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<span style="margin:0px;font-size:12pt;background-color:rgb(255, 255, 255) !important"><span style="margin:0px;background-color:rgb(255, 255, 255) !important"><span style="margin:0px;font-size:9pt;font-family:Arial, Helvetica, sans-serif">Merhabalar,</span></span></span><span style="background-color:rgb(255, 255, 255);display:inline !important"></span>
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<span style="margin:0px;background-color:rgb(255, 255, 255) !important"><span style="margin:0px;font-size:9pt;font-family:Arial, Helvetica, sans-serif">11 May<span style="background-color:rgb(255, 255, 255);display:inline !important">ı</span>s Çarşamba günü
saat 15.00'de Boğaziçi Üniversitesi'nden Yasemin Kara</span></span><span style="margin:0px;font-size:9pt;font-family:Arial, Helvetica, sans-serif"> Galatasaray Üniversitesi'nde bir konuşma verecektir. Konuşma yüz yüze H306 sınıfında yapılacaktır. </span><span style="margin:0px;font-size:9pt;font-family:Arial, Helvetica, sans-serif">Konuşmanın
detaylarını aşağıda bulabilirsiniz.</span><br>
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<span style="margin:0px;font-size:9pt;font-family:Arial, Helvetica, sans-serif">Özge Ülkem</span></div>
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<span style="margin:0px;font-size:9pt;font-family:Arial, Helvetica, sans-serif"><span style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255);display:inline !important">Title: Solving Fermat Type Equations Via Modular Approach</span><br style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255)">
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<span style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255);display:inline !important">Abstract: The asymptotic Fermat conjecture(AFC) states that for a </span><br style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255)">
<span style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255);display:inline !important">number field K and for sufficiently large primes, the equation </span><br style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255)">
<span style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255);display:inline !important">x^p+y^p+z^p=0 has only trivial solutions. The strategy which is </span><br style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255)">
<span style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255);display:inline !important">referred as the "modular method" to solve the Fermat equation, used by </span><br style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255)">
<span style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255);display:inline !important">Wiles in his famous proof, can be adapted to attack AFC and its </span><br style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255)">
<span style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255);display:inline !important">several different generalizations. Similar results are quite rare for </span><br style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255)">
<span style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255);display:inline !important">other Fermat type equations such as x^p+y^q=z^r although the solutions </span><br style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255)">
<span style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255);display:inline !important">of this equation have been studied over rationals. In this talk, I </span><br style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255)">
<span style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255);display:inline !important">will mention some recent asymptotic results for the classical Fermat </span><br style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255)">
<span style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255);display:inline !important">equation as well as some other Fermat type equations over number fields.</span><br style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255)">
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<span style="color:rgb(34, 34, 34);font-size:small;background-color:rgb(255, 255, 255);display:inline !important">This talk is based on joint works with Isik and Ozman.</span><br>
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