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SUMMARY:Sam Chow (Warwick)
DTSTART:20240924T161500Z
DTEND:20240924T173000Z
DTSTAMP:20260423T021828Z
UID:NEDNT/76
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/NEDNT/76/">S
 mooth discrepancy and Littlewood’s conjecture</a>\nby Sam Chow (Warwick)
  as part of New England Dynamics and Number Theory Seminar\n\nLecture held
  in Online.\n\nAbstract\nGiven \\boldsymbol \\alpha \\in [0\,1]^d\, we est
 imate the smooth discrepancy of the Kronecker sequence (n \\boldsymbol \\a
 lpha \\: \\mathrm{mod} \\: 1)_{n=1}^\\infty. We find that it can be smalle
 r than the classical discrepancy of any sequence when d \\le 2\, and can e
 ven be bounded in the case d=1. To achieve this\, we establish a novel det
 erministic analogue of Beck’s local-to-global principle (Annals 1994)\, 
 which relates the discrepancy of a Kronecker sequence to multiplicative di
 ophantine approximation. This opens up a new avenue of attack for Littlewo
 od’s conjecture.\n
LOCATION:https://researchseminars.org/talk/NEDNT/76/
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