[geometry-ml:01515] Seminar at Kavli IPMU on 2012 July 31 Mihalcea

[Satoshi Kondo]

Dear colleagues:

There will be a seminar as follows at Kavli IPMU
(Kavli Institute for the Physics and Mathematics of
the Universe).

Regards,

Satoshi Kondo (Kavli IPMU)
http://ipmu.jp/
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Speaker: Leonardo Mihalcea (Virginia Tech)

Date: 2012 July 31 (Tue)

Time: 15:30 - 17:00

Place: Balcony A, Kavli IPMU

Title:QUANTUM K-THEORY AND THE GEOMETRY OF SPACES OF
CURVES

Abstract:
The 3-point, genus 0, Gromov-Witten invariants on a flag manifold
count rational curves of degree d satisfying certain incidence
conditions - if the number of curves is expected to be finite. For
infinitely many curves, Givental and Lee defined the K-theoretic
Gromov-Witten invariants, which associates a measure to the space of
rational curves in question, embedded in Kontsevich's moduli space of
stable maps. The resulting quantum cohomology theory - the quantum
K-theory - encodes the associativity relations satisfied by the
K-theoretic Gromov-Witten invariants.
In this talk I will show how we can compute the K-theoretic
Gromov-Witten in several cases, with an emphasis on the case of
Grassmannians. In this case we can give a complete algorithm,
therefore obtaining a description of the quantum K-theory algebra. The
key is a "quantum=classical" phenomenon: the K-theoretic Gromov-Witten
invariants for Grassmannians are equal to structure constants of the
ordinary K-theory of certain two-step flag manifolds. My talk is based
on several collaborations with A. Buch, P.E. Chaput, C. Li and N.
Perrin.
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You can check the location from
http://www.ipmu.jp/access-0
The schedule of the seminar can be checked from
http://db.ipmu.jp/seminar/