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DTSTART:20240310T070000
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URL:https://uwaterloo.ca/pure-mathematics/events/number-theory-seminar-120
SUMMARY:Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:JAKUB KRÁSENSKÝ\, CZECH TECHNICAL UNIVERSITY IN PRAGUE\n\n\"C
 RITERION SETS FOR QUADRATIC FORMS OVER NUMBER FIELDS\"\n\nBy the celebrate
 d 15 theorem of Conway and Schneeberger\, a classical\npositive definite q
 uadratic form over Z is universal if it represents\neach element of {1\,2\
 ,3\,5\,6\,7\,10\,14\,15}. Moreover\, this is the minimal\nset with this pr
 operty. In 2005\, B.M. Kim\, M.-H. Kim and B.-K. Oh\nshowed that such a fi
 nite criterion set exists in a much general\nsetting\, but the uniqueness 
 of the criterion set is lost. Since then\,\nthe question of uniqueness for
  particular situations has been studied\nby several authors.\n\nWe will di
 scuss the analogous questions for totally positive definite\nquadratic for
 ms over totally real number fields. Here again\, the\nexistence of criteri
 on sets for universality is known\, and Lee\ndetermined the set for Q(sqrt
 5). We will show the uniqueness and a\nstrong connection with indecomposab
 le integers. A part of our\nuniqueness result is (to our best knowledge) n
 ew even over Z. This is\njoint work with G. Romeo and V. Kala.\n\nZoom\nli
 nk: https://uwaterloo.zoom.us/j/98937322498?pwd=a3RpZUhxTkd6LzFXTmcwdTBCM
 Ws0QT09
DTSTAMP:20260506T220645Z
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