Zoom 会议号：455 260 1552, 密码：YMSC （非常规时间的报告可能会使用其他Zoom会议号；如果使用了其他会议号，会在下面报告的具体信息中给出）。

**Upcoming talks**

Speaker: Professor Yi Hu (The University of Arizona)

Date: May 26, 2022

Time: 8:30--9:30, 9:50--10:50, 11:20--12:20 (3 lectures).

Zoom Meeting ID: 276 366 7254

Passcode: YMSC

Zoom link: https://zoom.us/j/2763667254?pwd=b0JoMWNBVFN4c0JXcmI0L01tblIxQT09

Lecture 1: Equations of canonical birational models of thin Schubert cells.

Time: 8:30--9:30

Abstract: By Mnev's universality, thin Schubert cells exhibit all possible singularities in algebraic geometry. In this first lecture, we introduce certain standard birational models of thin Schubert cells and describe their defining equations in certain smooth ambient schemes. These equations may be considered as the normalized equations of singularities. Based upon these normalized equations, we will then describe three sequential blowups of the smooth ambient schemes, collectively, called h-blowups.

Lecture 2: Birational transforms of thin Schubert cells after h-blowups

Time: 9:50--10:50

Abstract: We will continue to study the h-blowups, and more importantly, describe certain birational transforms of thin Schubert cells under the h-blowups, in terms of defining equations.

Lecture 3: Smoothness and applications to resolution of singularities

Time: 11:20--12:20

Abstract: Based upon the descriptions of their defining equations, we will prove that the birational transforms of thin Schubert cells after the final h-blowup are smooth. This immediately implies that every singularity type over a perfect field admits a resolution. By reviewing Lafforgue's version of Mnev's universality, we will apply the above to prove that every affine or projective singular variety over a perfect field admits a resolution.

**Past talks**

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Speaker: Mihai Paun (Universität Bayreuth)

Date: 19 May, 2022

Time: 15:30-16:30

Zoom Meeting ID: 455 260 1552

Passcode: YMSC

Zoom link: https://zoom.us/j/4552601552?pwd=cWxBUjlIN3dxclgrZWFEOC9jcmlwUT09

Title: Hermite-Einstein metrics in singular setting and applications

Abstract: We will report on a ongoing joint project with J. Cao, P. Graf, P. Naumann, T. Peternell and X. Wu. Our main goal is to revisit and improve an important result due to S. Bando and Y.-T. Siu. I will discuss some of the aspects of the proof, as well as an application to Chern classes inequalities (which initially was the principal motivation for our work).

Note: https://cloud.tsinghua.edu.cn/f/2126e5b2d547475db4df/

Speaker: Richard P W Thomas (Imperial College London)

Date: 12 May, 2022

Time: 15:30-16:30

Zoom Meeting ID: 455 260 1552

Passcode: YMSC

Zoom link: https://zoom.us/j/4552601552?pwd=cWxBUjlIN3dxclgrZWFEOC9jcmlwUT09

Title: Rank r DT theory from rank 1

Abstract: Fix a Calabi-Yau 3-fold X. Its DT invariants count stable bundles and sheaves on X. The generalised DT invariants of Joyce-Song count semistable bundles and sheaves on X. I will describe work with Soheyla Feyzbakhsh showing these generalised DT invariants in any rank r can be written in terms of rank 1 invariants. By the MNOP conjecture these rank 1 “abelian” invariants are determined by the GW invariants of X. Along the way we also express rank r DT invariants in terms of invariants counting “D4-D2-D0 branes”: rank 0 sheaves supported on surfaces in X. These invariants are predicted by physicists’ S-duality to be governed by (vector-valued, mock) modular forms.

Speaker: Bernd Sturmfels (MPI Leipzig and UC Berkeley)

Date: 5 May, 2022

Time: 15:30-16:30

Zoom Meeting ID: 455 260 1552

Passcode: YMSC

Zoom link: https://zoom.us/j/4552601552?pwd=cWxBUjlIN3dxclgrZWFEOC9jcmlwUT09

Title: Beyond Linear Algebra

Abstract: Our title challenge the audience to venture beyond linear algebra when designing models and numerical algorithms for solving them. Algebraic geometry is the key to this. We discuss recent advances in the study of critical point equations from optimization and statistics, and we explore the role of algebra in the study of linear PDE with constant coefficients.

