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SUMMARY:6th talk : Monge-Kantorovich problem for n-dimensional measures wi
th fixed k-dimensional marginals
DTSTART;VALUE=DATE-TIME:20190705T073000Z
DTEND;VALUE=DATE-TIME:20190705T082000Z
DTSTAMP;VALUE=DATE-TIME:20190721T085836Z
UID:indico-contribution-4497-3532@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nikita Gladkov (University of Moscow)\nThe classical
Monge-Kantorovich (transportation) problem deals with measures on a produ
ct of two spaces with two independent fixed marginals. Its natural general
ization (multimarginal Monge-Kantorovich problem) deals with the products
of n spaces X_1\, ...\, X_n with n independent marginals. We study the Mon
ge-Kantorovich problem on X_1 \\times X_2 ... \\times ... X_n with fixed p
rojections onto the products of X_{i_1} \, ... X_{i_k} for all k-tuples of
indices (k\n\nhttps://indico.math.cnrs.fr/event/4497/contributions/3532/
LOCATION:IRMA in Strasbourg Salle de conférence
URL:https://indico.math.cnrs.fr/event/4497/contributions/3532/
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SUMMARY:5th talk : Optimal transport planning with a non linear cost
DTSTART;VALUE=DATE-TIME:20190705T063000Z
DTEND;VALUE=DATE-TIME:20190705T072000Z
DTSTAMP;VALUE=DATE-TIME:20190721T085836Z
UID:indico-contribution-4497-3531@indico.math.cnrs.fr
DESCRIPTION:Speakers: Thierry Champion (Université de Toulon)\nIn this ta
lk\, I consider optimal transport problems that involve non-linear transpo
rtation costs which favour optimal plans non associated to a single valued
transport map. I will describe some results concerning this type of probl
em (existence\, duality principle\, optimality conditions) and focus on sp
ecific examples in a finite dimensional compact setting. I will consider
in particular the case where the cost involves the opposite of the varianc
e or the indicator of a constraint on the barycenter of $p$ (martingale tr
ansport).\nThis is from a joined work with J.J. Alibert and G. Bouchitté.
\n\nhttps://indico.math.cnrs.fr/event/4497/contributions/3531/
LOCATION:IRMA in Strasbourg Salle de conférence
URL:https://indico.math.cnrs.fr/event/4497/contributions/3531/
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SUMMARY:3rd Talk: The Monge problem in multi-marginal optimal mass transpo
rtation
DTSTART;VALUE=DATE-TIME:20190704T133000Z
DTEND;VALUE=DATE-TIME:20190704T142000Z
DTSTAMP;VALUE=DATE-TIME:20190721T085836Z
UID:indico-contribution-4497-3529@indico.math.cnrs.fr
DESCRIPTION:Speakers: Anna Kausamo (University of Jyväskylä)\nIn this ta
lk I will introduce the concept of Multi-Marginal Optimal Mass Transportat
ion (MOT) with the emphasis on repulsive cost functions. Then I will outli
ne the Monge problem\, discuss it's difficulty in the MOT setting\, and p
resent some nonexistence results that are joint work Augusto Gerolin and T
apio Rajala\n\nhttps://indico.math.cnrs.fr/event/4497/contributions/3529/
LOCATION:IRMA in Strasbourg Salle de conférence
URL:https://indico.math.cnrs.fr/event/4497/contributions/3529/
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SUMMARY:1st Talk: Continuous time Principal Agent and optimal planning
DTSTART;VALUE=DATE-TIME:20190704T110000Z
DTEND;VALUE=DATE-TIME:20190704T115000Z
DTSTAMP;VALUE=DATE-TIME:20190721T085836Z
UID:indico-contribution-4497-3527@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nizar Touzi (Ecole Polytechnique)\nMotivated by the
approach introduced by Sanninkov to solve principal-agent problems\, we pr
ovide a solution approach which allows to address a wider range of problem
s. The key argument uses a representation result from the theory of backwa
rd stochastic differential equations. This methodology extends to the mean
field game version of the problem\, and provides a connexion with the P.-
L. Lions optimal planning problem.\n\nhttps://indico.math.cnrs.fr/event/44
97/contributions/3527/
LOCATION:IRMA in Strasbourg Salle de conférence
URL:https://indico.math.cnrs.fr/event/4497/contributions/3527/
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SUMMARY:9th talk : Seidl conjecture in Density Functional Theory: results
and counterexamples
DTSTART;VALUE=DATE-TIME:20190705T121000Z
DTEND;VALUE=DATE-TIME:20190705T130000Z
DTSTAMP;VALUE=DATE-TIME:20190721T085836Z
UID:indico-contribution-4497-3535@indico.math.cnrs.fr
DESCRIPTION:Speakers: Simone Di Marino (Indam)\nThe Seidl conjecture in De
nsity Functional Theory is the equivalent of the Monge Ansatz for the clas
sical optimal transport problem with the cost $c(x\,y)=|x-y|$\, in the mul
timarginal case with the Coulomb cost. We provide positive results in the
one dimensional case as well as both positive and negative results in the
radial 2-dimensional case.\n\nhttps://indico.math.cnrs.fr/event/4497/contr
ibutions/3535/
LOCATION:IRMA in Strasbourg Salle de conférence
URL:https://indico.math.cnrs.fr/event/4497/contributions/3535/
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SUMMARY:8th talk : The inverse transform martingale coupling
DTSTART;VALUE=DATE-TIME:20190705T111000Z
DTEND;VALUE=DATE-TIME:20190705T120000Z
DTSTAMP;VALUE=DATE-TIME:20190721T085836Z
UID:indico-contribution-4497-3534@indico.math.cnrs.fr
DESCRIPTION:Speakers: Benjamin Jourdain (Université Paris-Est)\nWe exhibi
t a new martingale coupling between two probability measures $\\mu$ and $\
\nu$ in convex order on the real line. This coupling is explicit in terms
of the integrals of the positive and negative parts of the difference betw
een the quantile functions of $\\mu$ and $\\nu$. The integral of $|y-x|$ w
ith respect to this coupling is smaller than twice the Wasserstein distanc
e with index one between $\\mu$ and $\\nu$. When the comonotonous coupling
between $\\mu$ and $\\nu$ is given by a map $T$\, it minimizes the integr
al of $|y-T(x)|$ among all martingales couplings.\n\nhttps://indico.math.c
nrs.fr/event/4497/contributions/3534/
LOCATION:IRMA in Strasbourg Salle de conférence
URL:https://indico.math.cnrs.fr/event/4497/contributions/3534/
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SUMMARY:7th talk : Fine Properties of the Optimal Skorokhod Embedding Prob
lem.
