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CATEGORIES:Geometry and Mathematical Physics seminar
SUMMARY:Logarithmic stable maps and where to find them - N
avid Nabijou (Glasgow)
DTSTART:20190703T100000Z
DTEND:20190703T110000Z
UID:TALK3768AT
URL:/talk/index/3768
DESCRIPTION:In enumerative geometry\, we are interested in “co
unting” the number of curves on an algebraic varie
ty which satisfy certain conditions. Classical exa
mples include the 27 lines on the cubic surface\,
or the 12 rational cubics passing through 8 genera
l points in the plane.\n\nThese days\, enumerative
geometry is centred on Gromov-Witten theory - a r
obust framework for formulating and studying enume
rative problems\, with deep and subtle connections
to theoretical physics. The resulting counts are
referred to as Gromov-Witten invariants\, and sati
sfy a long (and ever expanding) list of remarkable
properties.\n\nLogarithmic Gromov-Witten theory i
s an enhancement of Gromov-Witten theory\, which i
ncorporates curves satisfying tangency conditions
with respect to a hypersurface. In this talk\, I w
ill discuss the basics of logarithmic Gromov-Witte
n theory\, focusing on examples and the beautiful
interplay with the combinatorial world of tropical
geometry. Time permitting\, I will present joint
work in progress with Lawrence Barrott\, in which
we study the behaviour of logarithmic Gromov-Witte
n invariants under degenerations of the hypersurfa
ce\, and employ logarithmic deformation theory in
order to relate the logarithmic invariants to the
standard ones.
LOCATION:Watson Building (Mathematics\, R15 on map) Lecture
Room C
CONTACT:Andrea Brini
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