fak_seminar

11. Fakultetski seminar: “On Mordell’s equation” i „Integral basis and monogenity in parametric families of number fields“

21/06/2017

Pozivamo Vas na 11. fakultetski seminar u srijedu 28. lipnja 2017. u amfiteatru 3F-A-0-1 u 12 sati na kojem će

prof. dr.sc.  István Gaál,

Mathematical Institute, University of  Debrecen,

održati predavanje pod naslovom

 On Mordell’s equation”, 

te

mag.math. László Remete,

Mathematical Institute, University of  Debrecen

održati predavanje pod naslovom

 Integral basis and monogenity in parametric families of number fields“. 

 

Sažetak predavanja „On Mordell’s equation”:  

We survey the history of Mordell’s classical equation x^3+k=y^2. Recently M.E.Pohst, M.Pohst and I.Gaál gave an improvement of Wildanger’s method which makes possible to solve the equation up to |k|<10^15. We give some details of the new method and give interesting examples.

Sažetak predavanja „Integral basis and monogenity in parametric families of number fields“:  

We consider infinite parametric families of number fields, pure extensions and the family of simplest sextic number fields. We show that the structure of their integral bases is periodic and explicitly give the integral bases. Using the integral basis we explicitly construct factors of the corresponding index form. This leads to conditions on the monogenity of the fields.

 

Kratki životopis – István Gaál:

  • 1979-84: studies in mathematics at University of Debrecen (formerly Lajos Kossuth University)
  • from 1984: staff member at University of Debrecen, Mathematical Institute, Department of Algebra and Number Theory
  • 1991-93: Fellow of the Alexander von Humboldt Foundation (host: Michael Pohst, Düsseldorf)
  • 1993-2010: vice director at the institute, vice dean of the faculty,
  • 2010-15: vice rector of the university
  • 2005-2016 head of the department
  • editor of Publicationes Mathematicae, Acta Mathematica Academiae Paedagogicae Nyíregyhaziensis, JP Journal of Algebra and Number Theory, local editor of Zentralblatt für Mathematik;
  • research topics: diophantine equations, Thue equation, monogenity of number fields, power integral bases infnite parametric families of number fields
  • author of about 75 paper and a book on power integral basis

Kratki životopis – László Remete:

  • 2012-17 mathematics BSc and Msc studies at University of Debrecen
  • from 2017: PhD student
  • research topics: diophantine equations, Thue equation, monogenity of number fields, power integral bases infnite parametric families of number fields
  • author of 8 papers