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SUMMARY:Stephen D. Cohen (University of Glasgow)
DTSTART:20200603T131000Z
DTEND:20200603T141000Z
DTSTAMP:20260404T094701Z
UID:TAUFA/2
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/TAUFA
 /2/">Existence theorems for primitive elements in finite fields</a>\nby St
 ephen D. Cohen (University of Glasgow) as part of Tel Aviv field arithmeti
 c seminar\n\nAbstract: TBA\n
LOCATION:https://stable.researchseminars.org/talk/TAUFA/2/
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BEGIN:VEVENT
SUMMARY:Michael Filaseta (University of South Carolina)
DTSTART:20200527T151000Z
DTEND:20200527T161000Z
DTSTAMP:20260404T094701Z
UID:TAUFA/3
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/TAUFA
 /3/">On a problem of Tur\\'an and sparse polynomials</a>\nby Michael Filas
 eta (University of South Carolina) as part of Tel Aviv field arithmetic se
 minar\n\n\nAbstract\nI will give a survey of various results associated wi
 th the factorization of sparse polynomials in $\\mathbb Z[x]$.  One motiva
 ting question that pushed some of the results to be considered is a questi
 on 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 $g(x) \\in Z[x]$ t
 hat is irreducible and within $C$ of being $f(x)$ in the sense that the su
 m of the 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 r
 estriction that $\\deg g \\le \\deg f$\, and the problem remains open in t
 his case with good evidence that such a $C$ probably does exist.\n
LOCATION:https://stable.researchseminars.org/talk/TAUFA/3/
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BEGIN:VEVENT
SUMMARY:Rainer Dietmann (Royal Holloway\, University of London)
DTSTART:20200506T131000Z
DTEND:20200506T141000Z
DTSTAMP:20260404T094701Z
UID:TAUFA/4
DESCRIPTION:Title: <a href="https://stable.researchseminars.org/talk/TAUFA
 /4/">Enumerative Galois theory for cubics and quartics</a>\nby Rainer Diet
 mann (Royal Holloway\, University of London) as part of Tel Aviv field ari
 thmetic seminar\n\n\nAbstract\nThis is joint work with Sam Chow. We consid
 er monic quartic polynomials with integer coefficients and growing box hei
 ght at most H. In this setting\, we exactly determine the order of magnitu
 de (from above and below) of such polynomials whose Galois group is D_4. M
 oreover\, 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 freq
 uent than reducible quartics. Similarly\, for integer monic cubic polynomi
 als we show that A_3 cubics are less frequent than reducible cubics. In pa
 rticular\, irreducible non-S_n polynomials are less numerous than reducibl
 e 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://stable.researchseminars.org/talk/TAUFA/4/
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