# Olivier Bernardi

Degrees

University of Bordeaux III, Ph.D.Ecole Normale Superieure, M.S.

Ecole Normale Superieure, B.S.

Expertise

Combinatorics and related fields (algorithmics, probability, statistical mechanics)Profile

My main research interests are in combinatorics and probability.In particular, I am interested in "discrete surfaces" (a.k.a maps), that is, surfaces obtained by gluing polygons along their edges. The applications range from the concrete (graph drawing algorithms, encoding of computer images), to the theoretical (representation theory, random matrices, random surfaces appearing quantum mechanics and string theory). I am particularly interested in the bijections between maps and trees which are at the core of recent advances in our understanding of discrete surfaces.

More generally, I am interested in bijective encoding of mathematical structures and the use of such encodings to answer questions coming from mathematics, computer science of physics.

Courses Taught

MATH | 8a | Introduction to Probability and Statistics |

MATH | 35a | Advanced Calculus and Fourier Analysis |

MATH | 39a | Introduction to Combinatorics |

MATH | 131a | Algebra I |

MATH | 131b | Algebra II |

MATH | 180a | Combinatorics |

MATH | 180b | Topics in Combinatorics |

MATH | 200a | Second-Year Seminar |

MATH | 298a | Specialized Mathematics Seminar Class |

MATH | 299a | Mathematics Seminar Class |

Awards and Honors

NSF grant DMS 1800681, 2018-2021 (2018 - 2021)

NSF research grant: "Maps: beyond boundaries" (2013)

Scholarship

Bernardi, Olivier and Holden Nina and Sun, Xin. "Percolation on triangulations: a bijective path to Liouville quantum gravity." __Memoirs of the American Mathematical Society__ To appear.. (2021): 152 pages.

Bernardi, Olivier and Fusy, Eric. "Unified bijections for planar hypermaps with general cycle-length constraints." __Annales de l'Institut Henri Poincare D__ 7. 1 (2020): 75-164.

Bernardi, Olivier and Nadeau Philippe. "Combinatorial reciprocity for the chromatic polynomial and the chromatic symmetric function.." __Discrete Mathematics__ 343. 10 (2020).

Olivier Bernardi, Tamas Kalman, Alex Postnikov. "Universal Tutte Polynomial." 2020.

Bernardi, Olivier and Jordan Awan. "Tutte polynomials for directed graphs." __Journal of Combinatorial Theory, Series B.__ 140. (2019): 192-247.

Bernardi, Olivier. __Percolation on triangulations and a bijective path to Liouville quantum gravity__. Proc. of Sectional AMS meeting (plenary lecture). Notices of the AMS, 2019.

Bernardi, Olivier. "Deformations of the braid arrangement and Trees." __Advances in Mathematics__ 335. (2018): 466-518.

Bernardi, Olivier and Bousquet-Melou Mireille. "Counting coloured planar maps: differential equations." __Communications in Mathematical Physics__ 354. 1 (2017): 31-84.

Bernardi, Olivier and Fusy, Eric. "Bijections for planar maps with boundaries." __Journal of Combinatorial Theory, Series A__ 158. (2017): 176-227.

Bernardi, Olivier, Mireille Bousquet-Melou and Kilian Raschel. "Counting quadrant walks via Tutte's invariant method." 2017.

Olivier Bernardi, Nicolas Curien, Gregory Miermont. "A Boltzmann approach to percolation on random triangulations." __Canadian Journal of Mathematics__ 71. 1 (2017): 1-43.

Bernardi, Olivier and Bousquet-Melou, Mireille and Raschel, Kilian. "Counting quadrant walks via Tutte's invariant method." FPSAC, Vancouver. 2016.

Bernardi, Olivier and Klivans, Caroline. "Directed rooted forests in higher dimension." __Electronic Journal of Combinatorics__ 23. 4 (2016): P4.35 (20 pages).

Bernardi, Olivier and Morales Alejandro. "Some probabilistic trees with algebraic roots." __Electronic Journal of Combinatorics, Vol 23(2), P2.36, 24pp__ 23. 2 (2016): P2.36 (24pages).

Bernardi, Olivier and Collet, Gwendal and Eric Fusy, Eric.. "On the distance-profile of random rooted plane graphs." Analysis of Algorithms (AofA) 2014, Paris. June 16–20, 2014.

Olivier Bernardi and Alejandro H. Morales.. "Counting trees using symmetries." __Journal of Combinatorial Theory, Series A__ 123. 1 (2014): 104–122.

Olivier Bernardi, Rosena R.X. Du, Alejandro H. Morales and Richard P. Stanley.. "Separation probabilities for products of permutations." __Combinatorics, Probability and Computing__ 23. 2 (2014): 201-222.

Olivier Bernardi, Gwendal Collet and Eric Fusy. "A bijection for plane graphs and its applications." ANALCO, Portland USA. January 2014.

Bernardi, Olivier. "A Short proof of Rayleigh's Theorem with extensions.." __The American Mathematical Monthly__ 120. 4 (2013): 362-364.

Olivier Bernardi and Alejandro Morales. "Bijections and symmetries for the factorizations of the long cycle." __Advances in Applied Mathematics__ 50. (2013): 702-722.

Bernardi Olivier, Eric Fusy. "Schnyder decompositions for regular plane graphs and application to drawing." __Algorithmica__ 62. 3 (2012): 1159-1197.

Bernardi Olivier, Eric Fusy. "Unified bijections for maps with prescribed degrees and girth." __Journal of Combinatorial Theory - Series A__ 119. 6 (2012): 1351-1387.

Bernardi, Olivier, Juanjo Rue. "Enumerating simplicial decompositions of surfaces with boundaries." __European Journal of Combinatorics__ 33. 4 (2012): 302-325.