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SUMMARY:Shagnik Das (National Taiwan University)
DTSTART:20231011T060000Z
DTEND:20231011T070000Z
DTSTAMP:20260423T035912Z
UID:MAC8028/8
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/MAC8028/8/">
 Covering grids with multiplicity</a>\nby Shagnik Das (National Taiwan Univ
 ersity) as part of Trends in Mathematical Research\n\nLecture held in NTNU
  Gongguan S101.\n\nAbstract\nIt is a fairly simple exercise to determine t
 he minimum number of hyperplanes needed to cover all the points of a finit
 e grid $S_1$ x $S_2$ x ... x $S_d \\in \\mathbb{F}^d$. However\, the situa
 tion becomes much more complex if you add the condition that one of the po
 ints of the grid must be avoided\, leading to a classic problem in combina
 torial geometry. This was resolved by Alon and Füredi in a classic result
  that popularised the use of algebraic methods in combinatorics.\n\nRecent
  work of Clifton and Huang\, in which they considered the question a varia
 nt of the problem where the nonzero points of a hypercube should be covere
 d multiple times while avoiding the origin\, brought renewed interest to t
 his problem. In addition to Alon-Füredi-style algebraic arguments\, they 
 used linear programming to asymptotically resolve the problem in certain r
 anges.\n\nDespite all the attention this problem has received\, there rema
 in many open problems\, even in the case of two-dimensional grids over $\\
 mathbb{R}$. In this talk\, after surveying the background and introducing 
 the techniques used\, we shall present some recent results that resolve th
 e problem for almost all two-dimensional grids.\n\nThe new results are joi
 nt work with Anurag Bishnoi\, Simona Boyadzhiyska and Yvonne den Bakker\, 
 and separately with Valjakas Djaljapayan\, Yen-Chi Roger Lin and Wei-Hsuan
  Yu.\n
LOCATION:https://researchseminars.org/talk/MAC8028/8/
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