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Humboldt-Universität zu Berlin - Mathematisch-Naturwissenschaftliche Fakultät - Institut für Mathematik

Humboldt-Universität zu Berlin | Mathematisch-Naturwissenschaftliche Fakultät | Institut für Mathematik | Forschung | Forschungsgebiete | Mathematische Physik | Mathematische Physik: Mathematische Aspekte der Quantenfeld- und Stringtheorie

Prof. Dr. Gaëtan Borot

Institute for Mathematics
& Institute for Physics
Chair in Mathematical Physics:
Mathematical aspects of QFT and strings 

Interests: enumerative geometry, quantum 
algebra/topology/geometry, topological recursion, 
integrability, moduli spaces, algebraic structures in
QFT and strings, random matrix theory, combinatorics, science outreach.


Email: gaetan.borot@hu-berlin.de

Address: Johann-von-Neumann-Haus, Rudower Chaussee 25

Office: Office 1.333 (Haus 1, 3rd floor, right corridor)

Phone: (030) 2093 45479

Secretary: Kristina Schulze, schulze@math.hu-berlin.de


Teaching and seminars

  • Online research seminar
    Algebra, Geometry & Physics
    Tuesdays 2-3.30pm
  • WiSe 2020/2021 (see AGNES)
  • Master course (M40/P25.1.b)
    Integrable systems
    Tuesdays 9-11am, Wednesdays 1-3pm
    Exercises : Tuesdays 11am-1pm
  • Master level
    Studentseminar (Mathe)/P27 SE
    Modular forms and applications
    Thursdays 9-11am
  • SoSe 2021
  • Master course (M40/P25.1.b)
    Topological recursion, matrix models and intersection theory
  • Master level
    Studentseminar (Mathe)/P27 SE
    TQFT and quantum computing
  • Bachelor level
    Funktionentheorie für Studierende in der Physik

Research group

Upcoming talks (all online)

QFT internal seminar, HU Berlin, 23 Apr. 2021: N = 2 supersymmetric gauge theories and topological recursion

Archive of talks (sometimes slides and videos)



(Org) Enumerative geometry of surfaces, 16-20 Jun. 2021, Oberwolfach

(Org) Workshop: Non-commutative geometry meets topological recursion, 16-20 Aug. 2021, Münster

(Org) Research group retreat, Matamzee, 21-25 August 2021.

Workshop: Tau functions, correlation functions and applications, 30 Aug.-3 Sept. 2021, Simons Centre for Geometry and Physics, Stony Brook

Thematic program: Universality and integrability in random matrix theory and interacting particle systems, 16 Aug.-17 Dec. 2021, MSRI

Summer school on topological recursion, 6-17 Sept. 2021, Otranto

MATRIX Program: Quantum curves, integrability and cluster algebras, 6-17 Dec. 2021, Creswick

Workshop: Random geometry, 17-21 Jan. 2022, CIRM Luminy

(Org) Thematic month: Integrability, enumerative geometry and quantization, 22 Aug.-24 Sept. 2022, Simons Center for Geometry and Physics, Stony Brook

(Org) Workshop: Non-commutative geometry meets topological recursion, 13-18 Nov. 2022, BIRS Hangzhou


  • Slides of the online reading group on Stability conditions and DT theory (Spring 2020).
  • A list of mathematical results that came out of topological recursion, that can also serve as bibliography guide (be welcome to propose me updates or corrections), latest version 2018
  • Video recordings of the Geometric recursion learning seminar (Winter 2018/2019, MPIM)
  • Lecture notes of a mini-course in Toulouse (May 2017): Topological recursion and geometry, math-ph/1705.09986, published in Rev. Math. Phys. (2020)
  • Lecture notes of a mini-course at CIMPA summer school, Ulanbataar: Introduction to random matrix theory, math.PR/1710.10792, published in Mong. J. Math. 20 1 (2016) 5-52. For a brief history of mathematics in Mongolia, see the article by Ninjbat Uuganbaatar.
  • Lecture notes for a mini-course A walk through the woods of integrability at Hannover University, June 2015
  • Lecture notes for a master course on Random matrix theory, Bonn University, Winter 2014/2015
  • Lectures notes by Alice Guionnet for her mini-course on Schwinger-Dyson equations, topological expansions and random matrices at Columbia, Aug. 2017.
  • Video recordings of mini-courses at a MPIM workshop in Fall 2014:
    - Jorgen E. Andersen, The Hitchin connection and the Witten-Reshetikhin-Turaev TQFT
    Bertrand Eynard, Topological recursion and moduli spaces
  • Video recordings of a Masterclass on topological recursion by Bertrand Eynard and Nicolas Orantin, at QGM Aarhus, January 2013.

Vacancies, News, Links, ...

  • Feb. 2021: two new postdocs will join our group in Fall 2021.
    - Guillaume Baverez (graduating from Cambridge University) is working on Liouville quantum gravity and probabilistic approaches to QFT
    - Pedro Tamaroff (graduating from Trinity College, Dublin) is working on operads and higher structures. He will also be a visitor at MIS-Leipzig in May-September 2021.
  • Feb. 2021: Raphaël Belliard and Reinier Kramer will move in Fall 2021 to a new postdoc position at Edmonton University with Vincent Bouchard.
  • Feb. 2021: An interview with Christian Blohmann (MPIM) about my scientific time at MPI Bonn.
  • 15 Jul. 2020: Alexandr Buryak and I were awarded the Dubrovin medal in 2020.
  • Oct. 2018: Elba Garcia-Failde defended her PhD thesis (MPIM/Bonn University) On discrete surfaces: enumerative geomety, matrix models and universality via topological recursion, math-ph/2002.00316
  • ERC ReNewQuantum (Andersen, Eynard, Kontsevich, Mariño), to which I am associated.
  • Kolleg Mathematik Physik Berlin
  • RTG 2575: research training group Rethinking QFT
  • BMS (Berlin doctoral school)
  • Conference poster gallery
  • Homepages of collaborators

Selected publications

  • Whittaker vectors for W-algebras from topological recursion
    with Vincent Bouchard, Nitin K. Chidambaram and Thomas Creutzig
  • On the Kontsevich geometry of the combinatorial Teichmüller space
    with Jørgen E. Andersen, Séverin Charbonnier, Alessandro Giacchetto,
    Danilo Lewanski and Campbell Wheeler
  • Double Hurwitz numbers: polynomiality, topological recursion and intersection theory
    with Norman Do, Max Karev, Danilo Lewanski and Ellena Moskowsky
  • Higher Airy structures, W algebras and topological recursion
    with Vincent Bouchard, Nitin K. Chidambaram, Thomas Creutzig and Dmitry Noshchenko
  • Geometric recursion
    with Jørgen E. Andersen and Nicolas Orantin
  • Large N asymptotic expansions for mean-field models with Coulomb gases interactions
    with Alice Guionnet and Karol K. Kozlowski
    Int. Math. Res. Not. 2015 (20): 10451-10524
  • All-order asymptotics of hyperbolic knot invariants from non-perturbative topological recursion of A-polynomials
    with Bertrand Eynard
    Quantum Topology, Volume 6, Issue 1 (2015) 39-138
  • Geometry of spectral curves and all-order dispersive integrable systems
    with Bertrand Eynard
    SIGMA 8 (2012) 100