BEGIN:VCALENDAR
VERSION:2.0
PRODID:researchseminars.org
CALSCALE:GREGORIAN
X-WR-CALNAME:researchseminars.org
BEGIN:VEVENT
SUMMARY:Noah Kravitz (Princeton University)
DTSTART:20220525T193000Z
DTEND:20220525T195500Z
DTSTAMP:20260423T011437Z
UID:CANT2022/27
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/CANT2022/27/
 ">Zero patterns of derivatives of polynomials</a>\nby Noah Kravitz (Prince
 ton University) as part of Combinatorial and additive number theory (CANT 
 2022)\n\n\nAbstract\nMotivated by recent work of Nathanson\, we study the 
 zero patterns of derivatives of polynomials.  For $P$ a polynomial of degr
 ee $n$ and $\\Lambda=(\\lambda_1\, \\ldots\, \\lambda_m)$ an $m$-tuple of 
 distinct complex numbers\, we consider the $m \\times (n+1)$ \\emph{dope m
 atrix} $D_P(\\Lambda)$ whose $ij$-entry equals $1$ if $P^{(j)}(\\lambda_i)
 =0$ and equals $0$ otherwise (for $1 \\leq i \\leq m$\, $0 \\leq j \\leq n
 $).  We address several natural questions: When $m$ is $1$ or $2$\, what d
 o the possible dope matrices look like\, and how many are there?  What can
  we say about general upper bounds on the number of $m \\times (n+1)$ dope
  matrices?  For which $m$-tuples $\\Lambda$ is the number of $m \\times (n
 +1)$ dope matrices maximized?  Does every $\\{0\,1\\}$-matrix appear as th
 e left-most portion of some dope matrix?  \n\nBased on joint work with Nog
 a Alon and Kevin O'Bryant.\n
LOCATION:https://researchseminars.org/talk/CANT2022/27/
END:VEVENT
END:VCALENDAR