• Journal of the Chungcheong Mathematical Society
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• v.34 no.1
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• pp.93-107
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• 2021

We study the Gromov-Witten invariants of $\underbrace{{\mathbb{P}}^1\;{\times}\;{\mathbb{P}}^1\;{\times}\;{\ldots}\;{\times}\;{\mathbb{P}}^1}_{n}.$ Our main result is a proof of some vanishing conditions on the Gromov-Witten invariants of ℙ1 × ℙ1 × … × ℙ1 in all genera.

• Journal of the Korean Mathematical Society
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• v.60 no.3
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• pp.479-501
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• 2023

We study the rationality and symmetry of the Gromov-Witten invariants of the projective line twisted by certain line bundles.

• Journal of the Chungcheong Mathematical Society
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• v.36 no.4
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• pp.231-244
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• 2023

We study the modularity and holomorphic anomaly equation for Hodge-Gromov-Witten invariants of elliptic curves.

• Journal of the Korean Mathematical Society
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• v.38 no.5
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• pp.1061-1068
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• 2001

We write down explicity a recursive formula of one-pointed gravitational Gromov-Witten invariants and reduce the computation of them to a combinatoric problem which is not solved yet. The one-pointed invariants were played important role in Givental’s program in mirror symmetry. In section 3, we describe the combinatoric problem which can be read independently.

• Journal for History of Mathematics
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• v.30 no.3
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• pp.185-199
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• 2017

In tropical geometry, the sum of two numbers is defined as the minimum, and the multiplication as the sum. As a way to build tropical plane curves, we could use Newton polygons or amoebas. We study one method to convert the representation of an algebraic variety from an image of a rational map to the zero set of some multivariate polynomials. Mikhalkin proved that complex curves can be replaced by tropical curves, and induced a combination formula which counts the number of tropical curves in complex projective plane. In this paper, we present close examinations of this particular combination formula.