### Venue

Laboratory of Mirror Symmetry, NRU HSE
Room 427
6 Usacheva St., Moscow, Russia

### Speakers

• Ivan Cheltsov HSE and University of Edinburgh
• Alexander Efimov HSE and Steklov Mathematical Institute
• Jun-Muk Hwang KIAS
• Dmitry Kaledin HSE and Steklov Mathematical Institute
• Jong-Hae Keum KIAS
• Alexander Kuznetsov HSE and Steklov Mathematical Institute
• Kyoung-Seog Lee IBS Center of Geometry and Physics
• Andrey Losev HSE and Institute for Theoretical and Experimental Physics
• Yong-Geun Oh IBS Center of Geometry and Physics
• Dmitry Orlov Steklov Mathematical Institute
• Jihun Park IBS Center of Geometry and Physics
• Victor Przyjalkowski HSE and Steklov Mathematical Institute

### Schedule

April 5
17:00 – 18:00 D. Orlov
Derived noncommutative schemes, geometric realizations, and finite dimensional algebras
18:15 – 19:15 J.-H. Keum
Examples of Mori dream surfaces of general type with $$p_g=0$$
April 6
10:30 – 11:30 A. Losev
Tropical mirror symmetry for toric variaties
12:00 – 13:00 Y.-G. Oh
Lagrangian Floer theory of Gelfand–Cetlin systems
14:30 – 15:30 D. Kaledin
Hodge-to-de Rham degeneration in the $$\mathbb{Z}/2$$-graded case
15:45 – 16:45 J.-M. Hwang
On Hirschowitz's conjecture on the formal principle
17:00 – 18:00 A. Kuznetsov
Intermediate Jacobian of Gushel–Mukai threefolds
April 7
10:30 – 11:30 I. Cheltsov
How to compute $$\delta$$-invariants of del Pezzo surfaces?
11:45 – 12:45 J. Park
Automorphism groups of the complements of hypersurfaces
14:00 – 15:00 A. Efimov
Homological mirror symmetry for generalized Tate curves
15:15 – 16:15 V. Przyjalkowski
Katzarkov-Kontsevich-Pantev conjectures for dimensions 2 and 3
16:30 – 17:30 K.-S. Lee
Semiorthogonal decompositions of derived categories of Fano varieties and Ulrich bundles

### Abstracts

Ivan Cheltsov

How to compute $$\delta$$-invariants of del Pezzo surfaces?

In this talk we show how to compute $$\delta$$-invariants of del Pezzo surfaces. As an application, we give a new proof of Park-Won estimate for $$\delta$$-invariants of smooth cubic surfaces.

Alexander Efimov

Homological mirror symmetry for generalized Tate curves

Jun-Muk Hwang

On Hirschowitz's conjecture on the formal principle

A compact complex submanifold of a complex manifold satisfies the formal principle if its formal neighborhood determines its germ. Hirschowitz's conjecture predicts that the zero-section of a globally generated vector bundle on a compact complex manifold satisfies the formal principle. We discuss a new approach to the conjecture, which verifies the prediction on Fano manifolds.

Dmitry Kaledin

Hodge-to-de Rham degeneration in the $$\mathbb{Z}/2$$-graded case

I want to describe some possible generalizations of the non-commutative Hodge-to-de Rham degeneration theorem; in particular, it seems that it is possible to do something for matrix factorizations.

Jong-Hae Keum

Examples of Mori dream surfaces of general type with $$p_g=0$$

We provide examples of minimal surfaces of general type with $$p_g=0$$ and $$K^2=2, 3,\ldots,8, 9$$ which are Mori dream spaces. On these examples we also give explicit description of their effective cones with all negative curves. We also present non-minimal surfaces of general type with $$p_g=0$$ that are not Mori dream surfaces. This is a joint work with Kyoung-Seog Lee.

Alexander Kuznetsov

Intermediate Jacobian of Gushel–Mukai threefolds

Gushel–Mukai threefolds are prime Fano threefolds of genus 6. In the talk I will discuss their geometry and show that their intermediate Jacobian of such $$X$$ is isomorphic to the Albanese variety of the Hilbert scheme of conics on $$X$$. This is a joint work in progress with Olivier Debarre.

Kyoung-Seog Lee

Semiorthogonal decompositions of derived categories of Fano varieties and Ulrich bundles

After its discovery, semiorthogonal decomposition has been one of the most important tools to understand derived categories of coherent sheaves on algebraic varieties. In this talk, I will discuss semiorthogonal decompositions of derived categories of Fano varieties and their applications to the study of Ulrich bundles on them. This talk is based on joint works with Yonghwa Cho, Young-Hoon Kiem, In-Kyun Kim, Yeongrak Kim, Hwayoung Lee and Kyeong-Dong Park.

Andrey Losev

Tropical mirror symmetry for toric variaties

We consider tropical curves in a tropical toric manifold that pass through the tropical cycles. Such curves are represented by a special kind of trees in the polygon that represents tropical toric manifold. The Gromov–Witten invariant appears from counting such trees with proper weights. We show that trees are just Feynman diagrams in the BCOV-like quantum field theory that represents the type B side of the mirror. We conjecture how this interpretation of mirror may be generalized to a general tropic manifold.

Yong-Geun Oh

Lagrangian Floer theory of Gelfand–Cetlin systems

In this talk, we will first explain a combinatorial description of Lagrangian fibers of Gelfand-Cetlin systems and then explain how bulk deformations of Lagrangian Floer cohomology produce a continuum of nondisplaceable Lagrangian tori. If time permits, I will indicate some aspect of homological mirror symmetry of Gelfand–Cetlin systems. This talk is based on a joint work with Yunhyung Cho and Yoosik Kim.

Dmitry Orlov

Derived noncommutative schemes, geometric realizations, and finite dimensional algebras

Based on arXiv:1808.02287.

Jihun Park

Automorphism groups of the complements of hypersurfaces

It is a well-known fact that every automorphism of a smooth hypersurface of degree $$d$$ in $$\mathbb{P}^n,$$ $$n\geq 2,$$ comes from the automorphism group of $$\mathbb{P}^n$$ unless $$(n,d)=(2,3), (3,4)$$. In my talk, I reinvestigate this phenomenon inside out, i.e., the problem when the automorphism group of the complement of the hypersurface in $$\mathbb{P}^n$$ coincides with the subgroup of the automorphismgroup of $$\mathbb{P}^n$$ that keeps the hypersurface fixed. This talk is base on a joint work with Ivan Cheltsov and Adrien Dubouloz.

Victor Przyjalkowski

Katzarkov-Kontsevich-Pantev conjectures for dimensions 2 and 3