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SUMMARY:Sections as a Computational Tool in Invariant Theory
DTSTART:20260604T120000Z
DTEND:20260604T130000Z
DTSTAMP:20260501T211700Z
UID:indico-event-16378@indico.math.cnrs.fr
DESCRIPTION:Speakers: Evelyne Hubert (Inria)\n\nInvariants are essential f
 or classifying mathematical objects up to a group of transformations. This
  talk will review several constructions of rational invariants where a sec
 tion to the orbits is an essential ingredient for tractable computations.\
 nWe will start with a general construction to obtain a generating set for 
 the field of invariants. The output of the algorithm further provides rewr
 ite rules so that any other invariants can be written explicitly as a rati
 onal function of the generating invariants. \nIn the case of linear actio
 ns of a torus - a.k.a. scalings - one can determine a section with a singl
 e point of intersection with most orbits. Furthermore this rational sectio
 n\, the generating rational invariants and the rewrite rules  can all be 
 computed with  linear algebra over the integers. This has application in 
 parameter reduction in mathematical models.\nAnother type of sections that
  proved relevant in a computational context are Seshadri slices. The ratio
 nal invariants are then characterized uniquely by their restriction to the
  slice\,  and these restrictions are invariants of a subgroup. This allow
 s to address actions of the orthogonal group relevant to applications\, ex
 hibiting mininal generating set of invariants\, how to evaluate them and e
 xamine their separation properties. \nThe material presented in this talk
  is based on the results of collaborations with Irina Kogan (North Carolin
 a State University)\, George Labahn (University of Waterloo)\, Paul Görla
 ch  (Otto von Guericke University Magdeburg) and Martin Jalard (Inria Cô
 te d'Azur).\n\nhttps://indico.math.cnrs.fr/event/16378/
LOCATION:Salle Pellos (1R2 - 207) (IMT)
URL:https://indico.math.cnrs.fr/event/16378/
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