%% Papers Published
@article{benoitjacques2,
Author = {Benoit Charbonneau and Jacques Hurtubise},
Title = {The Nahm transform for calorons},
Booktitle = {The many facets of geometry: a tribute to Nigel
Hitchin},
Publisher = {Oxford University Press},
Editor = {JeanPierre Bourguignon and Oscar GarciaPrada and Simon
Salamon},
Year = {2010},
Month = {July},
ISBN = {9780199534920},
url = {http://arxiv.org/pdf/0705.2412},
Abstract = {In this paper, we complete the proof of an equivalence given
by Nye and Singer of the equivalence between calorons
(instantons on $S^1\times R^3$) and solutions to Nahm's
equations over the circle, both satisfying appropriate
boundary conditions. Many of the key ingredients are
provided by a third way of encoding the same data which
involves twistors and complex geometry. Dedicated to Nigel
Hitchin on the occasion of his sixtieth birthday},
Key = {benoitjacques2}
}
@article{benoitjacques3,
Author = {Benoit Charbonneau and Jacques Hurtubise},
Title = {Singular HermitianEinstein monopoles on the product of a
circle and a Riemann surface},
Journal = {International Mathematics Research Notices},
Year = {2010},
Month = {April},
url = {http://dx.doi.org/10.1093/imrn/rnq059},
Doi = {10.1093/imrn/rnq059},
Key = {benoitjacques3}
}
@article{fds156863,
Author = {Benoit Charbonneau and Yuriy Svyrydov and P.F.
Tupper},
Title = {Convergence in the Prokhorov Metric of Weak Methods for
Stochastic Differential Equations},
Journal = {IMA Journal of Numerical Analysis},
Volume = {30},
Number = {2},
Pages = {579594},
Year = {2010},
url = {http://imajna.oxfordjournals.org/cgi/content/abstract/drn067?ijkey=oQbKpjUZWUEfl4K&keytype=ref},
Keywords = {stochastic differential equations • numerical methods
• convergence in distribution • weak convergence
• Prokhorov metric • Strassenâ€“Dudley theorem
• Wasserstein distance},
Abstract = {We consider the weak convergence of numerical methods for
stochastic differential equations (SDEs). Weak convergence
is usually expressed in terms of the convergence of expected
values of test functions of the trajectories. Here we
present an alternative formulation of weak convergence in
terms of the wellknown Prokhorov metric on spaces of random
variables. For a general class of methods we establish
bounds on the rates of convergence in terms of the Prokhorov
metric. In doing so, we revisit the original proofs of weak
convergence and show explicitly how the bounds on the error
depend on the smoothness of the test functions. As an
application of our result, we use the Strassenâ€“Dudley
theorem to show that the numerical approximation and the
true solution to the system of SDEs can be reembedded in a
probability space in such a way that the method converges
there in a strong sense. One corollary of this last result
is that the method converges in the Wasserstein distance,
another metric on spaces of random variables. Another
corollary establishes rates of convergence for expected
values of test functions, assuming only local Lipschitz
continuity. We conclude with a review of the existing
results for pathwise convergence of weakly converging
methods and the corresponding strong results available under
reembedding.},
Doi = {10.1093/imanum/drn067},
Key = {fds156863}
}
@article{fds166347,
Author = {J.A. van Meel and B. Charbonneau and A. Fortini and P.
Charbonneau},
Title = {Hardsphere crystallization gets rarer with increasing
dimension},
Journal = {Phys. Rev. E},
Volume = {80},
Pages = {061110},
Year = {2009},
Month = {November},
url = {http://link.aps.org/doi/10.1103/PhysRevE.80.061110},
Abstract = {We recently found that crystallization of monodisperse hard
spheres from the bulk fluid faces a much higher freeenergy
barrier in four than in three dimensions at equivalent
supersaturation, due to the increased geometrical
frustration between the simplexbased fluid order and the
crystal [J. A. van Meel, D. Frenkel, and P. Charbonneau,
Phys. Rev. E 79, 030201(R) (2009)]. Here, we analyze the
microscopic contributions to the fluidcrystal interfacial
free energy to understand how the barrier to crystallization
changes with dimension. We find the barrier to grow with
dimension and we identify the role of polydispersity in
preventing crystal formation. The increased fluid stability
allows us to study the jamming behavior in four, five, and
six dimensions and to compare our observations with two
recent theories [C. Song, P. Wang, and H. A. Makse, Nature
(London) 453, 629 (2008); G. Parisi and F. Zamponi, Rev.
Mod. Phys. (to be published)].},
Key = {fds166347}
}
@article{fds165687,
Author = {Juli Atherton and Benoit Charbonneau and Xiaojie Zhou and David
Wolfson, Lawrence Joseph and Alain C. Vandal},
Title = {Bayesian optimal design for changepoint problems},
Journal = {Canadian Journal of Statistics},
Volume = {37},
Number = {4},
Pages = {495513},
Year = {2009},
Month = {September},
url = {http://dx.doi.org/10.1002/cjs.10037},
Abstract = {We propose, for the first time, optimal design for
changepoint problems. Suppose that a sequence of
observations is taken in some subinterval of the real axis.
