Han-Bom Moon
Visitor (2025.6.8-2025.6.14) from Fordham University
Han-Bom Moon, Ulrich bundles on intersections of quadrics
An Ulrich bundle is a vector bundle with very strong cohomology vanishing conditions. Eisenbud and Schreyer conjectured that every smooth projective variety possesses an Ulrich bundle. Despite many results on low dimensional varieties and special varieties, the general existence is unknown. In this talk, I will describe recent work in progress with Kyoung-Seog Lee and Jiwan Jeong on the construction of Ulrich bundles on an intersection of quadrics.
Han-Bom Moon, Derived Category of Moduli of Vector Bundles II
The derived category of a smooth projective variety is an object expected to encode much birational geometric information. Recently, there have been many results on decomposing derived categories into simpler building blocks. In the first lecture, I will provide an elementary introduction to two independent topics — 1. the definition and basic properties of the derived category and 2. moduli spaces of vector bundles on a curve. In the second lecture, I will present recent progress on the structure of the derived category of the moduli space. Most of the lectures will be accessible to graduate students with basic knowledge of algebraic geometry. The second lecture is based on ongoing joint work with Kyoung-Seog Lee.
Han-Bom Moon, Derived Category of Moduli of Vector Bundles I
The derived category of a smooth projective variety is an object expected to encode much birational geometric information. Recently, there have been many results on decomposing derived categories into simpler building blocks. In the first lecture, I will provide an elementary introduction to two independent topics — 1. the definition and basic properties of the derived category and 2. moduli spaces of vector bundles on a curve. In the second lecture, I will present recent progress on the structure of the derived category of the moduli space. Most of the lectures will be accessible to graduate students with basic knowledge of algebraic geometry. The second lecture is based on ongoing joint work with Kyoung-Seog Lee.