Research
My research interests lie at the interface of theoretical physics, probability theory, combinatorics and algorithms. Research topcis include: (twodimensional) quantum gravity, general relativity, statistical physics, random planar maps, random walks, stochastic processes, and more.
For an overview of earlier research see my research summary [pdf].
Upcoming events
 2 Feb  23 Mar 2017. Master course on "Analytic combinatorics and applications" at Le Département de Mathématiques d'Orsay. (See Teaching below.)
 2023 Mar 2017. Talk at Quantum gravity in Paris, IHP, Paris.
 24 Apr 2017. Computations and Proofs seminar at SpecFun, INRIA, École Polytechnique, Palaiseau.
 28 Apr 2017. Combinatorics seminar at the Mathematics Institute, University of Warwick, UK.
 1519 May 2017. Lectures on "Peeling of random planar maps" at Minischool on Random Maps and the Gaussian Free Field, École normale supérieure de Lyon.
 28 May  3 Jun 2017. Workshop on Stochastic Analysis: Geometry of Random Processes, Oberwolfach, Germany.
 1923 Jun 2017. Lectures at Making Quantum Gravity Computable, Perimeter Institute, Waterloo, Canada.
 1722 Sept 2017. Workshop on Lattice walks at the Interface of Algebra, Analysis and Combinatorics, BIRS, Banff, Canada.
Teaching: Analytic Combinatorics and applications
In February and March of 2017 I'm teaching a Master's course on Analytic combinatorics as part of the M2 program on probability at Le Département de Mathématiques d'Orsay, Université de ParisSud.
Lectures will take place on Thursday mornings 9:0012:00 in room 117119 of Bâtiment 425 (math department) of the Orsay campus. First lecture will be on February 2nd (so no lecture yet on January 26th!). The lectures will mainly follow the excellent book of Flajolet and Sedgewick (F&S), "Analytic Combinatorics", Cambridge University Press, which is freely downloadable. The schedule for the course, with some keywords, is as follows:
 February 2nd
 Lecture 1: Formal power series; Combinatorial classes; Ordinary generating functions; Iterative and recursive constructions; Plane trees. (F&S, Chapter I)
 February 9th
 Lecture 2: Labelled combinatorial classes; Exponential generating functions (F&S, Chapter II); Review of various concepts of complex analysis.
 February 16th
 No Lecture (winter holiday).
 February 23rd
 Lecture 3: Complex analysis; singularities of generating functions; transfer theorems (F&S, Chapter IV + VI).
 March 2nd
 Lecture 4: Multivariate generating functions (F&S, Chapter III); planar maps and quadratic method.
 March 9th
 Lecture 5: Limit laws (F&S, Chapter IX).
 March 16th
 Lecture 6: Saddlepoint method (F&S, Chapter VIII).
 March 23rd
 Lecture 7: 6 * 25 minute student presentations
To the Master students: if you want to take part in the examination, by giving a presentation, please confirm by sending me an email (timothy.budd@cea.fr) by March 4th.
Interactive stuff
Papers

[17]Martingales in selfsimilar growthfragmentations and their connections with random planar maps
with J. Bertoin, N. Curien and I. Kortchemski, arXiv1605.00581, [pdf] 
[16]Generalized multicritical onematrix models
with J. Ambjorn and Y. Makeenko, Nucl. Phys. B 913 (2016) 357380, arXiv:1604.04522 
[15]

[14]The peeling process of infinite Boltzmann planar maps
Electronic journal of combinatorics 23(1) (2016) #P1.28, arXiv:1506.01590, [pdf] 
[13]Multipoint functions of weighted cubic maps
with Jan Ambjorn, Annales de l'Institut Henri Poincaré D 3 (2016) 144, arXiv:1408.3040, [pdf] 
[12]Scaledependent Hausdorff dimensions in 2d gravity
with J. Ambjorn and Y. Watabiki, Phys. Lett. B 736 (2014) 339343, arXiv:1406.6251, [pdf] 
[11]Geodesic distances in quantum Liouville gravity
with Jan Ambjorn, Nucl. Phys. B 889 (2014) 676691, arXiv:1405.3424, [pdf] 
[10]Twodimensional Quantum Geometry
with Jan Ambjorn, Acta Physica Polonica B 44 (2013) 2537, arXiv:1310.8552, [pdf] 
[9]Exploring Torus Universes in Causal Dynamical Triangulations
with Renate Loll, Phys. Rev. D 88 024015 (2013), arXiv:1305.4702 
[8]The toroidal Hausdorff dimension of 2d Euclidean quantum gravity
with Jan Ambjorn, Phys. Lett. B 724 (2013) 328332, arXiv:1305.3674 
[7]Trees and spatial topology change in CDT
with Jan Ambjorn, J. Phys. A: Math. Theor. 46 (2013) 315201, arXiv:1302.1763 (featured on journal front cover) 
[6]Semiclassical dynamical triangulations
with Jan Ambjorn, Phys. Lett. B 718 (2012) 200204, arXiv:1209.6031 
[5]

