# Gaëtan Borot

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## PhD Thesis

Here is my thesis (in French, 10MB), and the slides (5 MB) of the defense.

## Next conferences/talks

- January 23rd 2018: mathematical physics seminar, Köln Universität,
*Asymptotics of wave functions in 1d Coulomb gases and theta function*. - March 29th 2018: topology seminar, "Geometric recursion", National University of Singapore.
- April 12th-13rd 2018: pre-workshop "Geometric and categorical aspects of CFTs", Utrecht Universiteit.
- June 4th-9th 2018: workshop on Combinatorics of moduli spaces, Moscow.
- June 18th-22nd June 2018: workshop "Gauge theory and complex geometry", CIRM Luminy.
- June 25th-29th 2018: workshop "Random maps, random matrices and gauge theories", mini-course on
*Topological expansions*. - July 2nd-5th 2018: workshop, mini-course on
*Topological and geometric recursions*. - August 27th-31st 2018: summer school on "Topological recursion", Tübingen Universität.
- September 10th-14th 2018: BIRS-Banff workshop, "Quantum curves and Higgs bundles".
- September 23rd-27th 2018: BIRS-Oaxaca workshop, "Geometric and categorical aspects of CFTs".

## 2017

- [134] December 2017: séminaire de Topologie, Paris 7 Sophie Germain,
*Geometric recursion*. - [133] December 2017: Integrable systems day, Université d'Angers,
*Geometric recursion*. - [132] December 2017: séminaire de physique mathématique, IPhT CEA Saclay,
*Geometric recursion*. - [131] December 2017: algebraic geometry seminar, IST Austria,
*Geometric recursion*. - [130] November 2017: QGM Nielsen Retreat, Sandbjerg,
*Geometric recursion*. - [129] November 2017: Algebra, Geometry and Physics seminar, MPIM Bonn,
*Geometric recursion*. - [128] September 2017: Japanese-German open conference on stochastic analysis, Kaiserslautern TU,
*Asymptotics of large random matrices via Schwinger-Dyson equations*, [Slides, 7MB] - [127] September 2017: workshop on Moduli space of curves and integrable systems, Institut de Mathématiques de Bourgogne, Dijon,
*Around Hurwitz numbers*. - [126] August 2017: conference Dyson-Schwinger equations, topological expansion and random matrices, Columbia University,
*Some technical aspects of the discrete log-gases in the multi-cut regime*. - [125] August 2017: conference GEOQUANT, QGM at Sandbjerg Estate,
*Topological recursion as a quantization procedure*. - [124] August 2017: Algebra, Geometry and Physics seminar, MPIM Bonn,
*r-spin Hurwitz numbers, topological recursion and ELSV formula.* - [123] July 2017: summer school Random matrices, Park City Mathematics Institute, Utah,
*1d log-gases in the macroscopic regime*. - [122] June 2017: workshop for the thesis of Alexandr Popolitov, University of Amsterdam:
*The ABCD of topological recursion.* - [121] April 2017, conference Teichmüller en grande dimension et symétrie miroir, Université d'Angers,
*The ABCD of topological recursion*. - [120] March 2017: séminaire Flajolet, Institut Henri Poincaré, Paris,
*The ABCD of topological recursion*. - [119] January 2017: Inhomogeneous Random Systems workshop, "Random geometry day", IHP, Paris:
*Nesting of loops on random surfaces.*

