Σας προσκαλούμε στη διάλεξη του Γεωργίου Κοτσόβολη, Princeton University, η οποία θα πραγματοποιηθεί τη Δευτέρα 22 Απριλίου 2024 & ώρα 16:00.
Τίτλος: The infima of binary forms
Περίληψη: 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.
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