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Speaker:

Vita Kala
Affiliation:

Charles University, Prague
Date:

Mon, 2020-03-02 14:00 - 14:50
Location:

MPIM Lecture Hall
Parent event:

Number theory lunch seminar I will talk about several recent results on universal quadratic forms over rings of integers of totally real number fields (i.e., totally positive quadratic forms that represent all totally positive integers). Over real quadratic fields, one can obtain a fairly precise information concerning the smallest rank of a universal form in terms of the associated continued fraction; in particular, the rank can be arbitrarily large. Things are much more complicated in the higher degree case, but I will also discuss some partial results, e.g., related to the (non)existence of universal forms whose coefficients are rational integers.

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