describe character formulas and give a presentation of the category of tilting modules as an additive category via a quiver with relations. Turning to the monoidal structure, we describe fusion rules and obtain an explicit recursive description of the appropriate analog of Jones-Wenzl projectors. We also discuss certain theta values, the tensor ideals, mixed Verlinde quotients and the non-degeneracy of the braiding.

    With Louise Sutton, Daniel Tubbenhauer, and Jieru Zhu.

    Selecta Mathematica 29-3 (2023) Paper No. 39.

    19) gl(2) foams and the Khovanov homotopy type

    The Blanchet link homology theory is an oriented model of Khovanov homology, functorial over the integers with respect to link cobordisms. We formulate a stable homotopy refinement of the Blanchet theory, based on a comparison of the Blanchet and Khovanov chain complexes associated to link diagrams. The construction of the stable homotopy type relies on the signed Burnside category approach of Sarkar-Scaduto-Stoffregen.

    With Vyacheslav Krushkal.

    Indiana University Mathematics Journal 72-3 (2023) 731--755.

    18) Tangle addition and the knots-quivers correspondence

    We prove that the generating functions for the one row/column colored HOMFLY-PT invariants of arborescent links are specializations of the generating functions of the motivic Donaldson-Thomas invariants of appropriate quivers that we naturally associate with these links. Our approach extends the previously established tangles-quivers correspondence for rational tangles to algebraic tangles by developing gluing formulas for HOMFLY-PT skein generating functions under Conway's tangle addition. As a consequence, we prove the conjectural links-quivers correspondence of Kucharski–Reineke–Stošić–Sułkowski for all arborescent links.

    With Marko Stošić.

    Journal of the London Mathematical Society 104-1 (2021) 341-361

    17) The center of SL(2) tilting modules

    In this note we compute the centers of the categories of tilting modules for G=SL(2) in prime characteristic, of tilting modules for the corresponding quantum group at a complex root of unity, and of projective G_gT-modules when g=1,2.

    With Daniel Tubbenhauer.

    Glasgow Mathematical Journal 64 (2022) 165-184

    16) A coupled Temperley-Lieb algebra for the superintegrable chiral Potts chain

    The hamiltonian of the N-state superintegrable chiral Potts (SICP) model is written in terms of a coupled algebra defined by N-1 types of Temperley-Lieb generators. This generalises a previous result for N=3 obtained by J. F. Fjelstad and T. Månsson [J. Phys. A 45 (2012) 155208]. A pictorial representation of a related coupled algebra is given for the N=3 case which involves a generalisation of the pictorial representation of the Temperley-Lieb algebra to include a pole around which loops can become entangled. (shortened)

    With Remy Adderton and Murray T. Batchelor.

    Journal of Physics A: Mathematical and Theoretical 53-36 (2020)

    15) Derived traces of Soergel categories

    We study two kinds of categorical traces of (monoidal) dg categories, with particular interest in categories of Soergel bimodules. First, we explicitly compute the usual Hochschild homology, or derived vertical trace, of the category of Soergel bimodules in arbitrary types. Secondly, we introduce the notion of derived horizontal trace of a monoidal dg category and compute the derived horizontal trace of Soergel bimodules in type $A$. As an application we obtain a derived annular Khovanov--Rozansky link invariant with an action of full twist insertion, and thus a categorification of the HOMFLY-PT skein module of the solid torus.

    With Eugene Gorsky and Matthew Hogancamp.

    International Mathematics Research Notices published online

    14) Invariants of 4-manifolds from Khovanov-Rozansky link homology

    We use Khovanov-Rozansky gl(N) link homology to define invariants of oriented smooth 4-manifolds, as skein modules constructed from certain 4-categories with well-behaved duals. The technical heart of this construction is a proof of the sweep-around property, which makes these link homologies well defined in the 3-sphere.

    With Scott Morrison and Kevin Walker.

    Accepted for publication in Geometry & Topology 26-8 (2022) 3367--3420.

