BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Annie Carter (UCSD)
DTSTART:20220303T170000Z
DTEND:20220303T180000Z
DTSTAMP:20260423T022834Z
UID:UCSD_NTS/58
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/UCSD_NTS/58/
 ">Two-variable polynomials with dynamical Mahler measure zero</a>\nby Anni
 e Carter (UCSD) as part of UCSD number theory seminar\n\n\nAbstract\nIntro
 duced by Lehmer in 1933\, the classical Mahler measure of a complex ration
 al function $P$ in one or more variables is given by integrating $\\log|P(
 x_1\, \\ldots\, x_n)|$ over the unit torus. Lehmer asked whether the Mahle
 r measures of integer polynomials\, when nonzero\, must be bounded away fr
 om zero\, a question that remains open to this day. In this talk we genera
 lize Mahler measure by associating it with a discrete dynamical system $f:
  \\mathbb{C} \\to \\mathbb{C}$\, replacing the unit torus by the $n$-fold 
 Cartesian product of the Julia set of $f$ and integrating with respect to 
 the equilibrium measure on the Julia set. We then characterize those two-v
 ariable integer polynomials with dynamical Mahler measure zero\, condition
 al on a dynamical version of Lehmer's conjecture.\n
LOCATION:https://researchseminars.org/talk/UCSD_NTS/58/
END:VEVENT
END:VCALENDAR