DTSTART;VALUE=DATE-TIME:20190705T085000Z
DTEND;VALUE=DATE-TIME:20190705T094000Z
DTSTAMP;VALUE=DATE-TIME:20190721T085836Z
UID:indico-contribution-4497-3533@indico.math.cnrs.fr
DESCRIPTION:Speakers: Marcel Nutz (Columbia U. New York)\nWe study the pro
blem of stopping a Brownian motion at a given distribution $\\nu$ while op
timizing a reward function that depends on the (possibly randomized) stopp
ing time and the Brownian motion. Our first result establishes that the se
t $T(\\nu)$ of stopping times embedding $\\nu$ is weakly dense in the set
$R(\\nu)$ of randomized embeddings. In particular\, the optimal Skorokhod
embedding problem over $T(\\nu)$ has the same value as the relaxed one ove
r $R(\\nu)$ when the reward function is semicontinuous\, which parallels a
fundamental result about Monge maps and Kantorovich couplings in optimal
transport. A second part studies the dual optimization in the sense of lin
ear programming. While existence of a dual solution failed in previous for
mulations\, we introduce a relaxation of the dual problem and establish ex
istence of solutions as well as absence of a duality gap\, even for irregu
lar reward functions. This leads to a monotonicity principle which complem
ents the key theorem of Beiglbock\, Cox and Huesmann. These results can be
applied to characterize the geometry of optimal embeddings through a vari
ational condition. (Joint work with Mathias Beiglbock and Florian Stebegg)
s over the years.\n\nhttps://indico.math.cnrs.fr/event/4497/contributions/
3533/
LOCATION:IRMA in Strasbourg Salle de conférence
URL:https://indico.math.cnrs.fr/event/4497/contributions/3533/
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SUMMARY:4th talk: Weak optimal transport and applications to Caffarelli co
ntraction theorem.
DTSTART;VALUE=DATE-TIME:20190704T143000Z
DTEND;VALUE=DATE-TIME:20190704T152000Z
DTSTAMP;VALUE=DATE-TIME:20190721T085836Z
UID:indico-contribution-4497-3530@indico.math.cnrs.fr
DESCRIPTION:Speakers: Nathaël Gozlan (Université Paris 5)\nThe talk will
deal with a variant of the optimal transport problem first considered in
a joint paper with C. Roberto\, P-M Samson and P. Tetali\, where elementar
y mass transports are penalized through their barycenters. The talk will i
n particular focus on a recent result obtained in collaboration with N. Ju
illet describing optimal transport plans for the quadratic barycentric cos
t. A direct corollary of this result gives a new necessary and sufficient
condition for the Brenier map to be 1-Lipschitz. Finally we will present a
recent work in collaboration with M. Fathi and M. Prodhomme\, where this
contractivity criterion is used to give a new proof of the Caffarelli cont
raction theorem\, telling that any probability measure having a log-concav
e density with respect to the standard Gaussian measure is a contraction o
f it.\n\nhttps://indico.math.cnrs.fr/event/4497/contributions/3530/
LOCATION:IRMA in Strasbourg Salle de conférence
URL:https://indico.math.cnrs.fr/event/4497/contributions/3530/
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SUMMARY:2nd Talk : A counter-example to the Cantelli conjecture
DTSTART;VALUE=DATE-TIME:20190704T120000Z
DTEND;VALUE=DATE-TIME:20190704T125000Z
DTSTAMP;VALUE=DATE-TIME:20190721T085836Z
UID:indico-contribution-4497-3528@indico.math.cnrs.fr
DESCRIPTION:Speakers: Victor Kleptsyn (Université de Rennes)\nTake two Ga
ussian independent random variables X and Y\, both N(0\,1).\nThe Cantelli
conjecture addresses non-linear combinations of the form\nZ= X+f(X)*Y\, wh
ere f is a non-negative function. It states that if Z is Gaussian\,\nf sho
uld be constant almost everywhere. \nIn a joint work with Aline Kurtzmann\
, we have constructed a (measurable) counter-example \nto this conjecture\
, with a construction that uses a « Brownian » variation of a transport.
\nThis construction will be the subject of my talk.\n\nhttps://indico.math
.cnrs.fr/event/4497/contributions/3528/
LOCATION:IRMA in Strasbourg Salle de conférence
URL:https://indico.math.cnrs.fr/event/4497/contributions/3528/
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