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UID:9068@i2m.univ-amu.fr
DTSTART;TZID=Europe/Paris:20260416T110000
DTEND;TZID=Europe/Paris:20260416T120000
DTSTAMP:20260405T071413Z
URL:https://www.i2m.univ-amu.fr/evenements/invariants-of-ternary-quartics-
 under-the-action-of-the-orthogonal-group/
SUMMARY:Evelyne Hubert (Inria Côte d’Azur): Invariants of ternary quarti
 cs under the action of the orthogonal group
DESCRIPTION:Evelyne Hubert: Invariants are essential for classifying mathem
 atical objects up to a group of transformations. For a compact Lie group\,
  there is always a finite set of polynomial invariants that separate the o
 rbits. Yet such a set is challenging to compute and can have high cardinal
 ity.Motivated by an application to neuroimaging\, we consider here the rep
 resentation of the group O3(R) on the space of ternary quartics R[x\,y\,z]
 _4. We characterize generating and separating sets of rational invariants 
 by their restrictions to a Seshadri slice. These restrictions are invarian
 t under O2(R) or the octahedral group. Their explicit formulae are given b
 y trinomials. The invariants of O3(R) acting on R[x\,y\,z]_4 can then be o
 btained in an explicit way\, but their numerical evaluation can be achieve
 d more robustly using their restrictions. The exhibited set of invariants 
 futhermore allows us to solve the inverse problem\, i.e. find a quartic wi
 th prescribed invariants\, and the rewriting of any invariants in terms of
  the generators.
CATEGORIES:Séminaire,AGLR,Arithmétique et Théorie de l’Information
LOCATION:I2M Luminy - TPR2\, Amphithéâtre Herbrand 130-134 (1er étage)\,
  163 Avenue de Luminy\, Marseille\, 13009\, France
X-APPLE-STRUCTURED-LOCATION;VALUE=URI;X-ADDRESS=163 Avenue de Luminy\, Mars
 eille\, 13009\, France;X-APPLE-RADIUS=100;X-TITLE=I2M Luminy - TPR2\, Amph
 ithéâtre Herbrand 130-134 (1er étage):geo:0,0
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DTSTART:20260329T030000
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