복소기하학연구단
Speaker Yeongrak Kim Pusan National Univ. (This is a part of Algebraic Geometry Day at CCG in IBS.) Ulrich bundles are geometric objects corresponding to maximally generated maximal Cohen-Macaulay modules, whose existence has several interesting applications in commutative algebra, homological algebra, and linear algebra. After a pioneering work of Beauville and Eisenbud-Schreyer, existence …
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 …
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.
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 …
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. …
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. …
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 …
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 …
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 …
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 …
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 …
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 …