Olivier Martin, Measures of Association for Algebraic Varieties

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     Speaker Olivier Martin Stony Brook Univ. I will discuss recent work in collaboration with R. Lazarsfeld which explores the following question: Given varieties X and Y of the same dimension how far are they from being birational? I will define various "measures of association" which quantify the failure of X and Y to

Paul-Andi Nagy, Einstein Deformations of Hyperkaehler Cones

B236 IBS, Korea, Republic of

     Speaker Paul-Andi Nagy IBS CCG For a hyperkaehler cone with compact link (M, g) we describe the Einstein deformation theory of g and relate it to the algebraic geometry of the twistor space Z of M. This is joint work with Uwe Semmelmann.

Kento Fujita, The Calabi Problem for Fano Threefolds

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     Speaker Kento Fujita Osaka Univ. There are 105 irreducible families of smooth Fano threefolds, which have been classified by Iskovskikh, Mori and Mukai. For each family, we determine whether its general member admits a Kähler-Einstein metric or not. This is a joint work with Carolina Araujo, Ana-Maria Castravet, Ivan Cheltsov, Anne-Sophie Kaloghiros, Jesus

Han-Bom Moon, Derived Category of Moduli of Vector Bundles I

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     Speaker Han-Bom Moon Fordham University The derived category of a smooth projective variety is an object expected to encode much birational geometric information. Recently, there have been many results on decomposing derived categories into simpler building blocks. In the first lecture, I will provide an elementary introduction to two independent topics -- 1.

Han-Bom Moon, Derived Category of Moduli of Vector Bundles II

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     Speaker Han-Bom Moon Fordham University The derived category of a smooth projective variety is an object expected to encode much birational geometric information. Recently, there have been many results on decomposing derived categories into simpler building blocks. In the first lecture, I will provide an elementary introduction to two independent topics -- 1.

Sanghoon Baek, Relationship between the Chow and Grothendieck Rings for Generic Flag Varieties

B266 IBS, Korea, Republic of

     Speaker Sanghoon Baek KAIST Consider the canonical morphism from the Chow ring of a smooth variety X to the associated graded ring of the coniveau filtration on the Grothendieck ring of X. In general, this morphism is not injective. However, Nikita Karpenko conjectured that these two rings are isomorphic for a generic flag

Rostislav Devyatov, Multiplicity-free Products of Schubert Divisors and an Application to Canonical Dimension

B266 IBS, Korea, Republic of

     Speaker Rostislav Devyatov KAIST In the first part of my talk I am going to speak about Schubert calculus. Let G/B be a flag variety, where G is a linear simple algebraic group, and B is a Borel subgroup. Schubert calculus studies (in classical terms) multiplication in the cohomology ring of a flag

Jongbaek Song, Regular Hessenberg Varieties and Toric Varieties

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     Speaker Jongbaek Song KIAS A Hessenberg variety is a subvariety of the flag variety (G/B) determined by two parameters: one is an element of the Lie algebra of G and the other is a B-submodule containing the Lie algebra of B, known as a Hessenberg space. In this talk, we focus on elements

Sandor Kovacs, Hodge Sheaves for Singular Families

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     Speaker Sandor Kovacs Univ. of Washington This is a report on joint work with Behrouz Taji. Given a flat projective morphism f : X → B of complex varieties, assuming that B is smooth, we construct a functorial system of reflexive Hodge sheaves on B . If in addition, X is also smooth then

Young-Hoon Kiem, A New Construction of the Moduli Space of Pointed Stable Curves of Genus 0

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     Speaker Young-Hoon Kiem Seoul National University The moduli space of n points on a projective line up to projective equivalence has been a topic of research since the 19th century. A natural moduli theoretic compactification was constructed by Deligne and Mumford as an algebraic stack. Later, Knudsen, Keel, Kapranov and others provided explicit

Chenyang Xu, K-stability of Fano Varieties

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     Speaker Chenyang Xu Princeton Univ. K-stability of Fano varieties was initiated as a central topic in complex geometry, for its relation with the Kähler-Einstein metric. It turns out that the machinery of higher dimensional geometry, developed around the minimal model program, provides a fundamental tool to study it, and therefore makes it an

Gunhee Cho, The Lower Bound of the Integrated Carathéodory-Reiffen Metric and Invariant Metrics on Complete Noncompact Kähler Manifolds

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     Speaker Gunhee Cho UCSB We seek to gain progress on the following long-standing conjectures in hyperbolic complex geometry: prove that a simply connected complete Kähler manifold with negatively pinched sectional curvature is biholomorphic to a bounded domain and the Carathéodory-Reiffen metric does not vanish everywhere. As the next development of the important recent

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