[Turkmath:272] Levent Alpoge 13 Mart'ta TMD'de

[Turk Matematik Dernegi]

Degerli Liste uyeleri,

 

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. 

 

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
http://en.wikipedia.org/wiki/Morgan_Prize adresinden ulasilabilir.

 

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.

 

Levent Alpoge'nin ziyareti vesilesiyle, TMD'nin Matematik Arastirma Dostu
(MAD) projesine desteklerini esirgemeyen bagiscilarimiza bir kere daha
tesekkur ederiz.

 

TMD-Yonetim Kurulu

 

 

Title: The average elliptic curve has few integral points.

 

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. 

The same result also holds (though I have not computed an explicit constant)
for the families 

y^2 = x^3 + Ax, y^2 = x^3 + B, and y^2 = x^3 - n^2 x. 

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).

 

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