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BEGIN:VEVENT
SUMMARY:Stephen D. Cohen (University of Glasgow)
DTSTART:20200603T131000Z
DTEND:20200603T141000Z
DTSTAMP:20260422T225819Z
UID:TAUFA/2
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TAUFA/2/">Ex
 istence theorems for primitive elements in finite fields</a>\nby Stephen D
 . Cohen (University of Glasgow) as part of Tel Aviv field arithmetic semin
 ar\n\nAbstract: TBA\n
LOCATION:https://researchseminars.org/talk/TAUFA/2/
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BEGIN:VEVENT
SUMMARY:Michael Filaseta (University of South Carolina)
DTSTART:20200527T151000Z
DTEND:20200527T161000Z
DTSTAMP:20260422T225819Z
UID:TAUFA/3
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TAUFA/3/">On
  a problem of Tur\\'an and sparse polynomials</a>\nby Michael Filaseta (Un
 iversity of South Carolina) as part of Tel Aviv field arithmetic seminar\n
 \n\nAbstract\nI will give a survey of various results associated with the 
 factorization of sparse polynomials in $\\mathbb Z[x]$.  One motivating qu
 estion that pushed some of the results to be considered is a question due 
 to P\\'al Tur\\'an:  Is there an absolute constant $C$ such that if $f(x) 
 \\in \\mathbb Z[x]$\, then there is a polynomial $g(x) \\in Z[x]$ that is 
 irreducible and within $C$ of being $f(x)$ in the sense that the sum of th
 e absolute values of the difference $f(x) - g(x)$ is bounded by $C$?  This
  is known to be true as I stated it\, but Tur\\'an also added the restrict
 ion that $\\deg g \\le \\deg f$\, and the problem remains open in this cas
 e with good evidence that such a $C$ probably does exist.\n
LOCATION:https://researchseminars.org/talk/TAUFA/3/
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BEGIN:VEVENT
SUMMARY:Rainer Dietmann (Royal Holloway\, University of London)
DTSTART:20200506T131000Z
DTEND:20200506T141000Z
DTSTAMP:20260422T225819Z
UID:TAUFA/4
DESCRIPTION:Title: <a href="https://researchseminars.org/talk/TAUFA/4/">En
 umerative Galois theory for cubics and quartics</a>\nby Rainer Dietmann (R
 oyal Holloway\, University of London) as part of Tel Aviv field arithmetic
  seminar\n\n\nAbstract\nThis is joint work with Sam Chow. We consider moni
 c quartic polynomials with integer coefficients and growing box height at 
 most H. In this setting\, we exactly determine the order of magnitude (fro
 m above and below) of such polynomials whose Galois group is D_4. Moreover
 \, we show that C_4 and V_4 polynomials are less frequent that D_4 ones\, 
 and that D_4\, C_4\, V_4 and A_4 polynomials are together less frequent th
 an reducible quartics. Similarly\, for integer monic cubic polynomials we 
 show that A_3 cubics are less frequent than reducible cubics. In particula
 r\, irreducible non-S_n polynomials are less numerous than reducible ones 
 for n = 3 and n = 4\, for the first time solving two cases (namely degree 
 three and four) of a conjecture by van der Waerden from 1936.\n
LOCATION:https://researchseminars.org/talk/TAUFA/4/
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