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Workshop on tensors and interpolation |
Organisators: P. Comon, B. Mourrain, C. Simpson
Tensors appear in many problems in computer science and mathematics. The most famous family of tensors is certainly the family of matrices to which a huge amount of work has already been devoted. But there is nowadays an increasing interest in higher order tensors, since they show up in many applications: Statistics, Electrical engineering, Antenna Array Processing, Telecommunications, Chemometrics, Psychometrics, Data Analysis. Independent Component Analysis, Shape analysis, Complexity theory ... From a theoretical point of view, their study is also raising interesting and still unsolved problems connected to interpolation problems, Hilbert schemes, Secant varieties, Gorenstein Algebra, ... Tensor algebra plays an important role in modern algebraic topology, deformation theory, and the theory of operads.
The focus of this workshop is on higher order tensors such as symmetric tensors known as polynomials, antisymetric or tensors associated with general multilinear operators and its dual view via interpolation problems. In parallel the role of tensor algebras in algebraic topology will be explored, with an eye towards the interactions between these subjects.
More specifically but non-exhaustively, the topics include
tensors analysis
rank determination and decomposition,
multivariate interpolation problems,
approximation problems,
geometric and algebraic properties of tensors,
related algorithmic issues,
applications related to higher order tensors.
operads over monoidal categories,
Batalin-Vilkovisky algebras and deformation theory,
Koszul duality,
definition of tensors over subfields,
...
Tentative list of speakers:
J. M. Landsberg.
G. Ottaviani
A. Hirschowitz
C. Walter
P. Cassam-Chenaï
A. Dickenstein
J.-L. Loday
B. Tsygan
A. Hirotachi
M. Rosas
E. Briand
...
Programme: in preparation
Participation:
For participation, please go to the preregistration page.
To confirm you participation, visit the confirmation page
For a presentation, send a title and abstract to one of the organisators, before May 15th 2009.
No registration fee.
We have reserved a group of rooms at the hotel Monsigny (at a negociated price). If you are interested by this option, please contact us and indicating your arrival and departure dates.
How to reach the workshop meeting:
The lectures will take place at the Lab. J.A. Dieudonné, Mathematics Dep., University of Nice, in the main conference room (building W below):
For more details, see here or here.
Support: ANR DESCOTES 06-BLAN-0074