Caterina Campagnolo (Universitad Autónoma de Madrid)
Un nouveau critère d\'annulation pour la cohomologie bornée abstract
Abstract:
La définition de la cohomologie bornée des groupes remonte à Johnson et Gromov. C\'est un invariant puissant, mais qui demeure difficile à calculer audelàdes groupes moyennables.Dans un travail en commun avec Francesco Fournier-Facio, Yash Lodha et Marco Moraschini, nous présentons une nouvelle condition algébrique qui implique l\'annulation de la cohomologie bornée d\'un groupe pour une grande classe de coefficients. Cette condition est satisfaite par de nombreux groupes non-moyennables d\'origine topologique et dynamique.
10:30 • Université de Genève, Conseil Général 7-9, Room 1-05
Joackim Bernier (Université de Nantes)
Numerical integration of the nonlinear Klein-Gordon equations at low regularity and conservation properties abstract
Abstract:
Close to the origin, the nonlinear Klein--Gordon equations on the circle are nearly integrable Hamiltonian systems which have infinitely many almost conserved quantities called "harmonic energies" or "super-actions". In a series of works in 2008, D. Cohen, E. Hairer and C. Lubich proved that, at high regularity, classical symplectic numerical integrators preserve this qualitative property (even if the CFL number is not small). I will present a joint work with C. Abou Khalil (in progress), in which we extend this result for non-smooth solutions.
14:00 • Université de Genève, Conseil Général 7-9, Room 1-05
Sagnik Nandy (UPenn)
Orchestrated Approximate Message Passing: A New Way of Information Integration from Multimodal Data abstract
Abstract:
Integrating information from multiple correlated datasets is a crucial aspect of modern data science. Despite the existence of numerous methods for this purpose, their statistical properties remain unclear, making valid statistical inference challenging. In this talk, I shall introduce Orchestrated Approximate Message Passing for integrating information across multiple correlated datasets. This method is both computationally efficient and statistically optimal under certain stylized models. Subsequently, I shall show how to apply this technique to tackle two distinct problems, namely community detection in a balanced, two-community, contextual stochastic block model and compressed sensing in the presence of network-side information.
14:15 • EPF Lausanne, GA 3 21
Prof. Dr. Richard Sowers (University of Illinois Urbana-Champaign)
Lateral boundary conditions for a Kolmogorov-type PDE abstract
Abstract:
We consider a hypoelliptic Kolmogorov-type PDE corresponding to a particle under white noise force. We are interested in imposing Dirichlet conditions at a side boundary. We construct a simple Gaussian heat kernel inside the domain, and investigate a boundary-layer kernel. We show that this boundary layer heat kernel has a novel jump condition. We outline a polynomial expansion of the heat kernels, and then construct a Volterra equation.This Volterra equation has a periodic structure resulting from the novel jump condition.
15:15 • ETH Zentrum, Rämistrasse 101, Zürich, Building HG, Room G 43
Allan Peter Engsig-Karup (DTU)
High-Order Numerical Methods for Nonlinear Free Surface Wavesand Wave-Structure Interaction for Engineering Applications abstract
Abstract:
Advances in numerical simulation and modelling fidelity of water waves go in hand with continued improvements in computational resources, improving the efficiency ofnumerical algorithms and the adoption of modern and emerging many-core hardware for massively parallel computations. We discuss trends in scientific computing and link these to recent research in addressing scientific gaps to be able to address nonlinear wave and wave-structure interaction problems through designing new high-order numerical schemes for both nonlinear and dispersive wave propagation and nonlinear wave-structure interaction based on potential flow theory and more recently also Navier-Stokes modelling. Through simple benchmarks of increasing complexities ourresearch targetimprovements in numerical efficiencythrough accelerated iterative solver strategies based on defect corrections / multigrid preconditioning, simulation at large spatial scales in practical times and with ability to handlethe geometric complexities ofoffshore structures and marine environments in simulations. Highlights are given from our research spanning nearly adecade with scopes towards engineering applications of high relevance for renewablesapplications.Historically, and perhaps surprisingly, spectral element methods appear to have been somewhat ‘overlooked’ in world-wide research for marine hydrodynamics applications. We therefore given an overview of key scientific developments and benchmarks, and discuss some of the pros and cons, as well as the recent years progress on advancing theuse of high-order numerical schemes such as spectral element methods for free surface flows.
16:15 • EPF Lausanne, GA 3 21
Prof. Dr. Ivan Smith (University of Cambridge)
New directions in floer theory
16:30 • ETH Zentrum, Building KO, Room F 150
Frank Kutzschebauch (Uni Bern)
Factorization of Holomorphic Matrices abstract
Abstract:
Every complex symplectic matrix in Sp2npCq can be factorized as aproduct of the following types of unipotent matrices (in interchangingorder).‚ (i): ˆI B0 I˙, upper triangular with symmetric B “ BT.‚ (ii): ˆI 0C I˙, lower triangular with symmetric C “ CT.The optimal number TpCq of such factors that any matrix in Sp2npCqcan be factored into a product of T factors has recently been establishedto be 5 by Jin, P. Lin, Z. and Xiao, B.If the matrices depend continuously or holomorphically on a parameter, equivalently their entries are continuous functions on a topologicalspace or holomorphic functions on a Stein space X, it is by no meansclear that such a factorization by continuous/holomorphic unipotentmatrices exists. A necessary condition for the existence is the mapX Ñ Sp2npCq to be null-homotopic. This problem of existence of afactorization is known as the symplectic Vaserstein problem or GromovVaserstein problem. In this talk we report on the results of the speakerand his collaborators B. Ivarsson, E. Low and of his Ph.D. student J.Schott on the complete solution of this problem, establishing uniformbounds Tpd, nq for the number of factors depending on the dimensionof the space d and the size n of the matrices. It seems difficult to establish the optimal bounds. However we obtain results for the numbersTp1, nq, Tp2, nq for all sizes of matrices in joint work with our Ph.D.students G. Huang and J. Schott. Finally we give an application tothe problem of writing holomorphic symplectic matrices as product of exponentials.
17:15 • Université de Fribourg, room Phys 2.52