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SUMMARY:Advanced School and Workshop on Arithmetic of Hyperelliptic Curves
| (smr 3175)
DTSTART;VALUE=DATE-TIME:20170828T060000Z
DTEND;VALUE=DATE-TIME:20170908T200000Z
DTSTAMP;VALUE=DATE-TIME:20170329T111649Z
UID:indico-event-8123@cern.ch
DESCRIPTION:Hyperelliptic curves are a fundamental class of polynomial equ
ations\, that are rapidly becoming a major topic in number theory. Demands
for the theory are coming both from within pure mathematics (such as the
pioneering work or Bhargava and his collaborators\, and the Langlands prog
ramme\, which needs a supply of high-dimensional Galois representations)\,
as well as from areas bordering to theoretical physics (via hypergeometri
c motives) and from cryptography\, where one of the main methods for moder
n data encryption is based on hyperelliptic curves. \n\nThe advanced schoo
l will focus on the modern techniques in number theory that have previousl
y had major impacts on the theory of elliptic curves and that are likely t
o have great impact in the theory of hyperelliptic curves in the near futu
re. Specifically\, the topics to be covered are the following\, with a par
ticular emphasis on the setting of hyperelliptic curves: \n\n1. L-function
s and the Birch-Swinnerton-Dyer Conjecture\; \n2. Selmer groups\; \n3. Mod
ularity\; \n4. Galois representations. \n\nThe workshop will focus on the
most recent developments in the arithmetic of hyperelliptic curves\, inclu
ding the above mentioned four topics\, point counting techniques\, distrib
ution of locally soluble curves\, hypergeometric motives\, generalisations
of Chabauty's method\, Selmer ranks of Jacobians\, etc.\n\nhttp://indico.
ictp.it/event/8123/
LOCATION:ICTP Giambiagi Lecture Hall (AGH)
URL:http://indico.ictp.it/event/8123/
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