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SUMMARY:Gröbner bases in the free algebra: Introduction & advanced topics
DTSTART:20230112T103000Z
DTEND:20230112T113000Z
DTSTAMP:20241010T052100Z
UID:indico-event-9077@indico.math.cnrs.fr
DESCRIPTION:Speakers: Clemens Hofstadler\n\nGröbner bases have become a f
undamental and multi-purpose tool in computational algebra. Originally int
roduced to answer questions about ideals of multivariate (commutative) pol
ynomials\, they were subsequently generalized to several noncommutative se
ttings\, including noncommutative polynomials in the free algebra. We pres
ent the main constructions andresults of the theory of Gröbner bases in t
his setting and give several applications. We will see a lot of similariti
es but also some crucial differences tothe commutative case. Additionally\
, we touch on some advanced topics in the field of noncommutative Gröbner
bases\, that\, on the one hand\, aim atimproving the efficiency of comput
ations\, and\, on the other hand\, expand the applicability of the theory.
More precisely\, we discuss linear algebra reductions (as known from the
F4 algorithm)\, signature-based algorithms (such as F5 or GVW)\, and Gröb
ner bases in free algebras over coefficient rings.\n\nhttps://indico.math.
cnrs.fr/event/9077/
LOCATION:XR203 (XLIM)
URL:https://indico.math.cnrs.fr/event/9077/
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