Invited & Keynote Speakers
Guest Honorary speaker
Jean-Michel Bismut (professeur à l’Université Paris-Sud (Orsay), member of Académie des Sciences)
Jean-Michel Bismut was born in 1948 in Lisbon (Portugal). He studied at Ecole Polytechnique in 1967-1969, and he received his Doctorat d’Etat from Université Paris VI in 1973. He became a professor of Mathematics in Orsay in 1981. He was a plenary speaker at ICM-Berlin 1998, and a vice-president of International Mathematical Union from 2002 to 2006. His research has been devoted to stochastic control, to the Malliavin calculus, to index theory, and its connections with spectral theory and number theory.
The hypoelliptic Laplacian
If X is a Riemannian manifold, the hypoelliptic Laplacian is a family of hypoelliptic operators acting on X , the total space of the tangent bundle of X , that interpolates between the ordinary Laplacian and the geodesioc ﬂow. The probabilistic counterpart is an interpolation between Brownian motion and geodesics.
In the talk, I will explain the construction of the hypoelliptic Laplacian, and describe some of its properties.
J.-M. Bismut. The hypoelliptic Laplacian on the cotangent bundle. J. Amer. Math. Soc., 18(2):379-476 (electronic), 2005.
J.-M. Bismut and G. Lebeau. The hypoelliptic Laplacian and Ray-Singer metrics, volume 167 of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ, 2008.
J.-M. Bismut. Loop spaces and the hypoelliptic Laplacian. Comm. Pure Appl. Math., 61(4):559-593, 2008.
J.-M. Bismut. Hypoelliptic Laplacian and orbital integrals, volume 177 of Annals of Mathematics Studies. Princeton University Press, Princeton, NJ, 2011.
Invited Honorary speaker
Daniel Bennequin (Université Paris 7 - Institut Mathématique de Jussieu)
Born 3 January 1952. Graduate from Ecole Normale Supérieure. PHD in 1982 with Alain Chenciner at Paris VII. Then Professor at Strasbourg University. Today Professor at Paris-Diderot University, and member of the IMJ. During the 1980’s he was initiator of contact topology with Y.Eliashberg. During the 1990’s, he worked on integrable systems and geometry of Mathematical Physics. Since 2000 he has been working in Neurosciences (mainly with A.Berthoz, C-d-F, and T.Flash, Weizmann Institute); he made contributions to the study of human movements duration, vestibular informatin flow and gaze functions during locomotion. His most recent publications are on information topology (with P.Baudot), psychic pain (with M.Bompard-Porte) and labyrinths (with R.David et al.).
Geometry and Vestibular Information
Every complex living entities, as plants, insects or vertebrates, possess visuo-vestibular systems which sense their own motion in space and are crucial for controling volontary movements and for understanding space. We will show how the Galilée group guides the visuo-vestibular information flows. Differential Geometry permits to understand the particular forms of the end vestibular organs, that are situated in the inner ear of mammals and birds, from a principle of energy minimization and information maximization. These forms correspond to the surfaces of divisors of real (resp. imaginary) twisted curves, for the epithelia which sense linear accelerations (resp. rotations) of the head. The Hodge-DeRham theory, applied to the labyrinths volume of vertebrates, permits to explain how a complex fluid movement is transformed in six solutions of ordinary second order differential equations, for registering the head rotations in space. Combined with an original and delicate method of analysis of the membranous tissues, invented by Romain David, this allows for the first time, to describe the precise relation between the structure and the function of the labyrinth.
R.David, A.Stoessel, A.Berthoz, F.Spoor, D.Bennequin, “Assessing morphology and function of the semicircular duct system: introducing new in situ visualization and software toolbox ”, Scientific Reports, 2016.
P.Marianelli, A.Berthoz, D.Bennequin, “Crista egregia: a geometrical model of the crista ampullaris, a sensory surface that detects head rotations”, Biological Cybernetics, 2015.
M.Dimiccoli, B.Girad, A.Berthoz, D.Bennequin, “Striola Magica. A functional explanation of the otolith geometry”, J Comput Neurosciences, 2013.
D.Bennequin, A.Berthoz, “Non-linear Galilean receptive fields”, IEEE Med Biol Soc, Boston, 2011
Alain Trouvé (ENS Paris-Saclay, CMLA Department)
Alain Trouvé, bachelor’s degree from Ecole Normale Supérieure Ulm, a doctor of the University of Orsay, began his career as “agrégé préparateur” at the ENS Ulm before becoming a professor at the University of Paris13 (1996) and then at ENS Cachan (2003). Alain Trouvé is currently Professor at the Center of Mathematics and Their Application (CMLA) at ENS Paris-Saclay. He did his Ph.D. in Stochastic Optimization and Bayesian Image Analysis under the supervision of Robert Azencott. His main research interests are computational vision and shape analysis with a particular emphasis on the use of Riemannian geometry and infinite dimensional group actions driven by applications in computational anatomy and medical imaging.
