CIRM - Videos & books LibraryDocuments

Déposez votre fichier ici pour le déplacer vers cet enregistrement.

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 ...

Documents

Thesaurus

Revues

Documents 13P10 | enregistrements trouvés : 50

Invariants of ternary forms under the orthogonal group Hubert, Evelyne | CIRM H Nouveau

Software for algebraic geometry:papers of a workshopMinneapolis#october 23-27, 2006 Stillman, Michael E. ; Takayama, Nobuki ; Verschelde, Jan | Springer 2008 Nouveau

Advances in algebraic geometry motivated by physics :AMS special session on enumerative geometry in physics held at the University of Massachusetts#April 1-2 Previato, Emma | American Mathematical Society 2001 Nouveau

Finite fields and applications:international conference#July 9-13 Mullen, Gary L. ; Panario, Daniel ; Shparlinski, Igor E. | Amercian Mathematical Society 2008 Nouveau

Eléments de la théorie des systèmes différentiels géométriques :cours du C.I.M.P.A., école d'été Maisonobe, Philippe ; Narvaez Macarro, Luis | Société Mathématique de France 2004 Nouveau

Trends in optimization :AMS short course#Janv. 5-6 Hosten, Serkan ; Lee, Jon ; Thomas Rekha R. | American Mathematical Society 2004 Nouveau

Affine algebraic geometry :special session on affine algebraic geometry at the first joint AMS-RSME meeting#June 18-21 Gutierrez, Jaime ; Shpilrain, Vladimir ; Yu, Jie-Tai | American Mathematical Society 2005 Nouveau

Algorithmic algebra and number theoryselected papers from a conference held at the University of Heidelberg Oct. Greuel, Gert-Martin ; Hiss, Gerhard ; Matzat, B. Heinrich | Springer 1999 Nouveau

Computer algebra in scientific computing casc'99Proceedings of the second workshop on computer algebra in scientific computing, munich, may 31-june 4, 1999 Ganzha Victor G. ; Mayr, Ernst W. ; Vorozhtsov Evgenii V. | Springer-Verlag 1999 Nouveau

Combinatorial Aspects of Commutative Algebra : Exploratory Workshop on Combinatorial Commutative Algebra and Computer AlgebraMangalia # May 29-31, 2008 Ene, Viviana ; Miller, Ezra | American Mathematical Society 2009 Nouveau

Geometric methods in representation theory, IIGrenoble # june 16 - july 4, 2008 Brion, Michel | Société Mathématique de France 2012 Nouveau

Monomial ideals, computations and applications.Based on lectures of the conference MONICA: monomial ideals, computations and applicationsCastro Urdiales # july 2011 Bigatti, Anna M. ; Gimenez, Philippe ; Saenz-de-Cabezon, Eduardo | Springer 2013 Nouveau

Integer points in polyhedra-geometry, number theory, representation theory, algebra, optimization, statistics :AMS-IMS-SIAM joint summer research conference#June 11-15 Beck, Matthias ; Haase, Christian ; Reznick, Bruce ; Vergne , Michele | Amercian Mathematical Society 2008 Nouveau

Integer points in polyhedra-geometry, number theory, algebra, optimization :proceedings of an AMS-IMS-SIAM joint summer research conference on integer points in polyhedra#July 13-17 Barvinok, Alexander ; Beck, Matthias ; Haase, Christian ; Reznick, Bruce | American Mathematical Society 2005 Nouveau

Constructive commutative algebra : projective modules over polynomial rings and dynamical Gröbner bases Yengui, Ihsen | Springer 2015 Nouveau

Monomial algebras Villarreal, Rafael H. | CRC Press 2015 Nouveau

Computational methods in commutative algebra and algebraic geometry Vasconcelos, Wolmer V. ; Eisenbud, David ; Grayson, Daniel R. ; Herzog, Jürgen | Springer 1998 Nouveau

Lectures in geometric combinatorics Thomas Rekha R. | American Mathematical Society 2006 Nouveau

Algebraic statistics Sullivant, Seth | American Mathematical Society 2018 Nouveau

Filtrer

Type

Domaine

Codes MSC

Documents

Références

Auteurs

Thesaurus

Software for algebraic geometry:
papers of a workshop
Minneapolis#october 23-27, 2006 Stillman, Michael E. ; Takayama, Nobuki ; Verschelde, Jan | Springer 2008 Nouveau

Advances in algebraic geometry motivated by physics :
AMS special session on enumerative geometry in physics held at the University of Massachusetts#April 1-2 Previato, Emma | American Mathematical Society 2001 Nouveau

Finite fields and applications:
international conference#July 9-13 Mullen, Gary L. ; Panario, Daniel ; Shparlinski, Igor E. | Amercian Mathematical Society 2008 Nouveau

Eléments de la théorie des systèmes différentiels géométriques :
cours du C.I.M.P.A., école d'été Maisonobe, Philippe ; Narvaez Macarro, Luis | Société Mathématique de France 2004 Nouveau

Trends in optimization :
AMS short course#Janv. 5-6 Hosten, Serkan ; Lee, Jon ; Thomas Rekha R. | American Mathematical Society 2004 Nouveau

Affine algebraic geometry :
special session on affine algebraic geometry at the first joint AMS-RSME meeting#June 18-21 Gutierrez, Jaime ; Shpilrain, Vladimir ; Yu, Jie-Tai | American Mathematical Society 2005 Nouveau

Algorithmic algebra and number theory
selected papers from a conference held at the University of Heidelberg
Oct. Greuel, Gert-Martin ; Hiss, Gerhard ; Matzat, B. Heinrich | Springer 1999 Nouveau

Computer algebra in scientific computing casc'99
Proceedings of the second workshop on computer algebra in scientific computing, munich, may 31-june 4, 1999 Ganzha Victor G. ; Mayr, Ernst W. ; Vorozhtsov Evgenii V. | Springer-Verlag 1999 Nouveau

Combinatorial Aspects of Commutative Algebra :
Exploratory Workshop on Combinatorial Commutative Algebra and Computer Algebra
Mangalia # May 29-31, 2008 Ene, Viviana ; Miller, Ezra | American Mathematical Society 2009 Nouveau

Geometric methods in representation theory, II
Grenoble # june 16 - july 4, 2008 Brion, Michel | Société Mathématique de France 2012 Nouveau

Monomial ideals, computations and applications.
Based on lectures of the conference MONICA: monomial ideals, computations and applications
Castro Urdiales # july 2011 Bigatti, Anna M. ; Gimenez, Philippe ; Saenz-de-Cabezon, Eduardo | Springer 2013 Nouveau

Integer points in polyhedra-geometry, number theory, representation theory, algebra, optimization, statistics :
AMS-IMS-SIAM joint summer research conference#June 11-15 Beck, Matthias ; Haase, Christian ; Reznick, Bruce ; Vergne , Michele | Amercian Mathematical Society 2008 Nouveau