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

Foto Gaetan 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.



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,


Teaching and seminars

  • Online research seminar
    Algebra, Geometry & Physics
    Tuesdays 1.45-3.15pm
    - Contact Kristina Schulze if you want to be on the mailing list.
    - HU students can validate  2SWS/semester by regular attendance + writing a report on one talk of their choice during the semester.
  • WiSe 2021/2022
  • Bachelor level
    Analysis I für Studierende in der Physik
  • SoSe 2022
  • ♦ Bachelor/master level
    Mathematische Methoden der Physik
    ♦ Master reading group:
    Mathematics of conformal field theory
  • Sose 2023
  • Master level
    Differential geometry II
  • Former teaching

Research group


Nitin Chidambaram (postdoc, MPIM)


Giacomo Umer image.pdf

Giacomo Umer
(PhD student, 1.407)

REMI 4,31   x  5,31.jpg


Rémi Cocou Avohou
(Georg-Forster fellow, 1.325)



Guillaume Baverez
(postdoc, 1.325)

Thomas Buc-d'Alché
(master intern, 1.328)

Former members

Upcoming talks


Workshop Random geometry, 17-21 Jan. 2022, CIRM Luminy: Maps, Hurwitz numbers and formulas for free probability to all genera

Probabilistic operator algebra seminar, Berkeley, 21. Feb 2022, jointly with Elba Garcia-Failde: Analytic theory of higher order freeness

Archive of talks (sometimes slides and videos)



I list here announcements I received.
Below, events I take part to:

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

Conference VIIIth Combinatorics of moduli spaces, cluster algebras and topological recursion, 20-25 June 2022, Steklov/HSE/Skoltech, Moscow

(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

(Org) KMPB Spring school: 3 Facets of Gravity, 8-12 May 2023, HU Berlin.

(Org) Summer school: Enumerative geometry, quantization and moduli spaces, September 2023, CIME, Cetraro


  • 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
  • Lecture 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, ...

  • 7. Okt 2021: Alessandro Giacchetto defended his PhD Geometric and topological recursion and invariants of the moduli space of curves
  • Feb. 2021: two new postdocs will join our group.
    - Guillaume Baverez (graduating from Cambridge University) is working on Liouville quantum gravity and probabilistic approaches to QFT, arriving October 2021.
    - Pedro Tamaroff (graduating from Trinity College, Dublin) is working on operads and higher structures, arriving April 2022. He will also be a visitor at MIS-Leipzig in May 2021-March 2022.
  • 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

  • Analytic theory of higher order free cumulants
    with Séverin Charbonnier, Elba Garcia-Failde, Felix Leid and Sergey Shadrin
  • Around the combinatorial unit ball of measured foliations on bordered surfaces
    with Séverin Charbonnier, Vincent Delecroix, Alessandro Giacchetto and Campbell Wheeler
  • 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
  • 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