Invited Speakers

Kuan-Wen Lai

Steven Lu

Harry Richman

Erwan Rousseau 

Wanchun Rosie Shen

Sasha Viktorova        

Agenda
7/19 Sun.

12:00     Lunch

14:00 - 15:00 Kuan-Wen Lai
15:20 - 16:20 Steven Lu
18:00    Dinner

7/20 Mon.

09:00 - 11:50 Free morning
12:00     Lunch

14:00 - 15:00 Wanchun Rosie Shen

15:20 - 16:20 Sasha Viktorova       
18:00    Dinner

7/21 Tue.

09:20 - 10:20 Harry Richman

10:40 - 11:40 Erwan Rousseau
12:00     Lunch

Title & Abstract

 Kuan-Wen Lai (Tunghai University)
Title: Involutive autoequivalences on very general twisted K3 surfaces and Gushel–Mukai fourfolds 
Abstract: Gushel–Mukai fourfolds, together with cubic fourfolds, form an important class of prime Fano fourfolds with K3-like Hodge structures and derived categories. From earlier work with Yu-Wei Fan, one can deduce that a very general K3 surface admits an involution on its bounded derived category if and only if it is Hodge-theoretically associated with a Gushel–Mukai fourfold. In this talk, I will present ongoing joint work with Emma Brakkee that extends this connection to twisted K3 surfaces. 

Steven Lu (UQAM)
Title:  Pointed rigidity and hyperbolicity
Abstract: We will give a precise correspondence between (pointed) rigidity of (pseudo) holomorphic curves and hyperbolicity of the ambient space, and provide some examples and applications. The talk is based on a joint work with A. Javanpeykar, Ruiran Sun and Kang Zuo . 

Wanchun Rosie Shen (Harvard University) 

Title:  Higher singularities and negative K-theory
Abstract:  In this talk, we will give a gentle introduction to higher singularities, and explain some of their applications to the negative K-theory of singular varieties.

Sasha Viktorova (NCTS)

Title:  A new construction of non-special divisors in the moduli space of cubic fourfolds
Abstract: In a joint work with Lisa Marquand, we study cubic fourfolds that contain certain singular cubic threefolds as hyperplane sections. In particular, we show that the closures of the loci of cubic fourfolds containing a hyperplane section with certain prescribed singularities ($E_6, D_6, D_5+A_1$ or $D_4+A_2$) are irreducible divisors in the moduli space of cubic fourfolds. Moreover, a general such fourfold is not special; that is, it only contains surfaces homologous to complete intersections.

Harry Richman (NCTS)

Title:  Automorphisms and dynamics on K3 surfaces via planar linkages
Abstract: Hessian K3 surfaces are constructed as the Hessian of a cubic surface in 3-space, then resolving singularities. This family of K3's has been studied classically by many authors (Kondo, Dolgachev, Keum, Oguiso, Cantat, etc.), in particular with a focus on its automorphisms.  We can interpret such a surface as parametrizing a planar mechanical linkage with five rigid bars. Using this moduli interpretation and the geometry of the underlying linkage, we can recover many results on the automorphisms of such K3 surfaces. I will describe some details of how this correspondence to planar linkages naturally resolves the singularities of a classical Hessian K3 surface. More generally, a planar mechanical linkage with more bars is parametrized by a real Calabi-Yau variety in higher dimensions, which likewise has many automorphisms and rich dynamics. If time permits, I will also discuss the geometry of 3-dimensional linkages. This is based on joint work with Charles Doran and Flora Poon. 

Erwan Rousseau  (Université de Bretagne Occidentale)

Title: Surfaces of general type with extremal cotangent dimension  
Abstract: An important result of McQuillan implies that surfaces with big cotangent bundle don’t contain any Zariski dense entire curve. It follows from the Riemann-Roch Theorem that surfaces for which the Chern numbers satisfy $c_1^2>c_2$ have big cotangent bundle. But in general, a surface can have big cotangent bundle without satisfying the above inequality of Chern numbers, which raises the question of studying the geography of surfaces with big cotangent bundle, namely to study which Chern numbers can be realized by surfaces with big cotangent bundle, and in particular to look for the lowest possible bound on the slope $c_1^2/c_2$. Many such examples have been constructed over the years. In this talk, we will explain the situation of Horikawa surfaces, which are the surfaces of lowest possible slope among minimal surfaces of general type, and we will prove that on the one hand, generic Horikawa surfaces admit no symmetric differential forms, but that on the other hand, there exists examples of Horikawa surfaces with big cotangent bundle. This is a joint work with Damian Brotbek and Bruno de Oliveira. 

Organizing Committee
Hsueh-Yung Lin (National Taiwan University)