Goldsmith Building, 301
DegreesUniversity of Bordeaux III, Ph.D.
Ecole Normale Superieure, M.S.
Ecole Normale Superieure, B.S.
ExpertiseCombinatorics and Probability
ProfileMy 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.
|MATH||8a||Introduction to Probability and Statistics|
|MATH||39a||Introduction to Combinatorics|
|MATH||180b||Topics in Combinatorics|
Awards and Honors
NSF research grant: "Maps: beyond boundaries" (2013)
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.