Yunhyung Cho, Monotone Lagrangian Tori in Fano Varieties

B236-1 IBS, Korea, Republic of

     Speaker Yunhyung Cho Sungkyunkwan University This is a survey talk of current progress of mirror symmetry of Fano varieties. For a given smooth Fano variety X, it has been conjectured that there exists a Laurent polynomial called a (weak) Landau-Ginzburg mirror (or weak LG mirror shortly) which encodes a quantum cohomology ring structure

Donghoon Jang, Circle Actions on Almost Complex Manifolds with Isolated Fixed Points

B236-1 IBS, Korea, Republic of

     Speaker Donghoon Jang Pusan National University We briefly review group actions on manifolds and equivariant cohomology, which is cohomology of a manifold with a group action. We review classification results for circle actions on various types of manifolds in low dimensions. An almost complex manifold is a manifold with a complex structure on

Insong Choe, Subsheaves of Maximal Rank in a Symplectic and Orthogonal Bundle over a Curve

B236-1 IBS, Korea, Republic of

    Speaker Insong Choe Kunkuk University We first review the known results on the Quot schemes on a smooth algebraic curve. Next we explain how they can be generalized to the Lagrangian Quot scheme, which parametrizes Lagrangian subsheaves on a symplectic vector bundle. Also we discuss the parallel results for orthogonal bundles. This will

Donggun Lee, Birational Geometry of Generalized Hessenberg Varieties and the Generalized Shareshian-Wachs Conjecture

B236-1 IBS, Korea, Republic of

    Speaker Donggun Lee IBS-CCG Hessenberg varieties are subvarieties of flag varieties with interesting properties in both algebro-geometric and combinatorial perspectives. The Shareshian-Wachs conjecture connects their cohomology with the chromatic quasi-symmetric functions of the associated graphs, which are refinements of the chromatic polynomials. In this talk, we introduce generalized Hessenberg varieties and study their

Shin-Young Kim, Minimal Rational Curves on Complete Symmetric Varieties

B236-1 IBS, Korea, Republic of

    Speaker Shin-Young Kim IBS-CGP We describe the families of minimal rational curves on any complete symmetric variety, and the corresponding varieties of minimal rational tangents. In particular, we prove that these varieties are homogeneous and that for non-exceptional irreducible wonderful varieties, there is a unique family of minimal rational curves. We relate these

Qifeng Li, Rigidity of Projective Symmetric Manifolds of Picard Number 1 Associated to Composition Algebras

B236-1 IBS, Korea, Republic of

    Speaker Qifeng Li Shandong University To each complex composition algebra A, there associates a projective symmetric manifold X(A) of Picard number 1. The vareity X(A) is closed related with Freudenthal's Magic Square, which is a square starting from the adjiont varieties of F4, E6, E7 and E8. In a recent joint work with

Patrick Brosnan, How Markman Saves the Hodge Conjecture (for Weil Type Abelian Fourfolds) from Kontsevich, I

B236-1 IBS, Korea, Republic of

    Speaker Patrick Brosnan University of Maryland I'll explain what I know about two very interesting pieces of work: (1) Markman's proof of the Hodge conjecture for Weil type abelian fourfolds of discriminant 1. (2) Kontsevich's tropical approach to looking for counterexamples to the Hodge conjecture for Weil type abelian varieties. Then I'll explain

Patrick Brosnan, How Markman Saves the Hodge Conjecture (for Weil Type Abelian Fourfolds) from Kontsevich, II

B236-1 IBS, Korea, Republic of

    Speaker Patrick Brosnan University of Maryland I'll explain what I know about two very interesting pieces of work: (1) Markman's proof of the Hodge conjecture for Weil type abelian fourfolds of discriminant 1. (2) Kontsevich's tropical approach to looking for counterexamples to the Hodge conjecture for Weil type abelian varieties. Then I'll explain

Minseong Kwon, Spherical Geometry of Hilbert Schemes of Conics in Adjoint Varieties

B266 IBS, Korea, Republic of

    Speaker Minseong Kwon KAIST For each rational homogeneous space, the space of lines is now well-understood and can be described in terms of the induced group action. It is natural to consider rational curves of higher degree, and in this talk, we discuss geometry of conics in adjoint varieties, which are rational homogeneous

Kyeong-Dong Park, K-stability of Fano Spherical Varieties, I

B266 IBS, Korea, Republic of

    Speaker Kyeong-Dong Park Gyeongsang National University The aim of this seminar is to provide participants with a comprehensive understanding of the paper "K-stability of Fano spherical varieties" by Thibaut Delcroix. For a reductive algebraic group G, a normal G-variety is called spherical if it contains an open B-orbit, where B is a fixed

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