Reference: arxiv.org/abs/2108.09494

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Speaker: Junpeng Jiao (The University of Utah)

Date: 28 April, 2022

Time: 15:30-16:30

Zoom Meeting ID: 455 260 1552

Passcode: YMSC

Zoom link: https://zoom.us/j/4552601552?pwd=cWxBUjlIN3dxclgrZWFEOC9jcmlwUT09

Title: Boundedness of polarised Calabi-Yau fibrations.

Abstract: In this talk, we investigate the boundedness of good minimal models with intermediate Kodaira dimensions. We prove that good minimal models are bounded modulo crepant birational when the base (canonical models) are bounded and the general fibers of the Iitaka fibration are in a bounded family of polarized Calabi-Yau pairs. As a corollary, we prove that smooth Calabi-Yau varieties with a polarized fibration structure are bounded modulo flop.

Speaker: Radu Laza (Stony Brook University)

Date: 21 April, 2022

Time: 15:30-16:30

Zoom Meeting ID: 455 260 1552

Passcode: YMSC

Zoom link: https://zoom.us/j/4552601552?pwd=cWxBUjlIN3dxclgrZWFEOC9jcmlwUT09

Title: Deformations of singular Fano and Calabi-Yau varieties

Abstract: It is well known that Calabi-Yau manifolds have good deformation theory, which is controlled by Hodge theory. By work of Friedman, Namikawa, M. Gross, Kawamata, Steenbrink and others, some of these results have been extended to Calabi-Yau threefolds with canonical singularities. In this talk, I will report on further extensions in two directions: in dimension 3, we sharpen and clarify some of the existing results, and, secondly, we obtain some higher dimensional analogues. I will also briefly explain the related case of Fano varieties, where stronger results hold. One surprising aspect of our study is the role played by higher du Bois and higher rational singularities, notions that were recently introduced by Mustata, Popa, Saito and their collaborators. This is joint work with Robert Friedman.

** **

Speaker: Caucher Birkar (Tsinghua University)

Date: 14 April, 2022

Time: 15:30-16:30

Zoom Meeting ID: 455 260 1552

Passcode: YMSC

Zoom link: https://zoom.us/j/4552601552?pwd=cWxBUjlIN3dxclgrZWFEOC9jcmlwUT09

Title: Volume of canonical Fano 4-folds

Abstract: In this talk I will describe a result on effective bound for the anti-canonical volume of Fano 4-folds with canonical singularities.

Speaker: Jintai Ding (YMSC, Tsinghua University Ding Lab, BIMSA)

Date: 7 April, 2022

Time: 15:30-16:30

Zoom Meeting ID: 455 260 1552

Passcode: YMSC

Zoom link: https://zoom.us/j/4552601552?pwd=cWxBUjlIN3dxclgrZWFEOC9jcmlwUT09

Title: Multivariate public key cryptosystems – a Post-quantum Candidate

Abstract: Multivariate public key cryptosystems (MPKC) are one of the four main families of post-quantum public key cryptosystems. In a MPKC, the public key is given by a set of quadratic polynomials and its security is based on the hardness of solving a set of multivariate polynomials. This lecture gives a general introduction to the multivariate public key cryptosystems including the main designs, the main attack tools and the mathematical theory behind. We will present state of the art research in the area.

Speaker: Yuri Manin (Max Planck Institute for Mathematics)

Date: 31 March, 2022

Time: 16:30-17:30

Zoom Meeting ID: 455 260 1552

Passcode: YMSC

Zoom link: https://zoom.us/j/4552601552?pwd=cWxBUjlIN3dxclgrZWFEOC9jcmlwUT09

Title: Introduction to algebraic supergeometry and supersymmetric (susy) modular operads

Abstract: Main goal of this talk is an expostion of the necessary background for presentation of the recent research article [KeMaWu22]. The basic notions of algebraic supergeometry can be arranged into a system of definitions and constructions parallel to the one of Grothendieck schemes. Drastically new phenomena appear only when we begin studying the superversions of tangent vector fields and, dually, difierential 1-forms.