    13) Quivers for SL(2) tilting modules

    Using diagrammatic methods, we define a quiver algebra depending on a prime p and show that it is the algebra underlying the category of tilting modules for SL(2) in characteristic p. Along the way we obtain a presentation for morphisms between p-Jones-Wenzl projectors.

    With Daniel Tubbenhauer.

    Representation Theory 25 (2021) 440-480

    12) Evaluations of annular Khovanov-Rozansky homology

    We describe the universal target of annular Khovanov-Rozansky link homology functors as the homotopy category of a free symmetric monoidal category generated by one object and one endomorphism. This categorifies the ring of symmetric functions and admits categorical analogues of plethystic transformations, which we use to characterize the annular invariants of Coxeter braids. Further, we prove the existence of symmetric group actions on the Khovanov-Rozansky invariants of cabled tangles and we introduce spectral sequences that aid in computing the homologies of generalized Hopf links. Finally, we conjecture a characterization of the horizontal traces of Rouquier complexes of Coxeter braids in other types.

    With Eugene Gorsky.

    Math Z. 303-25 (2023)

    11) Algèbre diagrammatique et catégorification

    Nous proposons une illustration diagrammatique abordable du concept de catégorification qui s’est développé au cours des vingt dernières années.

    A friendly outreach article in French, written mostly by Hoel Queffelec, inspired by our joint work.

    La Gazette des mathématiciens 163 (janvier 2020)

    10) Khovanov homology and categorification of skein modules

    For every oriented surface of finite type, we construct a functorial Khovanov homology for links in a thickening of the surface, which takes values in a categorification of the corresponding gl(2) skein module. The latter is a mild refinement of the Kauffman bracket skein algebra, and its categorification is constructed using a category of gl(2) foams that admits an interesting non-negative grading. We expect that the natural algebra structure on the gl(2) skein module can be categorified by a tensor product that makes the surface link homology functor monoidal. We construct a candidate bifunctor on the target category and conjecture that it extends to a monoidal structure. This would give rise to a canonical basis of the associated gl(2) skein algebra and verify an analogue of a positivity conjecture of Fock–Goncharov and Turston. We provide evidence towards the monoidality conjecture by checking several instances of a categorified Frohman-Gelca formula for the skein algebra of the torus. Finally, we recover a variant of the Asaeda–Przytycki–Sikora surface link homologies and prove that surface embeddings give rise to spectral sequences between them.

    With Hoel Queffelec

    Quantum Topology 21-1 (2021) 129-209.

    9) Extremal weight projectors II

    In previous work, we have constructed diagrammatic idempotents in an affine extension of the Temperley–Lieb category, which describe extremal weight projectors for sl(2), and which categorify Chebyshev polynomials of the first kind. In this paper, we generalize the construction of extremal weight projectors to the case of gl(N) for N > 1, with a view towards categorifying the corresponding torus skein algebras via Khovanov–Rozansky link homology. As by-products, we obtain compatible diagrammatic presentations of the representation categories of gl(N) and its Cartan subalgebra, and a categorification of power-sum symmetric polynomials.

    With Hoel Queffelec.

    Algebraic Combinatorics (accepted, 2023)

    8) Rational links and DT invariants of quivers

    We prove that the generating functions for the colored HOMFLY-PT polynomials of rational links are specializations of the generating functions of the motivic Donaldson-Thomas invariants of appropriate quivers that we naturally associate with these links. This shows that the conjectural links-quivers correspondence of Kucharski–Reineke–Stošić–Sułkowski as well as the LMOV conjecture hold for rational links. Along the way, we extend the links-quivers correspondence to tangles and, thus, explore elements of a skein theory for motivic Donaldson-Thomas invariants.

    With Marko Stošić.

    International Mathematical Research Notices 6 (2021) 4169-4210.

    7) Functoriality of colored link homologies

    We prove that the bigraded, colored Khovanov–Rozansky type A link and tangle invariants are functorial with respect to link and tangle cobordisms.

