Keynote speakers

Alain Chenciner

Professeur émérite Université Paris 7, chercheur associé à l'Observatoire de Paris

https://perso.imcce.fr/alain-chenciner/

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 n-body problem.

Keynote address: n-body relative equilibria in higher dimensions

If one allows the dimension of the ambient Euclidean space to be greater than 3, the family of n-body 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 quasi-periodic.

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 quasi-periodic relative equilibrium may occur.

Keynote References

  • A. Albouy & A. Chenciner, Le problème des n corps et les distances mutuelles, Inventiones Mathematicae, 131, pp. 151-184 (1998)
  • A. Chenciner, The Lagrange reduction of the N-body problem: a survey, Acta Mathematica Vietnamica (2013) 38: 165-186,
  • A. Chenciner, The angular momentum of a relative equilibrium, Discrete and Continuous Dynamical Systems (dedicated to the memory of Ernesto Lacomba)  (2012), Volume 33, Number 3, March 2013, 1033-1047
  • A. Chenciner & H. Jiménez-Pérez, Angular momentum and Horn's problem,  Moscow Mathematical Journal, Volume 13, Number 4, October-December 2013, 621-630
  • A. Chenciner, Non-avoided crossings for n-body balanced configurations in R^3 near a central configuration, Arnold Math J. (2016) n°2, 213-248

Elena Celledoni

Professor 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.
Her research field is in numerical analysis and in particular structure preserving algorithms for differential equations and geometric numerical integration.

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 all-purpose 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 purpose-built 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.
In this talk, we will give an introduction to structure preserving algorithms, focussing in particular on Lie group methods and on integrators on Riemannian manifolds. We consider a selection of applications of these methods. Local and global error bounds are derived in terms of the Riemannian distance function and the Levi-Civita connection. Finally, the notion of discrete gradient methods is generalised to Lie groups and to Riemannian manifolds. This approach leads to structure preserving methods for energy preserving as well as energy dissipative systems. We show that the methods are competitive with other approaches when applied to Riemannian gradient flow systems arising in diffusion tensor imaging.

 

Keynote References

  • E Celledoni, S Eidnes, B Owren, T Ringholm, Energy preserving methods on Riemannian manifolds , arXiv preprint arXiv:1805.07578
  • Elena Celledoni, Sølve Eidnes, Brynjulf Owren, and Torbjørn Ringholm, Dissipative Numerical Schemes on Riemannian Manifolds with Applications to Gradient Flows, SIAM J. Sci. Comput., 40(6), A3789–A3806.
  • E Celledoni, S Eidnes, A Schmeding, Proceedings of the Abel Symposium 2016, Springer, Shape analysis on homogeneous spaces: a generalised SRVT framework
  • E Celledoni, M Eslitzbichler, A Schmeding, Shape Analysis on Lie Groups with Applications in Computer Animation , Journal of Geometric Mechanics (JGM). 8 (3)
  • Elena Celledoni, Håkon Marthinsen, Brynjulf Owren An introduction to Lie group integrators – basics, new developments and applications

Karl Friston

MB, BS, MA, MRCPsych, FMedSci, FRSB, FRS
Wellcome Principal Fellow
Scientific Director: Wellcome Trust Centre for Neuroimaging
Institute of Neurology, UCL

Biography

 

Karl Friston is a theoretical neuroscientist and authority on brain imaging. He invented statistical parametric mapping (SPM), voxel-based morphometry (VBM) and dynamic causal modelling (DCM). These contributions were motivated by schizophrenia research and theoretical studies of value-learning, 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 free-energy 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 self-organization—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 self-evidencing.

Gabriel Peyré

CNRS and Ecole Normale Supérieure

http://www.gpeyre.com/

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.numerical-tours.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 (SIGMA-Vision, 2010-2015) and is now supported by a ERC consolidator grant (NORIA 2017-2021). He is the 2017 recipient of the Blaise-Pascal 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 OT-related 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 OT-based 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
 

Jean-Baptiste Hiriart-Urruty

Toulouse University

https://www.math.univ-toulouse.fr/~jbhu/

Biography

Jean-Baptiste Hiriart-Urruty is professor emeritus at the Université Paul Sabatier in Toulouse since 2015. It holds a PhD in mathematics from the Université Blaise Pascal in Clermon-Ferrand 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.

 
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