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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: Carmen Zyska, zyska@math.hu-berlin.de


Teaching and seminars

  • Online research seminar
    Algebra, Geometry & Physics
    Tuesdays 2-3.30pm
  • WS 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
  • SW 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)

Geometry and Physics online seminar, Mathematics Institute of the Romanian Academy, 27th Jan. 2021: Double Hurwitz numbers, topological recursion and ELSV-like formulas

Topological recursion and integrability online seminar, 2nd Feb. 2021: Airy structures and W-algebra modules. I - The basic cases

Topological recursion and integrability online seminar, 9th Feb. 2021: Airy structures and W-algebra modules. II -  Spectral curves

Topological recursion and integrability online seminar, 16th Feb. 2021: Airy structures and W-algebra modules. III - Intersection theory

QFT group seminar, HU Berlin, 19th Feb. 2021: Chern-Simons on S3/ADE at large N, non-toric mirror symmetry and integrability

Colloquium RTG 2575, HU Berlin, 26th Feb. 2021: W-algebras: between representation theory, 2d geometry and 5d gauge theories

Archive of talks (sometimes slides and videos)




Thematic program: Moduli spaces, combinatorics and Poisson geometry, 15 May-15 Aug. 2021, St-Petersburg

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

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

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

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

(Org) Workshop: Non-commutative geometry meets topological recursion, postponed to Fall 2022, BIRS Hangzhou

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


  • 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, ...


Selected publications

  • 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