Talk 1 (10:00–11:00)

Speaker: Wenfei Liu (Xiamen University)

Title: On numerically and cohomologically trivial automorphisms of properly elliptic surfaces

Abstract: A proper elliptic surface is an elliptic surface f: S->B with Kodaira dimension \kappa(S)=1 (over the complex numbers for this talk). Recall that an automorphism of S is called numerically trivial (resp. cohomologically trivial) if it acts trivially

on H*(S,\mathbb Q) (resp. H*(S,\mathbb Z)). It has been believed since long time that a properly elliptic surface S does not have any numerically trivial automorphisms if the geometric genus p_g(S)>0 and cohomologically trivial automorphisms do not exist even when p_g(S)=0. Surprisingly, we have found recently examples of properly elliptic surfaces with an arbitrarily large numerical trivial (resp. nontrivial cohomologically trivial) automorphism group, which invalidates the above claims. In this talk, I will present these examples, and then give certain bound and classification of them. Based on joint work with Fabrizio Catanese, Matthias Schütt, and partly with Christian Gleißner and Davide Frapporti.

Talk 2 (11:30-12:30)

Speaker: Konstantin Loginov Valerievich (Steklov Mathematical Institute, Russian Academy of Sciences)

Title: Finite abelian subgroups acting on rationally connected threefolds

Abstract: Finite abelian groups are one of the simplest objectsstudied in algebra. In turn, rational varieties form a reasonably simple class of varieties considered in algebraic geometry. However, the question of which finite abelian groups can act on rational (or rationally connected) varieties, is far from being an easy question. In dimension 2 the answer to this question was given by A. Beauville and J. Blanc. In my talk I will consider this question in dimension three.

Talk 3 (14:00-15:00)

Speaker: Zhengyu Hu (Chongqing University of Technology)

Title: Zariski decompositions and a type of MMP for generalised pairs

Abstract: I will discuss some easy observations on "Zariski decompostions" for klt pairs (if exists). To generalize these observations to generalised dlt pairs, I will introduce a type of MMP which preserves the decomposition. As an application I will talk some of my recent progresses.

Talk 4 (15:30-16:30)

Speaker: Yen-An Chen (National Taiwan University)

Title: Foliated complements

Abstract: Recent progress has been made in the minimal model program for foliated varieties. A natural question arises: do Fano foliations form a bounded family? Building on Birkar's influential work on the Borisov-Alexeev-Borisov conjecture, we explore the theory of complements in the context of foliations and demonstrate the existence of complements for Fano algebraically integrable foliations. This is a joint work with Dongchen Jiao and Pascale Voegtli.

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