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CATEGORIES:Special DPMMS Colloquium
SUMMARY:Mirror symmetry and cluster algebras - Mark Gross
( University California\, San Diego)
DTSTART;TZID=Europe/London:20130702T140000
DTEND;TZID=Europe/London:20130702T150000
UID:TALK45793AThttp://talks.cam.ac.uk
URL:http://talks.cam.ac.uk/talk/index/45793
DESCRIPTION: Mirror symmetry is a subject which originated in
string theory in 1990\,\nand has since developed m
athematically in many different directions.\nRough
ly put\, mirror symmetry gives a correspondence be
tween different\nalgebraic varieties\, in which ce
rtain calculations on one variety (usually\ninvolv
ing counting curves) coincides with a different ty
pe of calculation\non the other (usually computing
integrals of certain forms).\nJoint work with Ber
nd Siebert over the last 10 years has explored the
\nunderlying geometry of mirror symmetry\, and the
structures that have\nemerged in this work can no
w be applied to diverse situation.\n\n In this t
alk I will discuss joint ongoing work with Keel\,
Kontsevich\nand Hacking. I will make a connection
between structures called\nscattering diagrams\, o
r wall-crossing structures\, which emerged in the\
nstudy of mirror symmetry\, and cluster algebras o
f Fomin and Zelevinsky\,\nwhich were developed to
model aspects of canonical bases of Lusztig and\nK
ashiwara. In particular\, a construction of an ana
logue of theta functions\,\nmotivated by the homol
ogical mirror symmetry conjecture\, allows the\nco
nstruction of canonical bases of cluster algebras
in many cases\, as\nwell as the proof of a number
of conjectures concerning cluster algebras.
LOCATION:CMS\, MR12
CONTACT:HoD Secretary\, DPMMS
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