    With Michael Ehrig and Daniel Tubbenhauer.

    Proceedings of the London Mathematical Society 117-5 (2018), 996-1040

    6) Extremal weight projectors

    We introduce a quotient of the affine Temperley-Lieb category that encodes all weight preserving linear maps between finite-dimensional sl(2)-representations. We study the diagrammatic idempotents that correspond to projections onto extremal weight spaces and find that they satisfy similar properties as Jones-Wenzl projectors, and that they categorify the Chebyshev polynomials of the first kind. This gives a categorification of the Kauffman bracket skein algebra of the annulus, which is well adapted to the task of categorifying the multiplication on the Kauffman bracket skein module of the torus.

    With Hoel Queffelec.

    Mathematical Research Letters 25-6 (2018), 1911-1936

    5) Exponential growth of colored HOMFLY-PT homology

    We define reduced colored sl(N) link homologies and use deformation spectral sequences to characterize their dependence on color and rank. We then define reduced colored HOMFLY-PT homologies and prove that they arise as large N limits of sl(N) homologies. Together, these results allow proofs of many aspects of the physically conjectured structure of the family of type A link homologies. In particular, we verify a conjecture of Gorsky, Gukov and Stošić about the growth of colored HOMFLY-PT homologies.

    Advances in Mathematics 353 (2019), 471-525

    4) Super q-Howe duality and web categories

    We use super q–Howe duality to provide diagrammatic presentations of an idempotented form of the Hecke algebra and of categories of gl(N)–modules (and, more generally, gl(N|M)–modules) whose objects are tensor generated by exterior and symmetric powers of the vector representations. As an application, we give a representation-theoretic explanation and a diagrammatic version of a known symmetry of colored HOMFLY–PT polynomials.

    With Daniel Tubbenhauer and Pedro Vaz.

    Algebraic & Geometric Topology 17-6 (2017), 3703-3749

    3) Deformations of colored sl(N) link homologies via foams

    We prove a conjectured decomposition of deformed sl(N) link homology, as well as an extension to the case of colored links, generalizing results of Lee, Gornik, and Wu. To this end, we use foam technology to give a completely combinatorial construction of Wu’s deformed colored sl(N) link homologies. By studying the underlying deformed higher representation-theoretic structures and generalizing the Karoubi envelope approach of Bar-Natan and Morrison, we explicitly compute the deformed invariants in terms of undeformed type A link homologies of lower rank and color.

    With David Rose.

    Geometry & Topology 20-6 (2016), 3431-3517

    2) q-holonomic formulas for colored HOMFLY polynomials of 2-bridge links

    We compute q-holonomic formulas for the HOMFLY polynomials of 2-bridge links colored with one-column (or one-row) Young diagrams.

    Journal of Pure and Applied Algebra 223-4 (2019), 1434-1439

    1) Categorified sl(N) invariants of colored rational tangles

    We use categorical skew Howe duality to find recursion rules that compute categorified sl(N) invariants of rational tangles colored by exterior powers of the standard representation. Further, we offer a geometric interpretation of these rules which suggests a connection to Floer theory. Along the way we make progress towards two conjectures about the colored HOMFLY homology of rational links and discuss consequences for the corresponding decategorified invariants.

    Algebraic & Geometric Topology 16-1 (2016), 427-482



    1. Simons Semester: "Knots, homologies, and physics". University of Warsaw. March - June 2024.
    2. Conference: "Diagrammatic Intuition and Deep Learning in Mathematics", University of York, 15th - 19th July 2024.
    3. Programme: "Quantum Symmetries Reunion", SLMath, July - August 2024.


