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SUMMARY:Irving Calderón (Université Paris-Saclay)
DTSTART:20220303T171500Z
DTEND:20220303T183000Z
DTSTAMP:20260423T021859Z
UID:NEDNT/41
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/41/">S
 -adic quadratic forms and Homogeneous Dynamics</a>\nby Irving Calderón (U
 niversité Paris-Saclay) as part of New England Dynamics and Number Theory
  Seminar\n\nLecture held in Online.\n\nAbstract\nWe present two new quanti
 tative results about quadratic forms.\nLet $S = {\\infty} \\cup S_f$ be a 
 finite set of places of Q. Consider the ring $Z_S$ of S-integers\, and $Q_
 S = \\prod{p \\in S} Q_p$. The first is a solution to the problem of decid
 ing if any given integral quadratic forms $Q_1$ and $Q_2$ are $Z_S$-equiva
 lent. The proof is based on a reformulation of the problem in terms of the
  action of $O(Q_1\, Q_S)$ on the space $X{d\,S}$ of lattices of $Q_{S\,d}$
 . A key tool are explicit mixing rates for the action of O(Q1\, QS) on clo
 sed orbits in X{d\,S}. As an application we obtain\, for any S-integral or
 thogonal group\, polynomial bounds on the S-norms of the elements of a fin
 ite generating set.\nThese two results and the methods of proof are based 
 on the work of H. Li and G. Margulis for $S = { \\infty }$.\n
LOCATION:https://researchseminars.org/talk/NEDNT/41/
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