JongHae Keum, Fake quadric surfaces

B236-1 IBS, Korea, Republic of

    Speaker JongHae Keum KIAS A smooth projective complex surface S is called a Q-homology quadric if it has the same Betti numbers as the smooth quadric surface. Let S be a Q-homology quadric. Then its cohomology lattice is of rank 2, (even or odd) unimodular. By the classification of surfaces, S is either

Gian Pietro Pirola, Asymptotic directions on the moduli space of curves

B236-1 IBS, Korea, Republic of

    Speaker Gian Pietro Pirola University of Pavia We present some computational improvements that allow us to study asymptotic lines in the tangent of the moduli space Mg of the curves of genus g. The asymptotic directions are those tangent directions that are annihilated by the second fundamental form induced by the Torelli map.

Benjamin McMillan, Secondary Characteristic classes and Chern-Weil theory of (Haefliger) singular foliations I

B236-1 IBS, Korea, Republic of

    Speaker Benjamin McMillan IBS CCG Foliations have a theory of characteristic classes that is much like that of vector bundles, but with notable differences. Some of the characteristic classes of a foliation come from its induced normal bundle, but there are additional secondary classes that depend on more detailed information about the foliation.

Benjamin McMillan, Secondary Characteristic classes and Chern-Weil theory of (Haefliger) singular foliations II

B236-1 IBS, Korea, Republic of

    Speaker Benjamin McMillan IBS CCG Foliations have a theory of characteristic classes that is much like that of vector bundles, but with notable differences. Some of the characteristic classes of a foliation come from its induced normal bundle, but there are additional secondary classes that depend on more detailed information about the foliation.

Benjamin McMillan, Secondary Characteristic classes and Chern-Weil theory of (Haefliger) singular foliations III

B236-1 IBS, Korea, Republic of

    Speaker Benjamin McMillan IBS CCG Foliations have a theory of characteristic classes that is much like that of vector bundles, but with notable differences. Some of the characteristic classes of a foliation come from its induced normal bundle, but there are additional secondary classes that depend on more detailed information about the foliation.

Gian Pietro Pirola, Sections of the Jacobian bundles of plane curves and applications

B236-1 IBS, Korea, Republic of

    Speaker Gian Pietro Pirola University of Pavia We study normal functions (sections of the Jacobian bundle) defined on the moduli space of pointed plane curves. Using the infinitesimal Griffiths invariant (refined by M. Green and C. Voisin) we show that a normal function with nontrivial but sufficiently "small" support cannot be "locally constant".

Han-Bom Moon, Ulrich bundles on intersections of quadrics

B236-1 IBS, Korea, Republic of

    Speaker Han-Bom Moon Fordham University An Ulrich bundle is a vector bundle with very strong cohomology vanishing conditions. Eisenbud and Schreyer conjectured that every smooth projective variety possesses an Ulrich bundle. Despite many results on low dimensional varieties and special varieties, the general existence is unknown. In this talk, I will describe recent

Sung Gi Park, Hodge symmetries of singular varieties

B236-1 IBS, Korea, Republic of

    Speaker Sung Gi Park Princeton U. / IAS The Hodge diamond of a smooth projective complex variety exhibits fundamental symmetries, arising from Poincaré duality and the purity of Hodge structures. In the case of a singular projective variety, the complexity of the singularities is closely related to the symmetries of the analogous Hodge-Du

Yoosik Kim, Disk Counting via GIT Quotients

B236-1 IBS, Korea, Republic of

    Speaker Yoosik Kim Pusan National University According to the Kempf–Ness theorem, the GIT quotient is equivalent to the symplectic reduction. Using this correspondence, we explain how to relate the counting of holomorphic disks between a symplectic manifold equipped with a Hamiltonian group action and its symplectic reduction. As an application, we derive the

Alex Abreu, On the Torelli Theorem for graphs and stable curves

B236-1 IBS, Korea, Republic of

    Speaker Alex Abreu Universidade Federal Fluminense The classical Torelli theorem states that a smooth curve can be recovered from its polarized Jacobian. In this talk, we will discuss the extensions of this theorem to stable curves and their dual graphs, as well as its dependence on the concept of compactified Jacobians. First, we

Yoonjoo Kim, Two results on Lagrangian fibrations

B236-1 IBS, Korea, Republic of

    Speaker Yoonjoo Kim Columbia U. I would like to report two ongoing results on Lagrangian fibrations of smooth symplectic varieties. The first is the construction of a delta-regular smooth group scheme that acts on a given Lagrangian fibration. It is a generalization of the result of Arinkin-Fedorov, who proved the result under the

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