    1. I co-organised a minisymposium on Algebra and Low-Dimensional Topology at the DMV Annual Meeting, Berlin, 12th - 16th September 2022.
    2. I co-organised a workshop on "Monoidal and 2-categories in representation theory and categorification" at the Hausdorff Research Institute for Mathematics, Bonn, 30th November - 4th December 2020. Video recordings
    3. I co-organised the Felix Klein Lectures 2020 by Markus Reineke at the Hausdorff Center for Mathematics, Bonn, 20th - 29th October 2020. Video recordings.
    4. I co-organised a Lecture series on modified traces in algebra and topology at the Hausdorff Institute for Mathematics, Bonn, 12th - 22th October 2020. Video recordings.
    5. I was a group leader in the HIM Junior Trimester Program: "New Trends in Representation Theory", September - December 2020.
    6. I coordinated the Oberseminar Darstellungstheorie (representation theory) at the University of Bonn, winter semester 2019/20.
    7. I co-organised a Workshop on "Categorification in quantum topology and beyond" at the Erwin Schrödinger Institut, Vienna, 7th - 18th January 2019. Video recordings.
    8. I co-organised a Workshop on "Classical and quantum three-manifold topology" at Monash University, Melbourne, 14th - 21st December 2018.
    9. I co-organised the "Mathematical Sciences Institute Colloquium" at the Australian National University, 2018 - 2019.
    10. I was part of the Junior Trimester Program on "Symplectic Geometry and Representation Theory" at the Hausdorff Institute for Mathematics, Bonn, September - December 2017.

    Conference talks and colloquia

    1. Conference: "Quantum Topology Biennial: Representation Theory", SwissMap, Les Diablerets, 14th - 19th January 2024.
    2. Workshop: "Algebra, geometry, and combinatorics of link homology", American Institute of Mathematics, 31st July 31 - 4th August 2023.
    3. Spring School in Representation Theory, Lecture series on "A Kirby color for Khovanov homology", Canterbury, 24th - 28th April 2023.
    4. Quantum Universe Lecture, DESY, 27th January 2023.
    5. Pure mathematics colloquium, University of Hamburg, 18th October 2022.
    6. DMV Annual Meeting, Geometry and Topology Section, Berlin, 12th - 16th September 2022.
    7. Conference: QUACKS II, University of Oregon, 8th June - 12th August 2022.
    8. Conference: From Subfactors to Quantum Topology -- in Memory of Vaughan Jones, Geneva, 27th June - 1st July 2022.
    9. Colloquium, University of Virginia, 7th April 2022.
    10. Conference: "Recent developments in link homology", SwissMAP, 31st January - 4th February 2022.
    11. Colloquium, Medgar Evers College Mathematics Colloquium, 29th November 2021.
    12. Colloquium, University of Göttingen, 25th November 2021.
    13. Workshop: "Foam Evaluation", ICERM, 5th - 7th November 2021.
    14. Colloquium, Max Planck Institute for Mathematics, Bonn, 9th September 2021.
    15. HCM Symposium, Hausdorff Center for Mathematics, Bonn, 24th - 26th August 2021.
    16. Workshop: "Perspectives on quantum link homology theories", series of four lectures, University of Regensburg, 9th - 15th August 2021. Videos
    17. Georgia Topology Conference 2021, UGA, 7th - 11th June 2021.
    18. Workshop: "Perspectives on Knot Homology", Banff International Research Station, 16th - 21st May 2021.
