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Dongsoo Shin, Deformations of Sandwiched Surface Singularities and the Minimal Model Program

B236-1 IBS, Korea, Republic of

     Speaker Dongsoo Shin Chungnam National U. (This is a part of Seminars on Algebraic Surfaces and Related Topics.) We investigate the correspondence between three theories of deformations of rational surface singularities: de Jong and van Straten's picture deformations, Kollár's P-resolutions, and Pinkham's smoothings of negative weights. We provide an explicit method for obtaining, …

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JongHae Keum, Mori Dream Surfaces of General Type with pg=0

B236-1 IBS, Korea, Republic of

     Speaker JongHae Keum KIAS (This is a part of Seminars on Algebraic Surfaces and Related Topics.) The Cox ring of a variety is the total coordinate ring, i.e., the direct sum of all spaces of global sections of all divisors. When this ring is finitely generated, the variety is called Mori dream (MD). …

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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 …

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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 …

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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 …

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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 …

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Jihun Yum, Stochastic Bergman Geometry

B266 IBS, Korea, Republic of

    Speaker Jihun Yum IBS-CCG For a bounded domain Ω in Cn, let P(Ω) be the set of all (real) probability distributions on Ω. Then, in general, P(Ω) becomes an infinite-dimensional smooth manifold and it always admit a natural Riemannian pseudo-metric, called the Fisher information metric, on P(Ω). Information geometry studies a finite-dimensional submanifold …

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Junyan Zhao, Moduli of Curves of Genus 6 and K-stability

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    Speaker Junyan Zhao University of Illinois Chicago A general curve C of genus 6 can be embedded into the unique quintic del Pezzo surface X5 as a divisor of class -2KX5. This embedding is unique up to the action of the symmetric group S5. Taking a double cover of X5 branched along C yields …

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Hoseob Seo, On L2 Extension from Singular Hypersurfaces

B266 IBS, Korea, Republic of

    Speaker Hoseob Seo IBS CCG In L2 extension theorems from a singular hypersurface in a complex manifold, important roles are played by certain measures such as the Ohsawa measure which determine when a given function can be extended. We show that the singularity of the Ohsawa measure can be identified in terms of …

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