<div dir="ltr"><div dir="ltr"><div dir="ltr"><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Değerli Liste Üyeleri, </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Bilecik Şeyh Edebali Üniversitesi Fen Fakültesi Matematik Bölümü Cebir ve Sayılar Teorisi Anabilim dalı öğretim üyeleri tarafından kurulan “Bilecik Algebra & Number Theory (BANT)” grubu tarafından organize edilen seminer serilerinin yeni konuşması<b> 13 Ocak 2026 Salı günü</b> online olarak zoom üzerinden düzenlenecektir. </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"><br></font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Etkinliğin web sitesi: <a href="https://bilecikalgebranumbertheory.github.io/" target="_blank">https://bilecikalgebranumbertheory.github.io/</a> dir. </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Sıradaki konuşmacı Zagreb Üniversitesi'nin (Hırvatistan) değerli öğretim üyesi<b> Andrej Dujella</b> olacaktır ve konuşma bilgileri aşağıda yer almaktadır. </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"><b>Konuşma Adı:</b> <span style="color:rgb(36,41,46)"> </span><span style="color:rgb(32,33,36)"><b>Diophantine m-tuples and elliptic curves</b></span></font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"><b>Özet:</b> <span style="color:rgb(32,33,36)">In this talk, we will describe some connections between</span><span style="color:rgb(32,33,36)"> </span></font><span style="font-family:arial,sans-serif;color:rgb(32,33,36)">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 a given torsion group (this is joint work with J. Aguirre and J. C. </span>Peral<span style="font-family:arial,sans-serif;color:rgb(32,33,36)">). We will also mention some of the open problems related to these topics.</span><br></p><div><font face="arial, sans-serif"><b><br></b></font></div><div><font face="arial, sans-serif"><b><br></b></font><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><b><font face="arial, sans-serif">Tarih: 13/01/2026 </font></b></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><b><font face="arial, sans-serif">Saat: 16:00 İstanbul / 14:00 Berlin / 13:00 Londra / 22:00 Tokyo / 08:00 New York / 00:00 Sydney(+1)</font></b></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Katılım için linkte yer alan formun doldurulması yeterlidir, </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Form linki: </font><a href="https://forms.gle/xaJ2uPTtvzxD6cTx9" target="_blank">https://forms.gle/xaJ2uPTtvzxD6cTx9</a> </p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><br></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Zoom linki formu doldurduktan sonra email ile paylaşılacaktır. Etkinlik posteri ekte yer almaktadır. </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Saygılarımla, </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Prof.Dr. İlker İnam</font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Düzenleme komitesi adına. </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">————————————————————— </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Dear list members, </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">The "Bilecik Algebra & Number Theory (BANT)" group, founded by the faculty members of the Department of Algebra and Number Theory at Bilecik Seyh Edebali University's Faculty of Science, will host its next semester on <b>Tue, Jan 13, 2026</b>. The event will be conducted online via Zoom. </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">The website for the event is:  <a href="https://bilecikalgebranumbertheory.github.io/" target="_blank">https://bilecikalgebranumbertheory.github.io/</a>. </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">The inaugural speaker will be </font><b style="font-family:arial,sans-serif">Andrej Dujella</b><font face="arial, sans-serif">, a faculty member at the University of Zagreb, Croatia. Details of the presentation are provided below. </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"><b>Title: </b></font><b style="color:rgb(32,33,36);font-family:arial,sans-serif">Diophantine m-tuples and elliptic curves</b></p><span style="color:rgb(36,41,46);font-family:-apple-system,BlinkMacSystemFont,"Segoe UI",Helvetica,Arial,sans-serif,"Apple Color Emoji","Segoe UI Emoji","Segoe UI Symbol""></span><font face="arial, sans-serif"></font><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"><b>Abstract: </b></font><font face="arial, sans-serif"><span style="color:rgb(32,33,36)">In this talk, we will describe some connections between</span><span style="color:rgb(32,33,36)"> </span></font><span style="font-family:arial,sans-serif;color:rgb(32,33,36)">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 a given torsion group (this is joint work with J. Aguirre and J. C. </span>Peral<span style="font-family:arial,sans-serif;color:rgb(32,33,36)">). We will also mention some of the open problems related to these topics.</span></p><font face="arial, sans-serif"></font><font face="arial, sans-serif"></font><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><span style="color:rgb(36,41,46);font-family:garamond,"times new roman",serif"><br></span></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><b><font face="arial, sans-serif">Date: Jan 13, 2026, Tuesday</font></b></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><b><font face="arial, sans-serif">Time: </font></b><b><font face="arial, sans-serif">16:00 İstanbul / 14:00 Berlin / 13:00 Londra / 22:00 Tokyo / 08:00 New York / 00:00 Sydney(+1)</font></b></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">To participate, simply fill out the form at the following link: </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Form Link: </font><a href="https://forms.gle/xaJ2uPTtvzxD6cTx9" target="_blank">https://forms.gle/xaJ2uPTtvzxD6cTx9</a> </p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">The Zoom link will be shared via email after filling out the form. The event poster is attached. </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif"> </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Best regards, </font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">Prof.Dr. Ilker Inam</font></p><p style="margin:0px;font-variant-numeric:normal;font-variant-east-asian:normal;font-variant-alternates:normal;font-kerning:auto;font-feature-settings:normal;font-stretch:normal;line-height:normal"><font face="arial, sans-serif">On behalf of the organizing committee</font></p></div></div>
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