    19. Online conference "QUAntum groups, Categorification, Knot invariants, and Soergel bimodules", University of Oregon, 10th - 14th August 2020. Video
    20. Workshop: "Soergel Bimodules and Categorification of the Braid Group", ICERM, 28th February - 1st March 2020. Video
    21. Conference: "Mathematics and Physics of Knots", Institute Mittag Leffler, 24th - 28st June 2019.
    22. Conference: "Hilbert schemes, categorification and combinatorics", UC Davis, 19th - 23rd June 2019.
    23. Conference: "Quantum Topology and hyperbolic geometry III", Da Nang, Vietnam, 27th - 31st May 2019. Video
    24. Workshop: "Hidden Algebraic Structures in Topology", Caltech, 13th-16th March 2019.
    25. Conference: Kioloa, 18th - 22nd February 2019.
    26. Conference: "Aspects in higher representation theory", Brussels, 21st - 25th January 2019.
    27. Workshop: "Categorified Hecke algebras, link homology, and Hilbert schemes", American Institute of Mathematics, 1st - 5th October 2018.
    28. Conference: "Interactions of low-dimensional topology and higher representation theory", Universität Zürich, 17th - 21st September 2018.
    29. Conference: "Categorification and Higher Representation Theory", Institute Mittag Leffler, 9th - 13th July 2018.
    30. Conference: TQFT and categorification, IESC, Corsica, 15th - 20th April 2018.
    31. Workshop: Categorification in mathematical physics, SCGP, Stony Brook, 9th - 13th April 2018. Video
    32. Workshop: Modular Forms and Quantum Knot Invariants, Banff International Research Station, 11th - 16th March 2018.
    33. Conference: Quantum knot homology and supersymmetric gauge theories, Aspen Center for Physics, 4th - 10th March 2018.
    34. Junior Trimester Programme: Symplectic Geometry and Representation Theory, Hausdorff Research Institute for Mathematics, Bonn, 20th November - 1st December 2017. Video
    35. Conference: Representation Theory and Combinatorics of Torus Links, University of Massachusetts, Amherst, 8th July 2017.
    36. INI workshop: Quantum topology and categorified representation theory, Isaac Newton Institute, Cambridge, 26th - 30th June 2017. Video
    37. Symposium in Mathematical Physics, Universität Zürich, 24th - 25th April 2017.
    38. INI workshop: Physics and knot homologies, Isaac Newton Institute, Cambridge, 10th - 13th April 2017. Video
    39. Quantum invariants and low-dimensional topology, MATRIX, Melbourne, Australia, 14th - 17th December 2016, Slides.
    40. Workshop on Homological Methods in Algebra and Geometry, African Institute for Mathematical Sciences, Ghana, August 2016.
    41. WARTHOG, University of Oregon, 25th - 29th July 2016.
    42. Conference: Knots in Hellas, Keynote talk, Olympic Academy, Greece, 17th - 23rd July 2016, Slides.
    43. Workshop: Categorification, Universität Bonn, Germany, 16th - 20th May 2016.
    44. SwissMAP Conference, Engelberg, Switzerland, 24th - 30th January 2016.
    45. Colloquium, George Washington University, Washington DC, 13th November 2015.
    46. Workshop: Physics and mathematics of knot homologies, SCGP, Stony Brook, 1st June - 3rd June 2015. Video, Slides.
    47. Conference: Winter Braids V, Université de Pau, 16th February - 19th February 2015.
    48. Young Topology Meeting, Imperial College London, 6th June 2014.