Hamiltonian modeling for shape evolution and Statistical modeling of shapes variability
In his book "Growth and Forms", first published in 1917, d’Arcy Thompson, a Scottish naturalist and mathematician, develops his theory of transformations, whose central idea is the morphological comparison of anatomies through groups of transformations of Space that act on it. This idea, a century later, remains at the heart of contemporary geometric approaches of quantitative comparison of forms but in a very different mathematical and technological context. In this talk, we present the ideas and techniques that underlie the "diffeomorphometric" approach developed in the context of computational anatomy, its links with infinite dimensional Riemannian geometry, the theory of control And Hamiltonian systems, but also the dimension reduction tools that underlie the algorithms used in the analysis of sub-varieties and make them effective. We will also present new prospects for extension on the geometric-functional objects that combine geometric and functional information and pose new and numerous challenges.
Devilliers, L., Allassonnière, S., Trouvé, A., & Pennec, X. (2017). Inconsistency of Template Estimation by Minimizing of the Variance/Pre-Variance in the Quotient Space. Entropy, 19(6), 288.
Lee, S., Charon, N., Charlier, B., Popuri, K., Lebed, E., Sarunic, M. V., ... & Beg, M. F. (2017). Atlas-based shape analysis and classification of retinal optical coherence tomography images using the functional shape (fshape) framework. Medical image analysis, 35, 570-581.
D. Tward, M. Miller, A. Trouvé and L. Younes, "Parametric Surface Diffeomorphometry for Low Dimensional Embeddings of Dense Segmentations and Imagery," in IEEE Transactions on Pattern Analysis and Machine Intelligence, vol. 39, no. 6, pp. 1195-1208, June 1 2017.
Charlier, B., Charon, N., & Trouvé, A. (2017). The fshape framework for the variability analysis of functional shapes. Foundations of Computational Mathematics, 17(2), 287-357.
M. Miller, L. Younes and A. Trouve. "Hamiltonian Systems in Computational Anatomy : 100 Years since D'Arcy Thompson". Annual Review of Biomedical Engineering 17 , 2015
S. Arguillere, E. Trélat, A. Trouvé, L. Younes. "Shape deformation analysis from the optimal control point of view". Journal de Mathématiques Pures et Appliquées 104 (1): 139-178, 2015
Mark Girolami (Imperial College London - Department of Mathematics)
Mark Girolami holds a Chair in Statistics in the Department of Mathematics of Imperial College London. He is an EPSRC Established Career Research Fellow (2012 - 2017) and previously an EPSRC Advanced Research Fellow (2007 - 2012). He is the Director of the Alan Turing Institute-Lloyds Register Foundation Programme on Data Centric Engineering and in 2011 was elected to the Fellowship of the Royal Society of Edinburgh when he was also awarded a Royal Society Wolfson Research Merit Award. He was one of the founding Executive Directors of the Alan Turing Institute for Data Science from 2015 to 2016. He has been nominated by the IMS to deliver a Medallion Lecture at JSM 2017 and has been invited to give a Forum Lecture at the European Meeting of Statisticians 2017. His paper on Riemann manifold Langevin and Hamiltonian Monte Carlo Methods was publicly read before the Royal Statistical Society and received the largest number of contributed discussions for any paper in the entire history of the society, discussants included Sir D.R. Cox and C.R. Rao.
Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods
The talk considers Metropolis adjusted Langevin and Hamiltonian Monte Carlo sampling methods defined on the Riemann manifold to resolve the shortcomings of existing Monte Carlo algorithms when sampling from target densities that may be high dimensional and exhibit strong correlations. The methods provide fully automated adaptation mechanisms that circumvent the costly pilot runs that are required to tune proposal densities for Metropolis–Hastings or indeed Hamiltonian Monte Carlo and Metropolis adjusted Langevin algorithms. This allows for highly efficient sampling even in very high dimensions where different scalings may be required for the transient and stationary phases of the Markov chain. The methodology proposed exploits the Riemann geometry of the parameter space of statistical models and thus automatically adapts to the local structure when simulating paths across this manifold, providing highly efficient convergence and exploration of the target density. The performance of these Riemann manifold Monte Carlo methods is rigorously assessed by performing inference on logistic regression models, log-Gaussian Cox point processes, stochastic volatility models and Bayesian estimation of dynamic systems described by non-linear differential equations. Substantial improvements in the time-normalized effective sample size are reported when compared with alternative sampling approaches.
