BEGIN:VCALENDAR
VERSION:2.0
PRODID:-//Sabre//Sabre VObject 4.6.0//EN
CALSCALE:GREGORIAN
BEGIN:VTIMEZONE
TZID:Europe/Zurich
X-LIC-LOCATION:Europe/Zurich
TZURL:http://tzurl.org/zoneinfo/Europe/Zurich
BEGIN:DAYLIGHT
TZOFFSETFROM:+0100
TZOFFSETTO:+0200
TZNAME:CEST
DTSTART:19810329T020000
RRULE:FREQ=YEARLY;BYMONTH=3;BYDAY=-1SU
END:DAYLIGHT
BEGIN:STANDARD
TZOFFSETFROM:+0200
TZOFFSETTO:+0100
TZNAME:CET
DTSTART:19961027T030000
RRULE:FREQ=YEARLY;BYMONTH=10;BYDAY=-1SU
END:STANDARD
END:VTIMEZONE
BEGIN:VEVENT
UID:news1915@dmi.unibas.ch
DTSTAMP;TZID=Europe/Zurich:20251013T102902
DTSTART;TZID=Europe/Zurich:20251016T141500
SUMMARY:Number Theory Seminar: Remke Kloosterman (University of Padova)
DESCRIPTION:The average Mordell--Weil rank of elliptic surfaces over number
  fields\\r\\nAbstract: Let $K$ be a number field and let $n$ be a non-nega
 tive integer.\\r\\nIn this talk we determine the average (arithmetic) Mord
 ell--Weil rank of elliptic surfaces over $K$ with base curve $\\mathbb{P}^
 1$ and geometric genus $n$.\\r\\nHereby we prove a conjecture of Alex Cowa
 n\, which in turn was inspired by Nagao's conjecture and subsequent work.\
 \r\\nThe proof consists of two parts\, the first part relies on work by An
 dr\\'e and Maulik--Poonen on the jump loci of the Picard Number in flat fa
 milies. This is sufficient to prove that the average Mordell--Weil rank eq
 uals the generic Mordell--Weil rank.\\r\\nThe second part of the proof use
 s an argument involving quadratic twists in order to show that the generic
  Mordell--Weil rank of elliptic surfaces over a number field with fixed to
 pological equals zero.\\r\\nSpiegelgasse 5\, Seminarraum 05.001
X-ALT-DESC:<h2>The average Mordell--Weil rank of elliptic surfaces over num
 ber fields</h2>\n<p>Abstract: Let $K$ be a number field and let $n$ be a n
 on-negative integer.</p>\n<p>In this talk we determine the average (arithm
 etic) Mordell--Weil rank of elliptic surfaces over $K$ with base curve $\\
 mathbb{P}^1$ and geometric genus $n$.</p>\n<p>Hereby we prove a conjecture
  of Alex Cowan\, which in turn was inspired by Nagao's conjecture and subs
 equent work.</p>\n<p>The proof consists of two parts\, the first part reli
 es on work by Andr\\'e and Maulik--Poonen on the jump loci of the Picard N
 umber in flat families. This is sufficient to prove that the average Morde
 ll--Weil rank equals the generic Mordell--Weil rank.</p>\n<p>The second pa
 rt of the proof uses an argument involving quadratic twists in order to sh
 ow that the generic Mordell--Weil rank of elliptic surfaces over a number 
 field with fixed topological equals zero.</p>\n<p><strong>Spiegelgasse 5\,
  Seminarraum 05.001</strong></p>
DTEND;TZID=Europe/Zurich:20251016T151500
END:VEVENT
END:VCALENDAR