Math Colloquia

1068

Date | May 18, 2023 |
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Speaker | 박진형 |

Dept. | 카이스트 |

Room | 129-101 |

Time | 16:00-18:00 |

서울대학교 상산수리과학관 강당(129동 101호)

Zoom 회의실 445 008 9509

It is a fundamental problem in algebraic geometry to study equations defining algebraic curves. In 1984, Mark Green formulated a famous conjecture on equations defining canonical curves and their syzygies. In early 2000's, Claire Voisin made a major breakthrough by proving that Green's conjecture holds for general curves. A few years ago, Aprodu-Farkas-Papadima-Raicu-Weyman gave a new proof of Voisin's theorem by studying equations defining tangent developable surfaces, and recently, I obtained a simple geometric proof of their result using equations defining secant varieties. In this talk, I first review the geometry of algebraic curves, and then, I explain the main ideas underlying the recent work on syzygies of algebraic curves and their tangent and secant varieties.

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