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CATEGORIES:Differential Geometry and Topology Seminar
SUMMARY:Counting torus fibrations on a K3 surface - Simion
Filip\, Chicago
DTSTART;TZID=Europe/London:20160302T160000
DTEND;TZID=Europe/London:20160302T170000
UID:TALK60831AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/60831
DESCRIPTION: Among all complex two-dimensional manifolds\, K3
surfaces are distinguished for having a wealth of
extra structures. They admit dynamically interesti
ng automorphisms\, have Ricci-flat metrics (by Yau
's solution of the Calabi conjecture) and at the s
ame time can be studied using algebraic geometry.
Moreover\, their moduli spaces are locally symmetr
ic varieties and many questions about the geometry
of K3s reduce to Lie-theoretic ones.\nIn this tal
k\, I will discuss the analogue on K3 surfaces of
the following asymptotic question in billiards - H
ow many periodic billiard trajectories of length a
t most L are there in a given polygon? The analogu
e of periodic trajectories will be special Lagrang
ian tori on a K3 surface. Just like for billiards\
, such tori come in families and give torus fibrat
ions on the K3.\n
LOCATION:MR13
CONTACT:Ivan Smith
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