Dano Kim, Canonical Bundle Formula and Degenerating Families of Volume Forms


     Speaker Dano Kim Department of Mathematical Sciences, Seoul National University We will talk about a metric version of Kawamata's canonical bundle formula for log Calabi-Yau fibrations: the L2 metric carries singularity described by the discriminant divisor and the moduli part line bundle has a singular hermitian metric with vanishing Lelong numbers. This answers

Baohua Fu, Normalized Tangent Bundle, Pseudoeffective Cone and Varieties with Small Codegree


     Speaker Baohua Fu Chinese Academy of Science We propose a conjectural list of Fano manifolds of Picard number one whose normalized tangent bundle is pseudoeffective and we prove it in various situations by relating it to the complete divisibility conjecture of Russo and Zak on varieties with small codegrees. The pseudoeffective cone of

Pak Tung Ho, Chern-Yamabe Problem


     Speaker Pak Tung Ho Sogang University I will explain what the Chern-Yamabe problem is, and talk about the Chern-Yamabe flow which is a geometric flow approach to solve the Chern-Yamabe problem. I will also mention other results related to the Chern-Yamabe problem.

Yong Hu, Noether-Severi Inequality and Equality for Irregular Threefolds of General Type

B266 IBS

     Speaker Yong Hu KIAS For complex smooth irregular 3-folds of general type, I will introduce the optimal Noether-Severi inequality. This answers an open question of Zhi Jiang in dimension three. Moreover, I will also completely describe the canonical models of irregular 3-folds attaining the Noether-Severi equality. This is a joint work with Tong

Sukmoon Huh, Logarithmic Sheaves on Projective Surfaces

B266 IBS

     Speaker Sukmoon Huh Sungkyunkwan University A logarithmic sheaf is a sheaf of differential one-forms on a variety with logarithmic poles along a given divisor. One of the main problems on this object is to see whether Torelli property holds, i.e. whether two different divisors define two non-isomorphic logarithmic sheaves. In this talk, after

Yonghwa Cho, Cohomology of Divisors on Burniat Surfaces

B266 IBS

     Speaker Yonghwa Cho KIAS A (primary) Burniat surface is a complex surface of general type that can be obtained as a bidouble cover of del Pezzo surface with K2 = 6. The Picard group is an abelian group of rank 4 with torsion part isomorphic to (Z/2)6. Alexeev studied the divisors on Burniat

Jinhyung Park, Comparing Numerical Iitaka Dimensions


     Speaker Jinhyung Park Sogang University There are several definitions of the "numerical" Iitaka dimensions of a pseudoeffective divisor, which are numerical analogues to the Iitaka dimension. Recently, Lesieutre proved that notions of numerical Iitaka dimensions do not coincide. In this talk, we prove that many of numerical Iitaka dimensions are equal to the

Sung Rak Choi, Subadditivity of Okounkov Bodies


     Speaker Sung Rak Choi Yonsei University We will investigate the subadditivity theorem of Okounkov bodies for algebraic fiber spaces. As an application, we obtain the subadditivity of the numerical Kodaira dimension and the restricted volume for algebraic fiber spaces. As a byproduct, we obtain a criterion of birational isotriviality in terms of Okounkov

Changho Han, Compact Moduli of Lattice Polarized K3 Surfaces with Nonsymplectic Cyclic Action of Order 3


     Speaker Changho Han University of Georgia Observe that any construction of "meaningful" compactification of moduli spaces of objects involve enlarging the class of objects in consideration. For example, Deligne and Mumford introduced the notion of stable curves in order to compactify the moduli of smooth curves of genus g, and Satake used the

Yoon-Joo Kim, The Dual Lagrangian Fibration of Compact Hyper-Kähler Manifolds


     Speaker Yoon-Joo Kim Stony Brook University A compact hyper-Kähler manifold is a higher dimensional generalization of a K3 surface. An elliptic fibration of a K3 surface correspondingly generalizes to the so-called Lagrangian fibration of a compact hyper-Kähler manifold. It is known that an elliptic fibration of a K3 surface is always "self-dual" in

Yuchen Liu, K-stability and Moduli of Quartic K3 Surfaces


     Speaker Yuchen Liu Northwestern University We show that K-moduli spaces of (P3, cS) where S is a quartic surface interpolates between the GIT moduli space and the Baily-Borel compactification as c varies in (0,1). We completely describe the wall crossings of these K-moduli spaces. As a consequence, we verify Laza-O’Grady's prediction on the

Yewon Jeong, Several Types of Dual Defective Cubic Hypersurfaces


     Speaker Yewon Jeong IBS, Center for Complex Geometry Given a hypersurface X = V(f) in a complex projective space, we say X is dual defective if the Gauss map of X, the restriction of the gradient map of f on X, has positive dimensional fibers. Especially for cubics, there is an interesting classification

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