일정
2:00-2:50
2:00-2:50
조창연 (서강대학교)
조창연 (서강대학교)
제목: Descent in derived algebraic geometry
제목: Descent in derived algebraic geometry
초록: 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.
초록: 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.
3:00-3:50
3:00-3:50
조다혜(연세대학교)
조다혜(연세대학교)
제목: Introduction to (Relative) Symplectic Cohomology and Applications
제목: Introduction to (Relative) Symplectic Cohomology and Applications
초록: For certain non-compact symplectic manifold with nice properties, we can apply Morse theory on the space of loops on the symplectic manifold, following Floer’s idea. In this talk, we will review definitions of symplectic cohomology, its relative version, and some geometric properties of them. There is a spectral sequence relating two versions of symplectic cohomology via the winding filtration. I will briefly explain the main idea constructing the spectral sequence and provide applications.
초록: For certain non-compact symplectic manifold with nice properties, we can apply Morse theory on the space of loops on the symplectic manifold, following Floer’s idea. In this talk, we will review definitions of symplectic cohomology, its relative version, and some geometric properties of them. There is a spectral sequence relating two versions of symplectic cohomology via the winding filtration. I will briefly explain the main idea constructing the spectral sequence and provide applications.
4:10-5:00
김재현 (이화여자대학교)
4:10-5:00
김재현 (이화여자대학교)
제목: Cylinders in del Pezzo surfaces
초록: Cylinder is an A^1-ruled Zariski open subset in a normal projective variety over some affine variety. If the boundary of cylinder is defi ned by an eff ective member in numerical class of given divisor, then the cylinder is called polar for the divisor. The existence of such a structure has deep connections to certain group actions on the corresponding affi ne cone. From this point of view, the ample polar cylindricity of del Pezzo surfaces of degrees at least 3 has been extensively studied in many areas. In this talk, we focus on the ample polar cylinders in smooth del Pezzo surfaces of lower degrees and explain some method to characterize hem.
제목: Cylinders in del Pezzo surfaces
초록: Cylinder is an A^1-ruled Zariski open subset in a normal projective variety over some affine variety. If the boundary of cylinder is defi ned by an eff ective member in numerical class of given divisor, then the cylinder is called polar for the divisor. The existence of such a structure has deep connections to certain group actions on the corresponding affi ne cone. From this point of view, the ample polar cylindricity of del Pezzo surfaces of degrees at least 3 has been extensively studied in many areas. In this talk, we focus on the ample polar cylinders in smooth del Pezzo surfaces of lower degrees and explain some method to characterize hem.
DINNER
DINNER