Keynote speakers
Alain ChencinerProfesseur émérite Université Paris 7, chercheur associé à l'Observatoire de Paris https://perso.imcce.fr/alainchenciner/ Biography Alain Chenciner was born in 1943 in France. He studied at Ecole Polytechnique from 1963 to 1965, and received his Doctorat d’Etat from Université Paris XI in 1971. He is currently emeritus professor at University Paris 7 and is associated to the Paris Observatory. In 1992 he created with Jacques Laskar the research group Astronomie et Systèmes Dynamiques inside the Bureau des Longitudes, now hosted by Paris Observatory.. He was an invited speaker at ICM Beijing 2002 and a plenary speaker at ICMP Lisbon 2003. His research has been mainly devoted to bifurcation theory, and to the nbody problem. Keynote address: nbody relative equilibria in higher dimensions If one allows the dimension of the ambient Euclidean space to be greater than 3, the family of nbody configurations which, when submitted to Newtonian or similar attraction, admit a relative equilibrium motion (the ``balanced" configurations) becomes much richer. Also, a given balanced configuration admits a variety of relative equilibria, namely one for each choice of a Hermitian structure on the space where the motion really takes place; in general, if the configuration is not central, such relative equilibria are quasiperiodic. I shall give an overview of balanced configurations and discuss some problems, like the one of deciding what is the smallest dimension in which a given configuration admits a relative equilibrium motion, or when bifurcations from periodic to quasiperiodic relative equilibrium may occur. Keynote References


Elena CelledoniProfessor at Department of Mathematical Sciences, Norwegian University of Science and Technology (NTNU), Trondheim, Norway https://www.ntnu.edu/employees/elena.celledoni Biography Elena Celledoni received her Master degree in mathematics from the University of Trieste in 1993, and her Ph.D in computational mathematics from the University of Padua, Italy, 1997. She held post doc positions at the University of Cambridge, UK, at the Mathematical Sciences Research Institute, Berkeley, California and at NTNU. Keynote Address: Structure preserving algorithms for geometric numerical integration Computations of differential equations are of fundamental importance in applied mathematics. While historically the main quest was to derive allpurpose algorithms such as finite difference, finite volume and finite element methods for space discretization, Runge–Kutta and linear multistep methods for time integration, in the last 25 years the focus has shifted to special classes of differential equations and purposebuilt algorithms that are tailored to preserve special features of each class. This has given rise to the new field of geometric numerical integration and structure preserving discretizations.
Keynote References


Karl FristonMB, BS, MA, MRCPsych, FMedSci, FRSB, FRS Biography
Karl Friston is a theoretical neuroscientist and authority on brain imaging. He invented statistical parametric mapping (SPM), voxelbased morphometry (VBM) and dynamic causal modelling (DCM). These contributions were motivated by schizophrenia research and theoretical studies of valuelearning, formulated as the dysconnection hypothesis of schizophrenia. Mathematical contributions include variational Laplacian procedures and generalized filtering for hierarchical Bayesian model inversion. Friston currently works on models of functional integration in the human brain and the principles that underlie neuronal interactions. His main contribution to theoretical neurobiology is a freeenergy principle for action and perception (active inference). Friston received the first Young Investigators Award in Human Brain Mapping (1996) and was elected a Fellow of the Academy of Medical Sciences (1999). In 2000 he was President of the international Organization of Human Brain Mapping. In 2003 he was awarded the Minerva Golden Brain Award and was elected a Fellow of the Royal Society in 2006. In 2008 he received a Medal, College de France and an Honorary Doctorate from the University of York in 2011. He became of Fellow of the Royal Society of Biology in 2012, received the Weldon Memorial prize and Medal in 2013 for contributions to mathematical biology and was elected as a member of EMBO (excellence in the life sciences) in 2014 and the Academia Europaea in (2015). He was the 2016 recipient of the Charles Branch Award for unparalleled breakthroughs in Brain Research and the Glass Brain Award, a lifetime achievement award in the field of human brain mapping. He holds Honorary Doctorates from the University of Zurich and Radboud University. https://www.fil.ion.ucl.ac.uk/~karl/ Keynote Address: Markov blankets and Bayesian mechanics This presentation offers a heuristic proof (and simulations of a primordial soup) suggesting that life—or biological selforganization—is an inevitable and emergent property of any (weakly mixing) random dynamical system that possesses a Markov blanket. This conclusion is based on the following arguments: if a system can be differentiated from its external milieu, heat bath or environment, then the system’s internal and external states must be conditionally independent. These independencies induce a Markov blanket that separates internal and external states. This separation means that internal states will appear to minimize a free energy functional of blanket states – via a variational principle of stationary action. Crucially, this equips internal states with an information geometry, pertaining to probabilistic beliefs about something; namely external states. Interestingly, this free energy is the same quantity that is optimized in Bayesian inference and machine learning (where it is known as an evidence lower bound). In short, internal states (and their Markov blanket) will appear to model—and act on—their world to preserve their functional and structural integrity. This leads to a Bayesian mechanics, which can be neatly summarised as selfevidencing. 

Gabriel PeyréCNRS and Ecole Normale Supérieure Biography Gabriel Peyré is senior researcher at the Centre Nationale de Recherche Scientiﬁque (CNRS) and professor at the Ecole Normale Supérieure, Paris. His research is focused on developing mathematical and numerical tools for imaging sciences and machine learning. He is the creator of the "Numerical tour of data sciences" (www.numericaltours.com), a popular online repository of Python/Matlab/Julia/R resources to teach mathematical data sciences. His research was supported by a ERC starting grant (SIGMAVision, 20102015) and is now supported by a ERC consolidator grant (NORIA 20172021). He is the 2017 recipient of the BlaisePascal prize from the French Academy of sciences, awarded each year to a young applied mathematician. Keynote address: Optimal Transport for Machine Learning Optimal transport (OT) has become a fundamental mathematical tool at the interface between calculus of variations, partial differential equations and probability. It took however much more time for this notion to become mainstream in numerical applications. This situation is in large part due to the high computational cost of the underlying optimization problems. There is a recent wave of activity on the use of OTrelated methods in fields as diverse as image processing, computer vision, computer graphics, statistical inference, machine learning. In this talk, I will review an emerging class of numerical approaches for the approximate resolution of OTbased optimization problems. This offers a new perspective for the application of OT in high dimension, to solve supervised (learning with transportation loss function) and unsupervised (generative network training) machine learning problems.
Keynote References


JeanBaptiste HiriartUrruty Toulouse University https://www.math.univtoulouse.fr/~jbhu/ Biography JeanBaptiste HiriartUrruty is professor emeritus at the Université Paul Sabatier in Toulouse since 2015. It holds a PhD in mathematics from the Université Blaise Pascal in ClermonFerrand and an habilitation. He was fulle time professor in mathematics at University Paul Sabatier from 1981 to 2015. His research topics are variational calculus (convex, non smooth and applications) and optimization (global optimization, non smooth, non convex). He has also many contributions in the history of mathematics and mathematicians and in dissemination of mathematical science towards general public. Keynote address: Fermat, Pascal: geometry and chance The presentation will focus on the contributions of these two great mathematicians of the 17th century from an historical perspective. The rich interactions within the mathematical community at that time and the problems arising in geometry and probability paved the way to modern mathematical science.Some enlightening examples will be given during the talk. 