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DTSTART:20240310T070000
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DTSTART:20231105T060000
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DTSTART;TZID=America/Toronto:20240319T100000
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TRANSP:TRANSPARENT
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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-118
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:AKASH SENGUPTA\, DEPARTMENT OF PURE MATHEMATICS\, UNIVERSITY OF
  WATERLOO\n\n\"APPROXIMATION OF RATIONAL POINTS AND A CHARACTERIZATION OF 
 PROJECTIVE\nSPACE\"\n\nGiven a real number x\, how well can we approximate
  it using rational\nnumbers? This question has been classically studied by
  Dirichlet\,\nLiouville\, Roth et al\, and the approximation exponent of a
  real number\nx measures how well we can approximate x. Similarly\, given 
 an\nalgebraic variety X over a number field k and a point x in X\, we can\
 nask how well can we approximate x using k-rational points? McKinnon\nand 
 Roth generalized the approximation exponent to this setting and\nshowed th
 at several classical results also generalize to rational\npoints algebraic
  varieties.\n\nIn this talk\, we will define a new variant of the approxim
 ation\nconstant which also captures the geometric properties of the variet
 y\nX. We will see that this geometric approximation constant is closely\nr
 elated to the behavior of rational curves on X. In particular\, I’ll\nta
 lk about a result showing that if the approximation constant is\nlarger th
 an the dimension of X\, then X must be isomorphic to\nprojective space. Th
 is talk is based on joint work with David\nMcKinnon.\n\nMC 5417
DTSTAMP:20260505T161632Z
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