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: 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
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)
- Former members
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)
Events
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
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, ...
- Sept-Nov. 2020: You may contact me if you would like to do a postdoc at the HU.
- 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
- 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 - Higher Airy structures, W algebras and topological recursion
with Vincent Bouchard, Nitin K. Chidambaram, Thomas Creutzig and Dmitry Noshchenko
math-ph/1812.08738 - 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