Jungkai Chen (National Taiwan University & NCTS)

Title.
Toward classification of threefold divisorial contractions to curves

Abstract.
Mimimal model program is a fundamental tool of birational geometry. In dimension three and characteristic zero, singularties are better understood and hence many geometric properties can be described explicitly. For example, threefolds divisorial contractions to points are classified thanks to the work of Kawamata, Hayakawa, Kawakita and others. 

In this talk, we will present the recent progress toward the classification of threefold divisorial contractions to curves. Most of the materials are joint work in progress with Jheng-Jie Chen and Hsin-Ku Chen.

Sergey Galkin (PUC-Rio)

Title.
Roger Apéry and the threefold that Fano missed.

Konstantin Loginov (Steklov Institute & Laboratory of Algebraic Geometry, HSE)

Title. Coregularity of smooth Fano threefolds.
Abstract.  A natural way to study Fano varieties is by looking at its (pluri-)anti-canonical divisors. Coregularity measures how singular such divisors could be. We explain how to compute the coregularity of smooth Fano varieties of dimension 3.

Keiji Oguiso (The University of Tokyo)

Title. An abelian fibered Calabi-Yau threefold with a relative automorphism of positive entropy.
Abstract. Positivity of entropy of an automorphism plays a substantial role in both algebraic dynamics and algebro-geometric study of automorphisms of projective varieties, as a measure of complexities of automorphisms. For surfaces including abelian surfaces and K3 surfaces, there are many concrete examples of automorphisms of positive entropy. In this talk, I would like to point out one sharp contrast between abelian fibered Calabi-Yau threefolds and K3 fibered Calabi-Yau threefolds in the view of entropy of relative automorphisms. More precisely, among other relevant results, I would like to show that there is exactly one abelian fibered Calabi-Yau threefold with relative automorphism of positive entropy up to isomorphisms as fibered varieties (explicit), whereas there are many examples of K3 fibered Calabi-Yau threefolds.with relative automorphisms of positive entropy.