BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//talks.cam.ac.uk//v3//EN
BEGIN:VTIMEZONE
TZID:Europe/London
BEGIN:DAYLIGHT
TZOFFSETFROM:+0000
TZOFFSETTO:+0100
TZNAME:BST
DTSTART:19700329T010000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0100
TZOFFSETTO:+0000
TZNAME:GMT
DTSTART:19701025T020000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
CATEGORIES:Number Theory Seminar
SUMMARY:The average elliptic curve has few integral points
- Levent Alpoge (Cambridge)
DTSTART;TZID=Europe/London:20150526T161500
DTEND;TZID=Europe/London:20150526T171500
UID:TALK58797AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/58797
DESCRIPTION:It is a theorem of Siegel that the Weierstrass mod
el `y^2 = x^3 + A x + B `

of an ellipti
c curve has finitely many integral points. A "rand
om" such curve should have no points at all. I wil
l show that the\naverage number of integral points
on such curves (ordered by height)\nis bounded --
in fact\, by 66. The methods combine a Mumford-ty
pe gap\nprinciple\, LP bounds in sphere packing\,
and results in Diophantine approximation. The same
result also holds (though I have not computed\nan
explicit constant) for the families ```
y^2 = x
^3 + A x
```

\, `y^2 = x^3 + B`

\,\nan
d `y^2 = x^3 - n^2 x`

.
LOCATION:MR13
CONTACT:Jack Thorne
END:VEVENT
END:VCALENDAR