## 2016

- [118] December 2016: conference Interactions between topological recursion, modularity, quantum invariants and low-dimensional topology, Matrix, Melbourne University @Creswick:
*The ABCD of topological recursion.* - [117] October 2016: QGM Retreat, Sandbjerg,
*Initial conditions for topological recursion*. - [116] October 2016: 2nd French-Russian conference, Random Geometry and Physics, IHP, Paris,
*Nesting statistics in the O(n) model on random surfaces.* - [115] October 2016: séminaire de Combinatoire, Paris 7, Batiment Sophie Germain,
*Counting maps with simple boundaries*. - [114] October 2016: séminaire de Geométrie Algébrique, LAREMA, Université d'Angers,
*CFTs, CohFTs and topological recursion*. - [113] October 2016: séminaire de Physique Mathématique et Topologie, LAREMA, Université d'Angers,
*Matrix models, topological recursion and applications*. - [112] September 2016: Oberseminar Université de Fribourg,
*Around a Riemann-Hilbert problem in P^1 related to Seifert spaces*. - [111] September 2016: mathematical physics seminar, Institut de Physique Théorique, Saclay,
*Asymptotic analysis on the vertical of random lozenge tilings*. - [110] September 2016: Cargese summer school, Quantum integrable systems, CFTs and stochastic processes,
*Nesting statistics in the O(n) model on random maps of any topology*. - [109] September 2016: seminar Algebra, Geometry and Physics, MPIM Bonn,
*Initial conditions for a topological recursion*. - [108] July 2016: AMS Von Neumann Symposium, Charlotte : Topological recursion and its influence in analysis, geometry, and topology.
*Topological recursion: TQFTs, CohFTs and CFTs*, [Slides, 12MB]. - [107] June 2016: String Math, Collège de France, Paris,
*Chern-Simons theory on S^3/G and topological strings*, [Video], [Slides, 8MB]. - [106] June 2016: Workshop on combinatorics of moduli spaces, Moscow,
*From 2d CFTs to CohFTs.* - [105] May 2016: geometry and topology seminar, Caltech,
*Modular functors, cohomological field theories, and topological recursion*. - [104] April 2016: mathematical physics seminar, UC Berkeley,
*Modular functors, cohomological field theories, and topological recursion*. - [103] March 2016: seminar, McGill University,
*Random matrices, geometry and physics*, [Slides, 12MB]. - [102] March 2016: mathematical physics seminar, MPIM Bonn,
*2d quantum gravity: loop nestings and CLE*. - [101] March 2016: geometry group seminar, EPFL Lausanne,
*Modular functors, cohomological field theories, and topological recursion*. - [100] February 2016: seminar Mathematische Strukturen in der modernen Quantenphysik, Göttingen University,
*An introduction to topological recursion*. - [99] January 2016: mathematical physics seminar, EPFL Lausanne,
*Nesting properties in the O(n) loop models on random maps*.

## 2015

- [98] December 2015: Algebra, Geometry and Physics seminar, MPIM Bonn,
*From modular tensor categories to modular functors*. - [97] November 2015: Séminaire des doctorants, Université de Marseille,
*Compter les surfaces: de la combinatoire a la géométrie hyperbolique*. - [96] November 2015: Complex geometry seminar, Hamburg University,
*Topological recursion and wave functions*. - [95] November 2015: ZMP Colloquium, Hamburg University,
*The topological content of 2d rational CFTs*. - [94] November 2015: QGM Retreat,
*Chern-Simons theory on Seifert spaces, topological stings and integrable systems*. - [93] October 2015: Algebra, Geometry and Physics seminar, MPIM Bonn:
*From vertex operator algebras to modular functors II.* - [92] October 2015: workshop on Topological recursion, Chebyshev Lab, St Petersburg,
*The topological content of 2d rational CFTs*. - [91] October 2015: Algebra, Geometry and Physics seminar, MPIM Bonn:
*From vertex operator algebras to modular functors I* - [90] August 2015: summer school Stochastic analysis and its applications, Ulanbataar, National University of Mongolia. 3 introductory lectures on random matrix theory, Lecture Notes.
- [89] July 2015: conference "New developments in TQFT", QGM Aarhus,
*Modular functors, cohomological field theories and topological recursion*. - [88] July 2015: 4 lectures on integrability, Hannover University, Lecture Notes.
- [87] June 2015: Arbeitstagung, MPIM Bonn,
*Modular functors, cohomological field theories and topological recursion*. - [86] June 2015: workshop Asymptotics in integrable systems, random matrices, random processes and universality, CRM, Montréal, Percy Deift 70th,
*Asymptotic analysis of the sinh model*. - [85] June 2015: workshop Geometric invariants and spectral curves, Leiden,
*Introduction to blobbed topological recursion*. - [84] June 2015: conference Swissknots, Geneva.
*Modular functors, cohomological field theories and topological recursion*. - [83] May 2015: conference "Chromatic and colored structures in geometry and statistical physics", Cortona,
*An introduction to topological recursion*. - [82] April 2015: Probability and Mathematical Physics reading seminar, Warwick University:
*Asymptotic expansions in 1d Coulomb gases*. - [81] April 2015: semester Random geometries, Isaac Newton Institute, Cambridge:
*Nesting statistics in the O(n) loop model*. - [80] April 2015: mathematical physics seminar, Bristol University:
*Asymptotics in matrix models via Schwinger-Dyson equations: the sinh-model*. - [79] April 2015: workshop "Quantum Gravity in Paris", Université d'Orsay:
*2d quantum gravity and topological recursion*. - [78] April 2015: Seminar on Stochastic Processes, Zürich Universität:
*Asymptotics in 1d Coulomb gases and applications*. - [77] March 2015: 3 lectures on the "Topological recursion", Maths Department, Berkeley.
- [76] March 2015: Geometry and Physics seminar, Caltech,
*Perturbative invariants of Chern-Simons theory on Seifert manifolds*. - [75] February 2015: Journées Matrices aléatoires, Université de Versailles:
*Asymptotiques dans les modeles de matrices via les equations de Schwinger-Dyson* - [74] February 2015: séminaire CALIN,
*Énumérer les cartes farcies de toute topologie*, Paris 13 Villetaneuse.

