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BEGIN:VEVENT
UID:news2003@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20260531T204111
DTSTART;TZID=Europe/Zurich:20260604T141500
SUMMARY:Number Theory Seminar: Martin Widmer (TU Graz)
DESCRIPTION:Height lower bounds for elements in highly composite rings\\r\\
 nAbstract: Let $\\alpha$ be a non-zero algebraic number and not a root of 
 unity. Then its absolute Weil height $h(\\alpha)$ is positive. How small c
 an it be in terms of the degree of $\\alpha$? Lehmer's conjecture states t
 hat the height does not decay faster than the reciprocal of the degree. Am
 oroso and Dvornicich showed that there is no decay at all\, provided $\\ma
 thbf{Q}(\\alpha)/\\mathbf{Q}$ is an abelian extension. If we further requi
 re that $\\alpha$ lies in $\\mathbf{Q}^{(d)}$\, the composite field of all
  number fields of degree at most $d$\, then the height tends to infinity\,
  as was shown by Bombieri and Zannier. What happens for arbitrary $\\alpha
  \\in \\mathbf{Q}^{(d)}$? We will present some new results on this unsolve
 d question. This is ongoing joint work with Siu Hang Man\, Niclas Technau\
 , and Pavlo Yatsyna.\\r\\nSeminarraum 05.002\, Spiegelgasse 5
X-ALT-DESC:<h2>Height lower bounds for elements in highly composite rings</
 h2>\n<p>Abstract: Let $\\alpha$ be a non-zero algebraic number and not a r
 oot of unity. Then its absolute Weil height $h(\\alpha)$ is positive. How 
 small can it be in terms of the degree of $\\alpha$? Lehmer's conjecture s
 tates that the height does not decay faster than the reciprocal of the deg
 ree. Amoroso and Dvornicich showed that there is no decay at all\, provide
 d $\\mathbf{Q}(\\alpha)/\\mathbf{Q}$ is an abelian extension. If we furthe
 r require that $\\alpha$ lies in $\\mathbf{Q}^{(d)}$\, the composite field
  of all number fields of degree at most $d$\, then the height tends to inf
 inity\, as was shown by Bombieri and Zannier. What happens for arbitrary $
 \\alpha \\in \\mathbf{Q}^{(d)}$? We will present some new results on this 
 unsolved question. This is ongoing joint work with Siu Hang Man\, Niclas T
 echnau\, and Pavlo Yatsyna.</p>\n<p>Seminarraum 05.002\, Spiegelgasse 5</p
 >\n\n
DTEND;TZID=Europe/Zurich:20260604T151500
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