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SUMMARY:Noy Soffer Aranov (Technion)
DTSTART:20231026T161500Z
DTEND:20231026T173000Z
DTSTAMP:20260423T021928Z
UID:NEDNT/63
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/63/">C
 overing Radii in Positive Characteristic</a>\nby Noy Soffer Aranov (Techni
 on) as part of New England Dynamics and Number Theory Seminar\n\nLecture h
 eld in Online.\n\nAbstract\nA fascinating question in geometry of number p
 ertains to the covering radius of lattice with respect to an interesting f
 unction. For example\, given a convex body C and a lattice L in R^d\, it i
 s interesting to ask what is the infimal r ≥ 0 such that L + rC = R^d. A
 nother interesting covering radius is the multiplicative covering radius\,
  which connects to dynamics due to its invariance under the diagonal group
 . It was conjectured by Minkowski that the multiplicative covering radius 
 is bounded above by 2^{-d} and that this upper bound is obtained only on A
 Z^d. In this talk I will discuss surprising results pertaining to covering
  radii in the positive characteristic setting and discover several surpris
 ing results. Some of my results include explicitly connecting between the 
 covering radii with respect to convex bodies and successive minima and pro
 ving a positive characteristic analogue of Minkowski’s function.\n
LOCATION:https://researchseminars.org/talk/NEDNT/63/
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