2023-1 Dynamics and Number Theory (이슬비)

Entropy of symplectic automorphisms

수학강연회 | 강연자 : 김준태 | 소속 : 서강대학교

※ 강연 뒷부분이 녹화되지 않았습니다.

A symplectic manifold is a space with a global structure on which Hamiltonian equations are defined. A classical result by Darboux says that every symplectic manifold locally looks standard,

so it has been interesting to study global properties of symplectic manifolds.

Since Gromov invented his famous theory of J-holomorphic curves in 1985, symplectic rigidity phenomena have been found in many different ways. In this talk, we explore it in terms of the symplectic mapping class groups and entropies.

Equations defining algebraic curves and their tangent and secant varieties

수학강연회 | 강연자 : 박진형 | 소속 : KAIST

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.

2023-1 Number Theory (김민규)

BK21 FOUR Rookies Pitch | 강연자 : 김민규 | 소속 : 성균관대학교

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2023-1 Number Theory (김대준)

BK21 FOUR Rookies Pitch | 강연자 : 김대준 | 소속 : KIAS

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2023-1 Symplectic Topology (노경민)

BK21 FOUR Rookies Pitch | 강연자 : 노경민 | 소속 : 서울대학교

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2023-1 Symplectic Topology (이상진)

BK21 FOUR Rookies Pitch | 강연자 : 이상진 | 소속 : IBS-CGP

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Descent in derived algebraic geometry

수학강연회 | 강연자 : 조창연 | 소속 : 서강대학교

Among many different ways to introduce derived algebraic geometry is an interplay between ordinary algebraic geometry and homotopy theory. The infinity-category theory, as a manifestation of homotopy theory, supplies better descent results even for ordinary algebro-geometric objets, not to mention objects of interest in the derived setting. I'll explain what this means in the first half. The second half will be devoted to my recent work on some excision and descent results for commutative ring spectra, generalizing Milnor excision for perfect complexes of ordinary commutative rings and v-descent for perfect complexes of locally noetherian derived stacks by Halpern-Leistner and Preygel, respectively. No prior experience on derived algebraic geometry is required for the talk.