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DTSTART:20250309T070000
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DTSTART;TZID=America/Toronto:20250919T110000
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URL:https://uwaterloo.ca/pure-mathematics/events/student-number-theory-semi
 nar-84
SUMMARY:Student Number Theory Seminar
CLASS:PUBLIC
DESCRIPTION:NIC BANKS\, UNIVERSITY OF WATERLOO\n\n_Classification results f
 or intersective polynomials with no integral\nroots_\n\nIn this bald-faced
  attempt to practice my thesis defence\, we introduce\nstrongly intersecti
 ve polynomials - polynomials with no integer roots\nbut with a root modulo
  every positive integer - of degree 5-10. We\nstart by describing their re
 lation to Hilbert's 10th Problem and an\nalgorithm of James Ax. These are 
 fascinating objects which make\ncontact with many areas of math\, includin
 g permutation group theory\,\nsplitting behaviour of prime ideals in numbe
 r fields\, and Frobenius\nelements from class field theory.\n\nIn particul
 ar\, we explain the computation of a list of possible Galois\ngroups of su
 ch polynomials. We also discuss constraints on the\nsplitting behaviour of
  ramified primes\; in the process\, we argue that\nintersectivity can be t
 hought of as a property of a Galois number\nfield\, together with its set 
 of subfields of specified degrees.\n\nMC 5479
DTSTAMP:20260502T042125Z
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