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</o:shapelayout></xml><![endif]--></head><body lang=TR link=blue vlink=purple><div class=WordSection1><p class=MsoNormal><span style='color:#1F497D'>Degerli Liste Uyeleri,<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'>Levent Alpoge’nin, Cuma gunu saat 14:00’te Karakoy’de TMD’nin davetlisi olarak yapacagi konusmaya ilgilenen tum matematikcileri ve matematikci adaylarini bekleriz. Konusmanin ayrintilarini ekte bulabilirsiniz.<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><p class=MsoNormal><span style='color:#1F497D'>sevgiler,<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'>TMD<o:p></o:p></span></p><p class=MsoNormal><span style='color:#1F497D'><o:p> </o:p></span></p><div><div style='border:none;border-top:solid #B5C4DF 1.0pt;padding:3.0pt 0in 0in 0in'><p class=MsoNormal><b><span lang=EN-US style='font-size:10.0pt;font-family:"Tahoma","sans-serif";mso-fareast-language:TR'>From:</span></b><span lang=EN-US style='font-size:10.0pt;font-family:"Tahoma","sans-serif";mso-fareast-language:TR'> Turk Matematik Dernegi<br><b>Sent:</b> Sunday, March 01, 2015 5:42 PM<br><b>To:</b> turkmath@listweb.bilkent.edu.tr<br><b>Subject:</b> [Turkmath:272] Levent Alpoge 13 Mart'ta TMD'de<o:p></o:p></span></p></div></div><p class=MsoNormal><o:p> </o:p></p><p class=MsoPlainText>Degerli Liste uyeleri,<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Matematikte alaninda seckin arastima yapmis olan lisans ogrencilerine AMS, MAA ve SIAM tarafindan verilen Morgan Odulu'nun 2015 yilindaki sahibi bilindigi uzere Levent Alpoge olmustur. <o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Morgan odulu bugune kadar aralarinda 2014 ICM Fields Madalyasi sahibi Manjul Bhargava'nin da bulundugu pek cok degerli matematikciye verilmistir. Morgan odulu verilenlerin listesine ve odul hakkinda daha genis bilgiye <a href="http://en.wikipedia.org/wiki/Morgan_Prize">http://en.wikipedia.org/wiki/Morgan_Prize</a> adresinden ulasilabilir.<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Levent Alpoge Turk Matematik Dernegi'nin davetlisi olarak 13 Mart Cuma gunu saat 14:00’te dernegimizin bulundugu Sabanci Universitesi – Karakoy Minerva Palas'ta baslik ve ozeti asagida paylasilan konusmayi gerceklestirecektir. Tum uyelerimize ve matematikcilere duyurulur.<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Levent Alpoge'nin ziyareti vesilesiyle, TMD'nin Matematik Arastirma Dostu (MAD) projesine desteklerini esirgemeyen bagiscilarimiza bir kere daha tesekkur ederiz.<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>TMD-Yonetim Kurulu<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Title: The average elliptic curve has few integral points.<o:p></o:p></p><p class=MsoPlainText><o:p> </o:p></p><p class=MsoPlainText>Abstract: It is a theorem of Siegel that the Weierstrass model y^2 = x^3 + Ax + B of an elliptic curve has finitely many integral points. A "random" such curve should have no points at all. I will show that the average number of integral points on such curves (ordered by height) is bounded - in fact, by 66. The methods combine a Mumford-type gap principle, LP bounds in sphere packing, and results in Diophantine approximation. <o:p></o:p></p><p class=MsoPlainText>The same result also holds (though I have not computed an explicit constant) for the families <o:p></o:p></p><p class=MsoPlainText>y^2 = x^3 + Ax, y^2 = x^3 + B, and y^2 = x^3 - n^2 x. <o:p></o:p></p><p class=MsoPlainText>If I have time I will also mention why the average is strictly smaller than one assuming the minimalist conjecture (that 50% of curves have rank zero and 50% have rank one).<o:p></o:p></p><p class=MsoNormal><o:p> </o:p></p></div></body></html>