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
 JunMuk Hwang KIAS
 Dmitry Kaledin HSE and Steklov Mathematical Institute
 JongHae Keum KIAS
 Alexander Kuznetsov HSE and Steklov Mathematical Institute
 KyoungSeog Lee IBS Center of Geometry and Physics
 Andrey Losev HSE and Institute for Theoretical and Experimental Physics
 YongGeun 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
Hodgetode 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
KatzarkovKontsevichPantev 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 ParkWon estimate for \(\delta\)invariants of smooth cubic surfaces. 
Alexander Efimov 

Homological mirror symmetry for generalized Tate curves

JunMuk 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 zerosection 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 

Hodgetode Rham degeneration in the \(\mathbb{Z}/2\)graded case I want to describe some possible generalizations of the noncommutative Hodgetode Rham degeneration theorem; in particular, it seems that it is possible to do something for matrix factorizations. 
JongHae 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 nonminimal surfaces of general type with \(p_g=0\) that are not Mori dream surfaces. This is a joint work with KyoungSeog 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. 
KyoungSeog 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, YoungHoon Kiem, InKyun Kim, Yeongrak Kim, Hwayoung Lee and KyeongDong 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 BCOVlike 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. 
YongGeun Oh 

Lagrangian Floer theory of Gelfand–Cetlin systems In this talk, we will first explain a combinatorial description of Lagrangian fibers of GelfandCetlin 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 wellknown 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 

KatzarkovKontsevichPantev conjectures for dimensions 2 and 3
