Abstracts
Speaker : 임보해 (Im, Bo-Hae) (Talk 1)
Title : A survey of finiteness results for rational points and the Mordell-Weil Theorem
Abstract : These lectures introduce the arithmetic theory of rational and integral points on algebraic curves, emphasizing the role of height functions and the Mordell–Weil theorem. We survey classical finiteness results on rational points, situating them within the broader landscape of Diophantine geometry, while avoiding technical proofs. Height functions on projective space and abelian varieties are introduced as fundamental tools for measuring arithmetic complexity and we prove the Mordell–Weil theorem for elliptic curves, illustrating how heights and descent combine to yield finite generation of rational points.
Speaker : 김완수 (Kim, Wansu) (Talk 1)
Title : An introduction to complex Siegel modular varieties and their compactifications
Abstract : Siegel modular varieties can be viewed in two distinct ways: as analytic quotients of the Siegel upper half-space and as algebraic moduli spaces classifying principally polarised abelian varieties with level structure. In this short course, we will review the basic properties of these varieties and discuss the construction of their compactifications—namely, the minimal and toroidal compactifications. The lectures will concentrate on the analytic theory, with a brief discussion of arithmetic aspects if time permits.
Speaker : 임보해 (Im, Bo-Hae) (Talk 2)
Title : A survey of finiteness results for rational points and the Mordell-Weil Theorem
Abstract : These lectures introduce the arithmetic theory of rational and integral points on algebraic curves, emphasizing the role of height functions and the Mordell–Weil theorem. We survey classical finiteness results on rational points, situating them within the broader landscape of Diophantine geometry, while avoiding technical proofs. Height functions on projective space and abelian varieties are introduced as fundamental tools for measuring arithmetic complexity and we prove the Mordell–Weil theorem for elliptic curves, illustrating how heights and descent combine to yield finite generation of rational points.
Speaker : 김완수 (Kim, Wansu) (Talk 2)
Title : An introduction to complex Siegel modular varieties and their compactifications
Abstract : Siegel modular varieties can be viewed in two distinct ways: as analytic quotients of the Siegel upper half-space and as algebraic moduli spaces classifying principally polarised abelian varieties with level structure. In this short course, we will review the basic properties of these varieties and discuss the construction of their compactifications—namely, the minimal and toroidal compactifications. The lectures will concentrate on the analytic theory, with a brief discussion of arithmetic aspects if time permits.
Speaker : 임보해 (Talk 3)
Title : A survey of finiteness results for rational points and the Mordell-Weil Theorem
Abstract : These lectures introduce the arithmetic theory of rational and integral points on algebraic curves, emphasizing the role of height functions and the Mordell–Weil theorem. We survey classical finiteness results on rational points, situating them within the broader landscape of Diophantine geometry, while avoiding technical proofs. Height functions on projective space and abelian varieties are introduced as fundamental tools for measuring arithmetic complexity and we prove the Mordell–Weil theorem for elliptic curves, illustrating how heights and descent combine to yield finite generation of rational points.
Speaker : 김완수 (Kim, Wansu) (Talk 3)
Title : An introduction to complex Siegel modular varieties and their compactifications
Abstract : Siegel modular varieties can be viewed in two distinct ways: as analytic quotients of the Siegel upper half-space and as algebraic moduli spaces classifying principally polarised abelian varieties with level structure. In this short course, we will review the basic properties of these varieties and discuss the construction of their compactifications—namely, the minimal and toroidal compactifications. The lectures will concentrate on the analytic theory, with a brief discussion of arithmetic aspects if time permits.