The European University of Post-Industrial Cities (UNIC) consortium is proud to announce the fourth seminar of 2022 as part of the ongoing UNIC Mathematics Seminar Series showcasing research from UNIC partners.
This round of the seminar series will include presentations from University College Cork, Koç University, University of Oulu and University of Zagreb.
Prof. Andrej Dujella of the University of Zagreb will give a talk titled:
"Elliptic curves and Diophantine m-tuples".
Abstract:
In this talk, we will describe some connections between Diophantine m-tuples and elliptic curves. A rational Diophantine m-tuple is a set of m nonzero rationals such that the product of any two of them increased by 1 is a perfect square. The first rational Diophantine quadruple was found by Diophantus. It is known that there are infinitely many Diophantine quadruples in integers (the first example, the set {1,3,8,120}, was found by Fermat),and He, Togbe and Ziegler proved recently that there are no Diophantine quintuples in integers. Euler proved that there are infinitely many rational Diophantine quintuples. In 1999, Gibbs found the first example of a rational Diophantine sextuple. It is still an open question whether there exists any rational Diophantine septuple. We will describe several constructions of infinite families of rational Diophantine sextuples (this is joint work with M. Kazalicki, M. Mikic, V. Petricevic and M. Szikszai). These constructions use properties of corresponding elliptic curves. We will also show how Diophantine m-tuples can be used in the construction of high-rank elliptic curves over Q and Q(t) with given torsion group (this is joint work with J. Aguirre and J. C. Peral).
The seminar will be held via MS Teams on April 19, 2022 at 17:00 Istanbul / 17:00 Oulu / 16:00 Zagreb / 15:00 Cork time.
Click here to join the meeting
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