## 2014

- [73] December 2014: seminar,
*Meromorphic connections on the sphere, loop equations and topological recursion*, QGM Aarhus. - [72] October 2014: Journées Cartes, IHES, Paris,
*Nesting statistics in the O(n) loop model*. - [71] October 2014: Oberseminar Stochastic, Bonn University,
*All-order asymptotic expansions in 1d Coulomb gases*. - [70] October 2014: workshop "Quantum curves, Hitchin fibrations and Gromow-Witten theory", AIM, Palo Alto.
- [69] September 2014: mathematical physics seminar, Urbana-Champaign University,
*Asymptotic expansions in matrix models, topological recursion and applications*. - [68] September 2014: analysis seminar, Northwestern University, Chicago.
*Asymptotic expansion in beta matrix models*. - [67] September 2014: mathematical physics seminar, Northwestern University, Chicago,
*Topological recursion and enumerative geometry*. - [66] September 2014: Yau student's seminar, Maths Department, Harvard,
*Topological recursion and some applications in geometry*. - [65] September 2014: conference Recent advances in quantum integrable systems, IMB, Dijon.

*Asymptotic expansions in 1d log-gas with many-body interactions*, [Slides, 11MB]. - [64] August 2014: workshop "Low-dimensional Topology and Number Theory", Oberwolfach.

*Analytic properties of certain knot invariants in Seifert spaces*. - [63] July 2014: conference Geometry, quantum topology and asymptotics, Confucius Institute, Geneva.

*SU(N) Chern-Simons in Seifert spaces at large N: a matrix model analysis*, all videos available here. - [62] June 2014: workshop "Knots and homologies", BIRS, Banff.

*SU(N) Chern-Simons theory on Seifert spaces : a matrix model analysis*, [Video] . - [61] May 2014: 4th workshop on Combinatorics of moduli spaces, Moscow.

*Blobbed topological recursion*. - [60] May 2014: Random Matrix Theory seminar, Bielefeld Universität.

*Large N asymptotic expansions in repulsive particle systems*. - [59] May 2014: seminar, Milano University,
*Loop equations and integrability*. - [58] March 2014: workshop Free probabilities and the large N limit, UC Berkeley.
- [57] March 2014: workshop Recent advances on log-gases, Institut Henri Poincaré, Paris,

*Large N asymptotic expansions in 1d repulsive particle systems*, [Slides, 9MB]. - [56] February 2014: Montréal seminar in Mathematical Physics, CRM.

*Asymptotic in Coulomb gases and related problems*. - [55] February 2014: Section de Mathématiques, Université de Genève.

*Problèmes asymptotiques et combinatoire des surfaces*, [Slides, 14MB].

## 2013

- [54] December 2013: Mathematical Physics Seminar, Northeastern University, Boston.