If the distribution of the sequence changes at some unknown
location then we refer to this location as a changepoint.
Changepoint inference usually concerns location testing for
a change and/or estimating the location of the change and
the unknown parameters of the distributions before and after
any change. In this paper, we investigate Bayesian optimal
designs for changepoint problems. We find robust optimal
designs which allow for arbitrary distributions before and
after the change, arbitrary prior densities on the
parameters before and after the change, and any logconcave
prior density on the changepoint. We define a new design
measure for Bayesian optimal design problems as a means of
finding the optimal design itself. Our results apply to any
design criterion function concave in the design measure. We
show that our method extends directly to a setting in which
there are several paths all with the same
changepoint.},
Key = {fds165687}
}
@article{benoitjacques1,
Author = {Benoit Charbonneau and Jacques Hurtubise},
Title = {Calorons, Nahm's equations on S^1 and bundles over
P^1xP^1},
Journal = {Communications in Mathematical Physics},
Volume = {280},
Number = {2},
Pages = {315349},
Year = {2008},
ISSN = {00103616},
MRCLASS = {53C07 (14D21 58D27)},
MRNUMBER = {MR2395473},
url = {http://dx.doi.org/10.1007/s0022000804687},
Abstract = {The moduli space of solutions to Nahm's equations of rank
(k,k+j) on the circle, and hence, of SU(2) calorons of
charge (k,j), is shown to be equivalent to the moduli of
holomorphic rank 2 bundles on P^1xP^1 trivialized at
infinity with c_2=k and equipped with a flag of degree j
along P^1x{0}. An explicit matrix description of these
spaces is given by a monad construction.},
Key = {benoitjacques1}
}
@article{benoitpaper,
Author = {Charbonneau, Benoit},
Title = {From spatially periodic instantons to singular
monopoles},
Journal = {Communications in Analysis and Geometry},
Volume = {14},
Number = {1},
Pages = {183214},
Year = {2006},
ISSN = {10198385},
MRCLASS = {53C07 (14D21 34L40 58D27)},
MRNUMBER = {MR2230575 (2007c:53036)},
url = {http://arxiv.org/pdf/math/0410561},
Abstract = {The main result is a computation of the Nahm transform of a
SU(2)instanton over RxT^3, called spatiallyperiodic
instanton. It is a singular monopole over T^3, a solution to
the Bogomolny equation, whose rank is computed and behavior
at the singular points is described.},
Key = {benoitpaper}
}
%% Papers Accepted
@article{fds201755,
Author = {Benoit Charbonneau and Patrick Charbonneau and Gilles
Tarjus},
Title = {Geometrical frustration and static correlations in a simple
glass former},
Journal = {Phys. Rev. L},
Year = {2011},
Month = {December},
url = {http://arxiv.org/abs/1108.2492},
Abstract = {We study the geometrical frustration scenario of glass
formation for simple hard spheres systems, and find it to be
an inefficient description. The possibility of a growing
static length is furthermore found to be physically
irrelevant in the simulation accessible regime, which
suggests that the study of any structural order in simple
fluids of spherical particles is there also
unhelpful.},
Key = {fds201755}
}
%% Papers Submitted
@article{fds201756,
Author = {Benoit Charbonneau and Mark Stern},
Title = {Asymptotic Hodge Theory of Vector Bundles},
Year = {2011},
url = {http://arxiv.org/abs/1111.0591},
Key = {fds201756}
}
%% Other
@misc{fds158049,
Author = {Benoit Charbonneau},
Title = {Various MathSciNet reviews},
Year = {2007},
url = {http://www.ams.org/mathscinet/search/publications.html?pg4=AUCN&s4=&co4=AND&pg5=TI&s5=&co5=AND&pg6=PC&s6=&co6=AND&pg7=RVCN&s7=charbonneau%2C+benoit&co7=AND&Submit=Search&dr=all&yrop=eq&arg3=&yearRangeFirst=&yearRangeSecond=&pg8=ET&s8=All},
Key = {fds158049}
}
@phdthesis{benoitthesis,
Author = {Benoit Charbonneau},
Title = {Analytic aspects of periodic instantons},
Organization = {Massachusetts Institute of Technology},
Institution = {Massachusetts Institute of Technology},
Address = {Cambridge, MA, USA},
Year = {2004},
url = {http://www.math.duke.edu/~benoit/ThesisBenoitCharbonneau.pdf},
Key = {benoitthesis}
}
@misc{fds70725,
Author = {Benoit Charbonneau},
Title = {Introduction au théorème de
RiemannRoch},
Year = {1999},
url = {http://www.math.duke.edu/~benoit/Textes/MemoireBenoitCharbonneau.pdf},
Key = {fds70725}
}
