Prof. Dr. Gaëtan Borot
Institute for Mathematics
& Institute for Physics
Institute for MathematicsChair 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
- Contact me 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 - Sose 2023
- Master level
Differential geometry II - Former teaching
Research group
If you are working in an area in relation with the group thems and consider applying for a Marie Curie, an Emmy Noether group leader fellowship, or a Humboldt postdoctoral fellowship hosted at the HU Maths Department, you may contact me to discuss it.
Nitin Chidambaram (postdoc, MPIM)
Giacomo Umer
(PhD student, 1.407)
Rémi Cocou Avohou
(Georg-Forster fellow, 1.325)
Guillaume Baverez
(postdoc, 1.325)
Thomas Buc-d'Alché
(master intern, 1.328)
Upcoming talks (all online)
Online Seminario de Álgebra, Combinatoria y Teoría de Lie, Bahia Blanca, 26. Nov 2021: Airy structures: from algebra to geometry via representation theory
Seminar in Algebra, Algebraic geometry and Algebraic topology, MIS Leipzig, 14. Jan 2022: Counting multicurves on combinatorial surfaces and integrals of volumes of polytopes
Archive of talks (sometimes slides and videos)
Events
I list here announcements I received.
Below, events I take part to:
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
(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
Resources
- 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
- Topological recursion for fully simple maps via ciliated maps
with Séverin Charbonnier and Elba Garcia-Failde
math.CO/2106.09002 - Whittaker vectors for W-algebras from topological recursion
with Vincent Bouchard, Nitin K. Chidambaram and Thomas Creutzig
math-ph/2104.04516 - On the Kontsevich geometry of the combinatorial Teichmüller space
with Jørgen E. Andersen, Séverin Charbonnier, Alessandro Giacchetto,
Danilo Lewanski and Campbell Wheeler
math.DG/2010.11806 - Double Hurwitz numbers: polynomiality, topological recursion and intersection theory
with Norman Do, Max Karev, Danilo Lewanski and Ellena Moskowsky
math.AG/2002.00900 - Geometric recursion
with Jørgen E. Andersen and Nicolas Orantin
math.GT/1711.04729 - Large N asymptotic expansions for mean-field models with Coulomb gases interactions
with Alice Guionnet and Karol K. Kozlowski
math-ph/1312.6664
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
math-ph/1205.2261
Quantum Topology, Volume 6, Issue 1 (2015) 39-138 - Geometry of spectral curves and all-order dispersive integrable systems
with Bertrand Eynard
math-ph/1110.4936
SIGMA 8 (2012) 100