Mike Betancourt, Simon Byrne, Sam Livingstone, and Mark Girolami (2016) "The Geometric Foundations of Hamiltonian Monte Carlo" to appear Bernoulli
Oates, C., Girolami, M. and Chopin, N. Control Functionals for Monte Carlo Integration. To appear Journal of Royal Statistical Society - Series B, 2017.
T.House, A.Ford, S.Lan, S. Bilson, E. Buckingham-Jeffery, M.A.Girolami. (August 2016) Bayesian Uncertainty Quantification for Transmissability of Influenza, Norovirus, and Ebola using Information Geometry. Journal of the Royal Society Interface, DOI: 10.1098/rsif.2016.0279
Shiwei Lan, Tan Bui-Thanh, Mike Christie, Mark Girolami (2016). Emulation of Higher-Order Tensors in Manifold Monte Carlo Methods for Bayesian Inverse Problems, Journal of Computational Physics Vol. 308, 81 - 101.
Bui, T. and Girolami, M. "Solving Large-Scale PDE-constrained Bayesian Inverse problems with Riemann Manifold Hamiltonian Monte Carlo", Inverse Problems, 30, 114014, doi:10.1088/0266-5611/30/11/114014.
T Xifara, C Sherlock, S Livingstone, S Byrne, M Girolami. Langevin diffusions and the Metropolis-adjusted Langevin algorithm. Statistics & Probability Letters 91, 14-19, 2014.
S Byrne, M Girolami. Geodesic Monte Carlo on Embedded Manifolds. Scandanavian Journal of Statistics, (with discussion) 40, 825 – 845, 2013.
Girolami, M., Calderhead, B., Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods (with discussion), Journal of the Royal Statistical Society – Series B, 73(2), 123 - 214, 2011.
Barbara Tumpach (Lille University/ Painlevé Laboratory)
Alice Barbara Tumpach is an Associate Professor in Mathematics (University Lille 1, France) and member of the Laboratoire Painlevé (Lille 1/CNRS UMR 8524), since 2007. She received a Ph.D degree in Mathematics in 2005 at the Ecole Polytechnique, Palaiseau, France. She spent two years at the Ecole Polytechnique Fédérale de Lausanne as a Post-Doc, and two years at the Pauli Institut in Vienna, Austria, as an invited researcher. Her research interests lie in the area of infinite-dimensional Geometry, Lie Groups and Functional Analysis. She gives Master courses on Lie groups and organizes conferences on infinite-dimensional geometry for the Federation of Mathematical Research of Nord-Pas-Calais, France. She also acts in videos for Exo7, available on youtube, where she explains basic notions of Linear Algebra.
Riemannian metrics on shape spaces of curves and surfaces
The aim of the talk is to give an overview of geometric tools used in Shape Analysis. We will see that we can interpret the Shape space of (unparameterized) curves (or surfaces) either as a quotient space or as a section of the Preshape space of parameterized curves (or surfaces). Starting from a diffeomorphism-invariant Riemannian metric on Preshape space, these two different interpretations lead to different Riemannian metrics on Shape space. Another possibility is to start with a degenerate Riemannian metric on Preshape space, with degeneracy along the orbits of the diffeomorphism group. This leads to a framework where the length of a path of curves (or surfaces) does not depend on the parameterizations of the curves (or surfaces) along the path. Of course the choice of the metrics has to be motivated either from the applications or from their mathematical behaviour. We will compare some natural metrics used in the litterature.
A.B.Tumpach and S. Preston, Quotient elastic metrics on the manifold of arc-length parameterized plane curves, to appear in Journal of Geometric Mechanics.
A.B.Tumpach, Gauge invariance of degenerate Riemannian metrics, Notices of AMS, April 2016.
A.B.Tumpach, H. Drira, M. Daoudi, A. Srivastava, Gauge invariant Framework for shape analysis of surfaces, IEEE TPAMI, vol 37, 2015.
A.B.Tumpach, Infinite-dimensional hyperkähler manifolds associated with Hermitian-symmetric affine coadjoint orbits, Annales de l'Institut Fourier, Tome 59, 2009.
A.B.Tumpach, Classification of infinite-dimensional Hermitian-symmetric affine coadjoint orbits, Forum Mathematicum 21:3, 2009.
D. Beltita, T. Ratiu, A.B. Tumpach, The restricted Grassmannian, Banach Lie-Poisson spaces, and coadjoint orbits, Journal of Functional Analysis 247, 2007.
A.B.Tumpach, Hyperkähler structures and infinite-dimensional Grassmannians, Journal of Functional Analysis 243, 2007.