Ομιλητής : Γεώργιος Κοτσόβολης, Princeton University.
Ημερομηνία : Δευτέρα, 22 Απριλίου, 2024.
Ώρα : 16:00.
Μέρος : Αίθουσα Σεμιναρίων (225) του Τομέα Μαθηματικών ΣΕΜΦΕ, κτ. Ε΄, 2ος όροφος
Τίτλος : “The infima of binary forms“
Abstract : ”For a binary form P(x,y) of non-zero discriminant and for a two dimensional lattice Λ of volume 1, what is the infimum of the values P attains on the non-trivial vectors of Λ? The spectrum of a binary form P is defined to be the set of these infima as Λ ranges over all unimodular lattices. Understanding this object is a fundamental project in the geometry of numbers and even though the case of n=2 is well understood, much less is known for higher degrees. In 1940, Mordell conjectured that for a binary cubic form P, the spectrum of P has a gap after its maximal value, a statement disproved later by Davenport, who constructed a sequence of infima converging to the top. As for n greater than 3, there has been, to our knowledge, no progress to understanding these spectra. In this talk, we show that for any binary form P, the spectrum of P is an interval, answering the problem for all degrees n.”
Το πρόγραμμα του σεμιναρίου για το ακαδημαϊκό έτος 2023-24 βρίσκεται στη διεύθυνση: https://sites.google.com/view/analysis-seminar-samps/