*Topological recursion and SU(N) Chern-Simons theory of spherical Seifert spaces*. - [53] December 2013: Probability Seminar, MIT, Cambridge.

*Asymptotics of multidimensional integrals arising in random matrix theory*. - [52] November 2013: special program on Non-equilibrium Dynamics and Random Matrices, IAS, Princeton.

*All-order asymptotics in beta ensembles in the multi-cut regime*, [Video]. - [51] November 2013: short seminar, MPIM Bonn.

*Asymptotics of multidimensional integrals in large dimensions*. - [50] October 2013: Seminar at Georgia Tech, Atlanta.

*(Blobbed) topological recursion and matrix models*. - [49] October 2013: Brandeis University, Colloquium.

*Counting surfaces and (abstractly) related problems*. - [48] October 2013: workshop "Mirror Symmetry and Physics", Perimeter Institute, Waterloo.

*Blobbed topological recursion*. - [47] October 2013: Columbia Probability Seminar.

*All-order asymptotics in beta ensembles in the multi-cut regime*. - [46] September 2013: workshop Number Theory and Physics, Clay Mathematics Institute, Oxford.

*Topological recursion and applications*. - [45] September 2013: Knot Theory Day, Korteweg de Vries Instituut voor Wiskunde, Universiteit van Amsterdam.

*SU(N) Chern-Simons theory at large N from the matrix model point of view*. - [44] September 2013: Seminar on Geometry and Mathematical Physics, Korteweg de Vries Instituut voor Wiskunde, Universiteit van Amsterdam.

*Rational connections on the sphere, loop equations, d-th reduction of KdV, and 2d quantum gravity*. - [43] September 2013: "Hamiltonian PDEs, Frobenius Manifolds and Deligne-Mumford Moduli Spaces", SISSA, Trieste.

*All-order asymptotics of beta ensembles in the multi-cut regime*, [Slides, 12MB] - [42] September 2013, Seminar, Bilkent University, Ankara.

*Around large random matrices*, [Slides, 8MB] - [41] August 2013 : workshop on Moduli Spaces and Integrable Systems, Banff.

*Why $\hbar^{2g - 2 + n}$ ? and (p,q) minimal models"*, [Video] - [40] July 2013 : Mathematical Physics seminar, MPIM Bonn.

*Formal multidimensional integrals, stuffed maps and topological recursion*. - [39] June 2013: Journée Cartes, IPhT, CEA Saclay.

*Topological recursion: computing asymptotics of knot invariants like counting maps ?*, [Slides, 12 MB] - [38] May 2013: Conference "Quantum topology and hyperbolic geometry", Nha Trang, Vietnam.

*Analysis of a Chern-Simons matrix model for Seifert homology spheres*. - [37] April 2013: séminaire Cordes et Matrices.

*Topological recursion in generalized matrix models and applications*. - [36] April 2013: Combinatorics and Free Probability seminar, Universität des Saarlandes.

*Analytic combinatorics of maps of all topologies*. - [35] March 2013: Theoretical Physics seminar, Université Montpellier 2.

*Abstract topological recursion and applications*. - [34] March 2013: Mathematical Physics seminar, Geneva University.

*All order asymptotics of beta ensembles in the multi-cut regime*. - [33] February 2013: seminar at LAREMA, Angers.

*Small dispersion regime in integrable systems, random matrices and topological recursion.* - [32] February 2013: Conference "Two-Dimensional statistical mechanics", Les Diablerets.

*All loop models satisfy a topological recursion.* - [31] January-1st February 2013: conference "Recursion and integrability", Center for Quantum Geometry of Moduli Spaces, Aarhus.

*Topological recursion and knot invariants: two early steps*. - [30] January 2013: Probability Seminar, Harvard,
*All-order asymptotics of beta ensembles in the multi-cut regime*. - [29] January 2013: research seminar in Mathematics, Northeastern University.

*Matrix models, non-perturbative topological recursion, and knot invariants*.

## 2012

- [28] December 2012: Mathematical Physics seminar, LPTHE, Paris 6.

*Topological expansion in generalized matrix models*. - [27] November 2012: Topology seminar, Université Montpellier 2.

