# Olivier Bernardi

Degrees

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

Ecole Normale Superieure, B.S.

Expertise

Combinatorics and ProbabilityProfile

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.

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 |

Awards and Honors

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

Scholarship

Bernardi, Olivier and Fusy, Eric. "Unified bijections for planar hypermaps with general cycle-length constraints." (2015). (forthcoming)

Bernardi, Olivier and Morales Alejandro. "Some probabilistic trees with algebraic roots." (2015). (forthcoming)

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

Bernardi, Olivier and Bousquet-Melou Mireille. "Counting coloured planar maps: differential equations." 2015.

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.

Bernardi, Olivier and Fusy, Eric. "Bijections for maps with boundaries: Krikun's formula for triangulations, and a quadrangulation analogue." 2015.

Bernardi, Olivier and Klivans, Caroline. "Directed rooted forests in higher dimension." 2015.

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.