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 - 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
Mondays and Wednesdays 9-11am
Exercises: Mondays 11am-1pm - Master level
Studentseminar (Mathe)/P27 SE
TQFT and quantum computing
Mondays 3-5pm - Bachelor level
Funktionentheorie für Studierende in der Physik
Tuesdays 11am-1pm
Übungen: Mondays 1-3pm (14 tgl). - 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
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.
Raphaël Belliard (postdoc, 1.325)
Nitin Chidambaram (postdoc, MPIM)
Reinier Kramer
(postdoc, MPIM)
Alessandro Giacchetto
(PhD student, MPIM)
Giacomo Umer (PhD student)
Rémi Avohou Cocou (Georg-Forster fellow, 1.325)
- Former members
Events
(Org) Enumerative geometry of surfaces, 16-20 Jun. 2021, Oberwolfach
Conference in memory of Boris Dubrovin: Integrable systems in geometry and mathematical physics, online, 28 Jun.-2.July, SISSA, Trieste.
(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.
Workshop: Counting problems, 6-12 Sept. 2021, Ventotene.
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
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
- 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
- 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