    Seminar talks

    1. Seminar talk, Higher structures and Field Theory (online), 13th July 2023.
    2. Seminar talk, UC Davis, 17th March 2023.
    3. Seminar talk, Stanford University, 14th March 2023.
    4. Seminar talk, UC Berkeley, 13th March 2023.
    5. Seminar talk, Université catholique de Louvain, 17th February 2023.
    6. Seminar talk, TU Dresden, 24th November 2022.
    7. Online seminar talk, Algebra seminar, Beijing Institute of Technology, 16th May 2022.
    8. Seminar talk, Boston College Geometry/Topology/Dynamics Seminar, 4th November 2021.
    9. Seminar talk, Research Seminar on Algebraic Topology, Hamburg, 28th October 2021.
    10. Seminar talk, IMJ-PRG, 28th May 2021.
    11. Online seminar talk, University of Hamburg, 2nd February 2021.
    12. Online seminar talk, Topology Seminar, MPIM, 21st December 2020.
    13. Two online seminar talks, Learning seminar on categorification, 9th and 16th July 2020. Video 1, Slides 1, Video 2, Slides 2
    14. Online seminar talk, Séminaire de Topologie LAGA/IMJ-PRG, Paris, 16th June 2020.
    15. Online seminar talk, Kansas State University, 8th May 2020.
    16. Online seminar talk, MSRI, 6th May 2020.
    17. Online seminar talk, Joint Los Angeles Topology Seminar, 4th May 2020.
    18. Seminar talk, George Washington University, 28th April 2020.
    19. Online seminar talk, Representation Theory and Mathematical Physics Seminar, UC Berkeley, 21st April 2020.
    20. Online Seminar talk, Stanford University, 14th April 2020.
    21. Seminar talk, University of Massachusetts, Amherst, 2nd March 2020.
    22. Seminar talk, UC Davis, 18th February 2020.
    23. Research talk, University of Birmingham, 13th January 2020.
    24. Seminar talk and research visit, Instituto Superior Técnico 9th - 12th December 2019.
    25. Seminar talk, University of Stuttgart, 19th November 2019.
    26. Seminar talk, University of Kaiserslautern, 7th November 2019.
    27. Seminar talk, University of Bielefeld, 25th October 2019.
    28. Seminar talk and research visit, Universität Zürich, 24th - 27th September 2019.
    29. Seminar talk, The Australian National University, 26th July 2019.
    30. Seminar talk and research visit, Université de Montpellier, 14th - 18th April 2019.
    31. Seminar talk and research visit, Universität Zürich, 10th - 14th April 2019.
    32. Research talk, University of Vienna, 6th March 2019.
    33. Research talk, University of Leicester, 14th February 2019.
    34. Research talk, University of Oklahoma, 5th February 2019.
    35. Research talk, Montana State University, 31st January 2019.
    36. Research talk, University of Essex, 28th January 2019.
    37. Research talk, University of Hamburg, 25th January 2019.
    38. Seminar talk, Claremont topology seminar, 6th December 2018.
    39. Seminar talk, UCSB, 4th December 2018.
    40. Seminar talk, Uppsala Universitet, 16th July 2018.
    41. Research talk, TU München, 16th July 2018.
    42. Seminar talk, The Australian National University, 18th May 2018.
    43. Seminar talk and research visit, Monash University, 7th - 9th May 2018.
    44. Seminar talk, University of Melbourne, 7th May 2018.
    45. Seminar talk, University of Southern California, 19th March 2018.
    46. Seminar talk, The Australian National University, 14th November 2017.
    47. Seminar talk, Algebra Seminar, Sydney University, 27th October 2017.
    48. Seminar talk, The Australian National University, 20th October 2017.
    49. Seminar talk and research visit, QGM, Aarhus University, 28th August - 1st September 2017.
    50. Seminar talk and research visit, Instituto Superior Técnico 22nd - 24th May 2017.
    51. Seminar talk, Universität Wien, 2nd May 2017.
    52. Seminar talk, Symplectic cut, London, 22nd March 2017.
    53. Seminar talk, Geometry Tea, Cambridge, 17th March 2017.
    54. Seminar talk, Symplectic cut, London, 15th February 2017.
    55. Seminar talk, Université de Montpellier, 1st December 2016.
    56. Seminar talk, Université catholique de Louvain, 28th November 2016.
    57. Seminar talk, Universität Wien, 30th June 2016.
    58. Seminar talk, Oberseminar Darstellungstheorie, Universität Bonn, Germany, 15th April 2016.
    59. Seminar talk, MPI Oberseminar, Max-Planck-Institut für Mathematik Bonn, Germany, 14th April 2016.
    60. Seminar talk and research visit, Physics and Geometry Seminar, Caltech, 15th November - 25th November 2015.
    61. Seminar talk, Columbia University, New York, 12th November 2015.
    62. Seminar talk and research visit, Université catholique de Louvain, 22nd April - 25th April 2015.
    63. Seminar talk and research visit, Universität Zürich 17th March - 20th March 2015.
    64. Seminar talk, Durham University, 29th January 2015.
    65. Seminar talk, Differential Geometry and Topology Seminar, University of Cambridge, 28th January 2015.
    66. Seminar talk and research visit, QGM, Aarhus University, 12th January - 17th January 2015.
    67. Seminar talk, Institut de Mathématiques de Jussieu-Paris Rive Gauche (IMJ-PRG), 4th December 2014.
    68. Seminar talk, Université de Genève, 27th November 2014.
    69. Seminar talk and research visit, QGM, Aarhus University, 8th July - 12th July 2014.
    70. Seminar talk, Erwin Schrödinger Institut, 30th June 2014.

