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FMSP Lectures
Seminar information archive ～04/17｜Next seminar｜Future seminars 04/18～
2015/03/16
13:30-15:00, 15:30-17:30 Room #Balcony A, Kavli IPMU (Graduate School of Math. Sci. Bldg.)
Hiroshi Iritani (Kyoto University)
Toric mirror symmetry via shift operators (ENGLISH)
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Iritani.pdf
Hiroshi Iritani (Kyoto University)
Toric mirror symmetry via shift operators (ENGLISH)
[ Abstract ]
Recently, shift operator for equivariant quantum cohomology
has been introduced in the work of Braverman, Maulik, Okounkov and
Pandharipande. This can be viewed as an equivariant lift of the
Seidel representation, and intertwines quantum connections with
different equivariant parameters.
In this series of talks, I will explain that shift operators essentially
"reconstruct" mirrors of toric varieties. More precisely we obtain the
following from basic properties of shift operators:
1. Givental's mirror theorem.
2. Landau-Ginzburg potential and primitive form.
3. Extended I-functions.
We will also see that the Gamma integral structure arises as
a solution to the difference equation defined by shift operators.
[ Reference URL ]Recently, shift operator for equivariant quantum cohomology
has been introduced in the work of Braverman, Maulik, Okounkov and
Pandharipande. This can be viewed as an equivariant lift of the
Seidel representation, and intertwines quantum connections with
different equivariant parameters.
In this series of talks, I will explain that shift operators essentially
"reconstruct" mirrors of toric varieties. More precisely we obtain the
following from basic properties of shift operators:
1. Givental's mirror theorem.
2. Landau-Ginzburg potential and primitive form.
3. Extended I-functions.
We will also see that the Gamma integral structure arises as
a solution to the difference equation defined by shift operators.
http://fmsp.ms.u-tokyo.ac.jp/FMSPLectures_Iritani.pdf
