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Complex Geometry Seminar
Minseong Kwon, Integrability of G-structures
B266 IBS, Korea, Republic ofInsong Choe, Minimal Rational Curves on the Moduli Spaces of Symplectic and Orthogonal Bundles over a Curve
B266 IBS, Korea, Republic ofSpeaker Insong Choe Konkuk University Let M be the moduli of vector bundles over a curve of fixed determinant. It is known that the Hecke curves are rational curves of minimal degree on M passing through a general point of M. We prove a similar result for the moduli of symplectic and orthogonal bundles. …
Eunjeong Lee, Geometry of Flag Varieties and Related Combinatorics
B266 IBS, Korea, Republic ofSpeaker Enjeong Lee IBS-CGP For a semisimple algebraic group G and a Borel subgroup B, the homogeneous space G/B, called the flag variety, is a smooth projective variety which has a fruitful connection with G-representations. Indeed, the set of global sections H0(G/B, L) is an irreducible G-representation for a very ample line bundle …
Kyeong-Dong Park, Kähler-Einstein Metrics on Smooth Fano Symmetric Varieties with Picard Number One
B266 IBS, Korea, Republic ofSpeaker Kyeong-Dong Park IBS-CGP Symmetric varieties are normal equivarient open embeddings of symmetric homogeneous spaces and they are interesting examples of spherical varieties. I will prove that all smooth Fano symmetric varieties with Picard number one admit Kähler-Einstein metrics using a combinatorial criterion for K-stability of Fano spherical varieties obtained by Delcroix. To …
Minseong Kwon, Integrability of G-structures II
B266 IBS, Korea, Republic ofSpeaker Minseong Kwon KAIST This is a working seminar to introduce the notion of an integrable G-structure and its obstruction class. In the first talk, I discussed the definition of an integrable G-structure and introduced the existence theorem for the structure tensor. In this talk, I will construct the structure tensor of a …
Minseong Kwon, Integrability of G-structures III
B266 IBS, Korea, Republic ofSpeaker Minseong Kwon KAIST This is a working seminar to introduce the notion of an integrable G-structure and its obstruction class. In the previous two talks, we discussed the definition of the k-th order structure tensor of a G-structure. In the third talk, we will discuss how the structure tensors can be characterized …
Sangbum Yoo, Spectral Data for Principal Higgs Bundles over a Singular Curve
B266 IBS, Korea, Republic ofSpeaker Sangbum Yoo Gongju National University of Education Spectral data for Higgs bundles over a smooth curve has been studied by several mathematicians. The studies in this direction are originated by N.J.Hitchin. Specially, it has contributed to the studies on the fibers of the Hitchin map. In this talk, I will introduce spectral …
Seung-Jo Jung, Hodge Ideals and Spectra of Hypersurface Singularities
B266 IBS, Korea, Republic ofSpeaker Seung-Jo Jung Jeonbuk National University Recently Mustata-Popa introduced a generalisation of multiplier ideals, which is called Hodge ideals. This talk introduces the Hodge ideals and explains the relations with other invariants, e.g. Bernstein-Sato polynomials, Hodge spectra, log canonical thresholds, minimal exponents etc. Mainly this talk concerns the relation between Hodge ideals and …
Hyungryul Baik, Limits of Canonical Metrics in Low-dimensions
B266 IBS, Korea, Republic ofSpeaker Hyungryul Baik KAIST For a tower of finite normal covers of graphs or surfaces, one can consider a sequence of metrics on the base given by pull-back of canonical metric of the covers. We show that such a sequence has a limit and it depends only on the cover approximated by the …
Sungmin Yoo, Fiberwise Kähler-Ricci Flows on Families of Strongly Pseudoconvex Domains
B266 IBS, Korea, Republic ofSpeaker Sungmin Yoo IBS, Center for Complex Geometry A study on the positive variation of Kähler-Einstein metrics is first developed by Schumacher. More precisely, he has proved that the fiberwise Kähler-Einstein metrics on a family of canonically polarized compact Kähler manifolds is positive-definite on the total space. Later, Berman constructed the fiberwise Kähler-Ricci …
Sungmin Yoo, Bergman Metrics and Kähler-Einstein Metrics on Projective Manifolds
B266 IBS, Korea, Republic ofSpeaker Sungmin Yoo IBS, Center for Complex Geometry After Yau suggested the problem of approximations of Kähler-Einstein metrics by Bergman type metrics, various types of Bergman metrics have been developed and studied by Tian, Donaldson, Tsuji, etc. They showed that if a polarized manifold admits a Kähler-Einstein metric, there exist a sequence of …