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SUMMARY:Lisa Sauermann (IAS)
DTSTART:20210129T140000Z
DTEND:20210129T150000Z
DTSTAMP:20260423T020958Z
UID:WCS/17
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/WCS/17/">On 
 polynomials that vanish to high order on most of the hypercube</a>\nby Lis
 a Sauermann (IAS) as part of Warwick Combinatorics Seminar\n\n\nAbstract\n
 Motivated by higher vanishing multiplicity generalizations of Alon's Combi
 natorial Nullstellensatz and its applications\, we study the following pro
 blem: for fixed k and n large with respect to $k$\, what is the minimum po
 ssible degree of a polynomial $P$ in $R[x_1\,...\,x_n]$ such that $P(0\,
 …\,0)$ is non-zero and such that P has zeroes of multiplicity at least $
 k$ at all points in $\\{0\,1\\}^n$ except the origin? For $k=1$\, a classi
 cal theorem of Alon and Füredi states that the minimum possible degree of
  such a polynomial equals $n$. We solve the problem for all $k>1$\, provin
 g that the answer is $n+2k−3$. Joint work with Yuval Wigderson.\n
LOCATION:https://researchseminars.org/talk/WCS/17/
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