[4]Roaming moduli space using dynamical triangulations
with J. Ambjorn, J. Barkley, Nucl. Phys. B 858 (2012) 267292, arXiv:1110.4649 
[3]Baby Universes Revisited
with J. Ambjorn, J. Barkley and R. Loll, Phys. Lett. B 706 (2011) 8689, arXiv:1110.3998 
[2]Shape Dynamics in 2+1 Dimensions
with Tim Koslowski, Gen. Rel. Grav. 44 (2012) 16151636, arXiv:1107.1287, [pdf] 
[1]In Search of Fundamental Discreteness in 2+1 Dimensional Quantum Gravity
with Renate Loll, Class. Quant. Grav. 26 (2009) 185011, arXiv:0906.3547, [pdf]
Talks and Slides
▼ Show/hide full list of talks ▼ 15 May 2017
 Peeling of random planar maps, Minicourse at Minischool on Random Maps and the Gaussian Free Field, École normale supérieure de Lyon.
 28 Apr 2017
 Combinatorics seminar at the Mathematics Institute, University of Warwick, UK.
 24 Apr 2017
 Computations and Proofs seminar at SpecFun, INRIA, École Polytechnique, Palaiseau, France.
 21 Mar 2017
 Escaping universality in twodimensional quantum gravity, Invited conference talk at Quantum gravity in Paris, IHP, Paris.
 10 Mar 2017
 On a connection between planar map combinatorics and lattice walks, Seminar at the Laboratoire de Mathématiques et Physique Théorique, Université de Tours, France.
 25 Jan 2017
 Winding of walks on the square lattice, Invited conference talk at Journées de combinatoire de Bordeaux, LaBRI, Bordeaux. [slides]
 19 Jan 2017
 On a connection between planar map combinatorics and lattice walks, Invited conference talk at Workshop on Random maps and Dimer models, part of the Combinatorics and interactions trimester, IHP, Paris. [slides]
 7 Jun 2016
 Geometry of random planar maps with high degrees, Invited conference talk at Random trees and maps: probabilistic and combinatorial aspects, CIRM, Marseille.
 12 May 2016
 Geometry of random planar maps with high degrees, Seminar at LPT, ParisSud.
 28 Apr 2016
 Geometry of random planar maps with high degrees, Seminar at UMPA, ENS de Lyon. [slides]
 20 Apr 2016
 QMATH Quantum Lunch seminar, Math department, University of Copenhagen.
 17 Mar 2016
 Random planar maps, outreach talk for students participating in a study trip organized by AEskwadraat, University of Copenhagen.
 7 Mar 2016
 On the universality of 2d quantum gravity, Journal club, Niels Bohr Institute, University of Copenhagen.
 3 Dec 2015
 The peeling process on random planar maps with loops, Invited conference talk at Séminaire Philippe Flajolet, l'Institut Henri Poincaré, Paris. [slides]
 26 Nov 2015
 From random walks to loops on random planar maps, Seminar at LMO, Orsay, France.
 24 Jun 2015
 The O(n) model on random surfaces, Journal club, Niels Bohr Institute, University of Copenhagen.
 12 Jun 2015
 Peeling of infinite Boltzmann planar maps, Invited conference talk at 20th Itzykson conference, IPTh, Saclay, France.
 20 Apr 2015
 Scaling constants and the lazy peeling of infinite Boltzmann planar maps, Invited conference talk at Random Planar Structures and Statistical Mechanics, Isaac Newton Institute, Cambridge. [slides], [video]
 15 Sep 2014
 Firstpassage percolation on random planar maps, Invited conference talk at Probability on Trees and Planar Graphs, Banff International Research Station, Banff, Canada. [slides], [video]
 14 Apr 2014
 Relating discrete and continuum 2d quantum gravity, Quantum gravity seminar, Radboud University Nijmegen, The Netherlands. [slides]
 6 Jan 2014
 Fractal dimensions of 2d quantum gravity, Invited conference talk at Approaches to Quantum Gravity, Meeting of GDR, Université Blaise Pascal, ClermontFerrand, France. [slides]
 20 Jun 2013
 From planar maps to spatial topology change in 2d gravity, Invited conference talk at Journées Cartes, l'Institut de Physique Théorique, CEA Saclay, France. [slides]
 20 Mar 2013
 Generalized CDT as a scaling limit of planar maps, Invited conference talk at Quantum Gravity in Paris, Orsay, France. [slides]
 14 Dec 2012
 CDT and trees, Invited conference talk at the CDT and Friends, Nijmegen, The Netherlands. [slides]
 20 Sep 2012
 Adding colors to dynamical triangulations in 3d, Seminar, Niels Bohr Institute, Copenhagen. [slides]
 15 Mar 2012
 Effective dynamics in nonperturbative quantum gravity, PhD thesis seminar, ITP, Utrecht. [slides]
 14 Dec 2011
 Effective dynamics of CDT in 2+1 dimensions, Seminar, Perimeter Institute, Waterloo, Canada. [slides]
 7 Nov 2011
 Probing moduli space using dynamical triangulations, Seminar, ITP, Utrecht. [slides]
 24 May 2011
 The effective kinetic term in CDT, conference talk at LOOPS `11, Madrid, Spain. [slides]
 30 Nov 2010
 Having fun with cute little universes, PhD lunch seminar, ITP, Utrecht.
 2 Feb 2010
 Conformal trouble in quantum gravity, talk at PhD School on Theoretical High Energy Physics, Driebergen, The Netherlands.
 9 Jan 2009
 Geometric observables in 2+1 dimensional quantum gravity, ENRAGE Young quantum gravity meeting, Imperial college, London.
Theses
Videos
Overview of all videos on [Youtube].3d models of 2d gravity
See all models on [Sketchfab]Older projects
 Publications [4] and [6]
 Chapter 3 in my PhD thesis
 Slides #2
 Publications [3], [4], [6] and [8]
 Slides #5
 Preprint [7]
 Slides #6, #7, and #8
 Random quadrangulations embedded in 3D (requires browser/OS with WEBGL support)
 Movie of random quadrangulations appearing in the cup function.