*Algebraic geometry on character variety and a conjecture on all-order asymptotics of knot invariants*. - [26] October 2012: Random Matrix theory seminar, Universität Bielefeld.

*All order finite size corrections in repulsive particles systems*. - [25] October 2012: informal seminar, LPT-ENS, Paris.

*O(n)-type singular integral equations and applications*, [Slides, 12 MB] - [24] September 2012: Number theory seminar, MPI Bonn.

*Asymptotics of the colored Jones polynomial, topological recursion and theta functions*. - [23] August 2012: workshop "Low dimensional topology and number theory", Oberwolfach.

*Asymptotics of invariants of 3-manifolds and topological recursion*. - [22] July 2012: informal Mathematical Physics seminar, SISSA, Trieste.

*Asymptotics of wave functions and application to knot theory*. - [21] May 2012: 3rd workshop on "Combinatorics of moduli spaces, cluster algebras, knots, and topological recursion", Moscow.

*Non-perturbative topological recursion and application to knot invariants*. - [20] May 2012: workshop in honour of Sasha Its, "Integrable systems and random matrices", IHP, Paris.

*Integrability, topological recursion for A-spectral curves, and knot invariants*, [Slides, 13MB] - [19] May 2012: workshop "Contemporary ways of integrability", Lisbon University.

*Integrability, non-perturbative topological recursion and an application to knot invariants*. - [18] May 2012: Strings seminar, IST Lisbon.

*Matrix models, knot invariants and non-perturbative topological recursion*, [Slides, 13MB] - [17] April 2012: knot theory seminar, Université de Genève.

*A conjecture for the all-order asymptotics of the colored Jones polynomial of hyperbolic knots*. - [16] April 2012: workshop "Integrability in topological field theory", Hausdorff Center for Mathematics, Bonn.

*Topological recursion, theta functions, and perturbative knot invariants*. - [15] March 2012: workshop in mathematical physics, Les Diablerets.

*Map enumeration problems in the O(n) loop model and Potts model*. - [14] March 2012: winter school "Integrable systems and random matrices", Les Houches.

*Integrable systems, loop equations and topological recursion*. - [13] February 2012: Stochastic Processes Seminar, Zürich Universität.

*All order finite size corrections in Coulomb gases*.

## 2011 and before

- [12] October 2011: informal presentation at the workshop "New recursion formulae in Gromov-Witten theory", BIRS, Banff.

*A candidate for a dispersive solution to Hirota equations*. - [11] October 2011: Mathematical Physics seminar, Concordia Univesity, Montréal.

*Integrability and geometry of spectral curves*. - [10] August 2011: Functional Analysis seminar, UCLA Maths Department.

*Analytic combinatorics: counting maps with self-avoiding loops*. - [9] June 2011: chosen talk at the Arbeitstagung, MPI Bonn.

*Loop equations and spectral curves*. - [8] May 2011: joint seminar with C. Nadal at Spring School "Vicious walkers and random matrices", les Houches.

*All order left-tail asymptotics of Tracy-Widom beta law*. - [7] December 2010: Strings seminar, Bethe Center for Theoretical Physics, Bonn University.

*Topological strings and matrix models*. - [6] November 2010: introductory seminar at SGCSC Conference, IHP Paris.

*Introduction to the BKMP conjecture*. [Slides, 1MB] - [5] September 2010: talk at the conference "Random matrix theory and its applications", MSRI, Berkeley.

*Asymptotics of Tracy-Widom beta law*, [Slides, 5MB] - [4] April 2010: Mathematical Physics seminar, SISSA, Trieste.

*Construction of a dispersive integrable system via geometry of algebraic curves*. - [3] January 2010: young scientists' seminar SINJE, LPT Orsay.

*Algebraic geometry applied to enumeration of self-avoiding loops*. - [2] November 2009: seminar at IST Lisbon.

*Simple Hurwitz numbers and a proposition of Bouchard and Mariño*. - [1] June 2009: joint informal presentation with B.Safnuk at AIM Workshop "Recursion structures in topological strings and enumerative geometry", Palo Alto.

*A matrix model proof of Bouchard-Mariño conjecture*.

Last modified: June 32th 2015.