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<span style="font-family: Arial, Helvetica, sans-serif; font-size: 9pt;">Merhabalar,</span></div>
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<div style="margin:0px"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 9pt;">29 Aralık Çarşamba günü Boğaziçi Üniversitesi'nden Özlem Ejder Galatasaray Üniversitesi'nde bir konuşma verecektir. Konuşma yüzyüze A324 sınıfında saat 15.00'de
yapılacaktır. Konuşmanın detaylarini aşağıda bulabilirsiniz. </span></div>
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<div style="margin:0px"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 9pt;">Tüm ilgilenenler davetlidir.</span></div>
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<div style="margin:0px"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 9pt;">Sevgiler,</span></div>
<div style="margin:0px"><span style="font-family: Arial, Helvetica, sans-serif; font-size: 9pt;">Özge Ülkem</span></div>
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<div style="font-family: Calibri, Helvetica, sans-serif; font-size: 12pt;"><span dir="auto" style="color: rgb(34, 34, 34); font-family: Arial, Helvetica, sans-serif; background-color: rgb(255, 255, 255); font-size: 12.8px;">Title: Isolated points</span><span dir="auto" style="font-family: Arial, Helvetica, sans-serif; font-size: 12.8px;"><font color="#222222"><span style="background-color: rgb(255, 255, 255);"> on
Modular Curves</span></font></span>
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Abstract: <span style="color: rgb(34, 34, 34); font-family: helvetica; font-size: 12px;">One of the oldest areas of mathematics is the study of integer or rational solutions to polynomial equations with integer coefficients and it remains active till today.
The most natural question we can ask about such an equation is whether its set of rational solutions is finite or infinite. This can be determined by the genus of the curve defined by such equations. In particular, if the genus is greater than one, there are
finitely many rational points </span><span style="color: rgb(34, 34, 34); font-family: helvetica; font-size: 12px;">on a curve. </span></div>
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<p style="margin:0px;font-size:12px;font-family:helvetica">What happens when one allows for solutions involving square-roots of integers or cubic roots? Perhaps in general all complex numbers that are roots of a degree d polynomial? We call such solutions
of degree 2,3 or d in general. In this talk, we will discuss when a curve has infinitely many degree d <span style="background-color:rgb(255, 255, 255);display:inline !important">points</span> focusing particularly on <span style="background-color:rgb(255, 255, 255);display:inline !important">points</span> on
modular curves</p>
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