    Other events


    I'm a Fellow of the Higher Education Academy.


  • Knot homology and categorification, hybrid lecture course + exercises, Universität Hamburg, summer semester 24
  • Research seminar on Quantum Topology and Categorification (QTcat), Universität Hamburg, summer semester 24


    • Algebra, lecture course + exercises, Universität Hamburg, winter semester 23/24
    • Proseminar on Symmetric Functions, Universität Hamburg, winter semester 23/24
    • ZMP Seminar on Knot Homology, Universität Hamburg, winter semester 23/24
    • Research seminar on Quantum Topology and Categorification (QTcat), Universität Hamburg, winter semester 23/24
    • Mathematik 2, lecture course + exercises + tutorials, Universität Hamburg, summer semester 23
    • Seminar on Low-Dimensional Topology, Universität Hamburg, summer semester 23
    • Research seminar on Quantum Topology and Categorification (QTcat), Universität Hamburg, summer semester 23
    • Mathematik 1, lecture course + exercises + tutorials, Universität Hamburg, winter semester 22/23
    • Seminar on Representation Theory: highest weight categories and tilting theory, Universität Hamburg, winter semester 22/23
    • Research seminar on Quantum Topology and Categorification (QTcat), Universität Hamburg, winter semester 22/23
    • Advanced algebra, lecture course + exercises, Universität Hamburg, summer semester 22
    • Seminar on Categorical Algebra: Braids, Bimodules, and Bicategories, jointly with David Reutter, Universität Hamburg, summer semester 22
    • Lie Algebras, lecture course + exercises, Universität Hamburg, winter semester 21/22
    • Beweismethoden und schulnahe Beispiele aus der Linearen Algebra, LSV, Universität Hamburg, winter semester 21/22
    • S4A2 Graduate Seminar on Representation Theory - Knot homology (with Catharina Stroppel), University of Bonn, winter semester 2020/21.
    • Mini-course on skein theory, workshop at Quy Nhon University, Vietnam, 2th - 4th June 2019.
    • Mini-course on "Conjectures in Quantum Topology", workshop on "Classical and quantum three-manifold topology" at Monash University, Melbourne, 14th - 21st December 2018.
    • MATH1013, first year linear algebra, The Australian National University, Semester 2, 2018.
    • INI winter school tutorial, Isaac Newton Institute, Cambridge, January 2017.
    • London Taught Course Center Intensive Course Introduction to Khovanov homology, November 2016.
    • ESI Simons Lecture Series Knot homologies and higher representation theory, October 2016.
    • Series of talks on Khovanov homology, TAKTIC Seminar, Imperial College London, November - December 2015.
    • Supervisor for undergraduate Geometry (Part IB) and Algebraic Topology (Part II), University of Cambridge, 2012-2015.
    • Repetitorium Analysis, Universität Wien, 2010-2011.
    • Seminars on measure theory and analysis, Universität Wien, 2010-2011.

    Extracurricular activities:

    • Running: In April 2022 I was part of team from the Algebra and Number Theory group that took part in the Hamburg Marathon Relay Race. We finished in 3h 02min 26sec. In October 2017 I was part of a team (photo below) from the Mathematical Sciences Institute at ANU which won Division 5 of Inward Bound, an overnight adventure footrace over roughly 50km in mountainous terrain.
    • Sailing: During my PhD, I was a skipper and racing team member at CUYC and received a Cambridge Half Blue. (Improvised sailing also happened on the river Cam, see below.) Currently, I am sailing 470s on the Alster.
    MSI Team for Inward Bound
    Punt sailing in Cambridge
    Updated: 9th April 2024 or later