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

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

Bo-Hae Im, A Hyperelliptic Curve Mapping to Specified Elliptic Curves

B266 IBS

     Speaker Bo-Hae Im KAIST (This is a part of Arithemetic Geometry Day in IBS-CCG.) We are interested in the existence and non-existence of rational curves on certain Kummer varieties which can be applied to the rank problem of quadratic twists of elliptic curves. In this talk, we prove that if the j-invariants of

WonTae Hwang, Jordan Constants of Simple Abelian Varieties over Fields of Positive Characteristic

B266 IBS

     Speaker WonTae Hwang Jeonbuk National Univ. (This is a part of Arithemetic Geometry Day in IBS-CCG.) We compute the Jordan constants of simple abelian surfaces over fields of positive characteristic, with the aid of a similar computation on the Jordan constants of some arithmetic objects. As an update, we also briefly record a

Junho Peter Whang, Decidable Diophantine Problems on Character Varieties

B266 IBS

     Speaker Junho Peter Whang Seoul National Univ. (This is a part of Arithemetic Geometry Day in IBS-CCG.) Character varieties of manifolds are basic objects in geometry and low-dimensional topology. We motivate the Diophantine study of their integral points. After discussing an effective finite generation theorem for integral points on SL2-character varieties of surfaces,

Atsushi Ito, Projective Normality of General Polarized Abelian Varieties

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     Speaker Atsushi Ito Okayama Univ. Projective normality is an important property of ample line bundles on algebraic varieties. In this talk, I will explain that a general g-dimensional polarized abelian variety is projectively normal if χ(X, L) > 22g-1. We note that this bound is sharp. A key tool is basepoint-freeness threshold, which

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

B266 IBS

     Speaker Dongsoo Shin Chungnam National Univ. A sandwiched surface singularity is a rational surface singularity that admits a birational map to the complex projective plane. de Jong and van Straten prove that deformations of sandwiched surface singularities are induced from special deformations of germs of plane curve singularities (called picture deformations). On the

Nam-Hoon Lee, Mirror Pairs of Calabi-Yau Threefolds from Mirror Pairs of Quasi-Fano Threefolds

B266 IBS

     Speaker Nam-Hoon Lee Hongik Univ. We present a new construction of mirror pairs of Calabi-Yau manifolds by smoothing normal crossing varieties, consisting of two quasi-Fano manifolds. We introduce a notion of mirror pairs of quasi-Fano manifolds with anticanonical Calabi-Yau fibrations using conjectures about Landau-Ginzburg models. Utilizing this notion, we give pairs of normal

Radu Laza, Deformations of Singular Fano and Calabi-Yau Varieties

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     Speaker Radu Laza Stony Brook University It is well known that Calabi-Yau manifolds have good deformation theory, which is controlled by Hodge theory. By work of Friedman, Namikawa, M. Gross, Kawamata, Steenbrink and others, some of these results have been extended to Calabi-Yau threefolds with canonical singularities. In this talk, I will report

Keiji Oguiso, On Kawaguchi-Silverman Conjecture for Birational Automorphisms of Irregular Threefolds

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     Speaker Keiji Oguiso Univ. of Tokyo This is a joint work in progress with Professors Jungkai-Alfred Chen and Hsueh-Yung Lin. We study the main open parts of Kawaguchi-Silverman Conjecture (KSC), asserting that for a birational self-map f of a smooth projective variety X defined over K, the arithmetic degree αf(x) exists and coincides

Brendan Hassett, Recent Progress and Questions on Stable Rationality

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     Speaker Brendan Hassett ICERM / Brown Univ. A complex variety X is rational if its field of meromorphic functions is isomorphic to C(t1, ..., td), the function field of projective space Pd. It is stably rational if X × Pm is rational for some m. Topological and complex invariants give criteria for whether

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