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SUMMARY:Lisa Sauermann (Stanford University)
DTSTART:20201019T140000Z
DTEND:20201019T150000Z
DTSTAMP:20260423T052449Z
UID:EPC/25
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/EPC/25/">On 
 polynomials that vanish to high order on most of the hypercube</a>\nby Lis
 a Sauermann (Stanford University) as part of Extremal and probabilistic co
 mbinatorics webinar\n\n\nAbstract\nMotivated by higher vanishing multiplic
 ity generalizations of Alon's Combinatorial Nullstellensatz and its applic
 ations\, we study the following problem: for fixed k and n large with resp
 ect to k\, what is the minimum possible 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 o
 f multiplicity at least k at all points in ${0\,1}^n$ except the origin? F
 or k=1\, a classical theorem of Alon and Füredi states that the minimum p
 ossible degree of such a polynomial equals n. We solve the problem for all
  k>1\, proving that the answer is n+2k−3. Joint work with Yuval Wigderso
 n.\n
LOCATION:https://researchseminars.org/talk/EPC/25/
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