기초과학 자율운영 중점연구소

수학과에서 아래와 같이 colloquium를 실시합니다.

많은 관심과 참여 부탁드립니다.

주관: 기초과학연구소(자율운영 중점연구소지원사업)

일시: 2025년 3월 6일 목요일 16:30

장소: 팔달관 621호

연사: 박한철 교수(제주대학교 수학교육과)

주제: Moduli space of vector bundles and their variations

Abstract: Vector bundles are important objects in geometry. Tangent bundles, cotangent bundles, Möbius bundle are examples of vector bundles.

In algebraic geometry, we consider vector bundles over algebraic varieties with holomorphic transition map. Rank 1 vector bundles are called line bundles and (holomorphic) line bundles over a projective line or elliptic curves are classified by Grothendieck and Atiyah.  For higher ranks, their moduli spaces are firstly defined by using geometric invariant theory(GIT) in the 1960s and it has been actively studied since then.

In this talk, I will start from introducing definition of vector bundles and examples of vector bundles, and operations on the space of vector bundles. After that I will introduce holomorphic vector bundles over algebraic curves, and some famous results on moduli space of line bundles(=Picard groups) and moduli space of vector bundles with higher ranks. I will also introduce variations of vector bundles(principal G-bundles, bundles with parabolic structures, Higgs bundles) and their moduli spaces. I will also introduce some of my research on them.