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Documents  Szanto, Agnes | enregistrements trouvés : 4

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Research talks;Computer Science

Classical invariant theory has essentially addressed the action of the general linear group on homogeneous polynomials. Yet the orthogonal group arises in applications as the relevant group of transformations, especially in 3 dimensional space. Having a complete set of invariants for its action on ternary quartics, i.e. degree 4 homogeneous polynomials in 3 variables, is, for instance, relevant in determining biomarkers for white matter from diffusion MRI.
We characterize a generating set of rational invariants of the orthogonal group acting on even degree forms by their restriction on a slice. These restrictions are invariant under the octahedral group and their explicit formulae are given compactly in terms of equivariant maps. The invariants of the orthogonal group can then be obtained in an explicit way, but their numerical evaluation can be achieved more robustly using their restrictions. The exhibited set of generators futhermore allows us to solve the inverse problem and the rewriting.
Central in obtaining the invariants for higher degree forms is the preliminary construction, with explicit formulae, for a basis of harmonic polynomials with octahedral symmetry, dif- ferent, though related, to cubic harmonics.
This is joint work with Paul Görlach (now at MPI Leipzig), in a joint project with Téo Papadopoulo (Inria Méditerranée).
Classical invariant theory has essentially addressed the action of the general linear group on homogeneous polynomials. Yet the orthogonal group arises in applications as the relevant group of transformations, especially in 3 dimensional space. Having a complete set of invariants for its action on ternary quartics, i.e. degree 4 homogeneous polynomials in 3 variables, is, for instance, relevant in determining biomarkers for white matter from ...

05E05 ; 13A50 ; 13P10 ; 68W30 ; 92C55

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- x; 238 p.
ISBN 978-1-107-60407-0

London mathematical society lecture note series , 0403

Localisation : Collection 1er étage

analyse numérique # traitement de données

00B25 ; 20B40 ; 57N25 ; 65-06 ; 76D05

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Research talks

41A50 ; 43A25 ; 34A34 ; 34A26 ; 65L05 ; 65L06 ; 65Txx

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Research talks

Many PDEs arising in physical systems have symmetries and conservation laws that are local in space. However, classical finite element methods are described in terms of spaces of global functions, so it is difficult even to make sense of such local properties. In this talk, I will describe how hybrid finite element methods, based on non-overlapping domain decomposition, provide a way around this local-vs.-global obstacle. Specifically, I will discuss joint work with Robert McLachlan on multisymplectic hybridizable discontinuous Galerkin methods for Hamiltonian PDEs, as well as joint work with Yakov Berchenko-Kogan on symmetry-preserving hybrid finite element methods for gauge theory. Many PDEs arising in physical systems have symmetries and conservation laws that are local in space. However, classical finite element methods are described in terms of spaces of global functions, so it is difficult even to make sense of such local properties. In this talk, I will describe how hybrid finite element methods, based on non-overlapping domain decomposition, provide a way around this local-vs.-global obstacle. Specifically, I will ...

65N30 ; 37K05

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