Reference: [KeMaWu22] E. Keßler, Yu. Manin, Y. Wu. Moduli spaces of SUSY curves and their operads. arXiv:2202.10321. 21 pp.

Speaker: Hamid Abban (Loughborough University)

Date: 24 March, 2022

Time: 15:30-16:30

Zoom Meeting ID: 455 260 1552

Passcode: YMSC

Zoom link: https://zoom.us/j/4552601552?pwd=cWxBUjlIN3dxclgrZWFEOC9jcmlwUT09

Title: On K-stability of Fano varieties

Abstract: K-stability is an algebraic notion that detects the existence of Kahler-Einstein metrics on Fano varieties. I will give an overview of the theory of K-stability from a birational geometer’s perspective. Then I go through the existing methods of verifying K-stability for a given Fano variety before introducing the new method (joint work with Ziquan Zhuang) which is based on linear algebra and induction. Several results will be illustrated.

Speaker: Fujita Kento (Osaka University)

Date: 17 March, 2022

Time: 15:30-16:30

Zoom Meeting ID: 455 260 1552

Passcode: YMSC

Zoom link: https://zoom.us/j/4552601552?pwd=cWxBUjlIN3dxclgrZWFEOC9jcmlwUT09

Title: The Calabi problem for Fano threefolds

Abstract: There are 105 irreducible families of smooth Fano threefolds, which have been classified by Iskovskikh, Mori and Mukai. For each family, we determine whether its general member admits a Kaehler-Einstein metric or not. This is a joint work with Carolina Araujo, Ana-Maria Castravet, Ivan Cheltsov, Anne-Sophie Kaloghiros, Jesus Martinez-Garcia, Constantin Shramov, Hendrik Suess and Nivedita Viswanathan.

Speaker：Paolo Cascini (Imperial College London)

Date: 10 March, 2022

Time: 15:30-16:30

Zoom Meeting ID: 455 260 1552

Passcode: YMSC

Zoom link: https://zoom.us/j/4552601552?pwd=cWxBUjlIN3dxclgrZWFEOC9jcmlwUT09

Title: On the Minimal Model for algebraically integrable foliations.

Abstract: Every fibration, or more in general, every dominant rational map between normal varieties, defines a natural foliation, which is called algebraically integrable. The canonical sheaf of such a foliation behaves, in many aspects, as the canonical sheaf of a normal variety. I will describe some recent results in this direction, such as a cone theorem, and some applications on the canonical bundle formula. In particular, this provides a proof of a conjecture by Shokurov. This is joint work with Ambro, Shokurov and Spicer.

Speaker: Ivan Cheltsov (The University of Edinburgh)

Date: 3 March, 2022

Time: 15:30-16:30

Zoom Meeting ID: 455 260 1552

Passcode: YMSC

Zoom link: https://zoom.us/j/4552601552?pwd=cWxBUjlIN3dxclgrZWFEOC9jcmlwUT09

Title: Equivariant birational geometry of three-dimensional projective space.

Abstract: We will describe G-equivariant birational geometry of the three-dimensional projective space in the case when G is a finite group that G does not fix a point and does not leave a pair of skew lines invariant. In particular, we describe all possibilities for G such that the projective space is G-rigid, i.e. it is not G-birational to a conic bundles and it is not G-birational to a del Pezzo fibration. For these groups, we will explicitly describe all G-Mori fibre spaces that are G-birational to the projective space. This is a joint project with Arman Sarikyan.

Speaker: Meng Chen (Fudan University)

Date: Feb 24, 2022

Time: 15:30-16:30

Zoom Meeting ID: 455 260 1552

Passcode: YMSC

Zoom link: https://zoom.us/j/4552601552?pwd=cWxBUjlIN3dxclgrZWFEOC9jcmlwUT09

Title: On explicit birational geometry of higher dimensional varieties

Abstract: In this seminar, I will talk about some new progress on estimating the lower bound of canonical volumes and the upper bound of canonical stability indices for higher dimensional varieties of general type. I will mainly introduce the construction of examples with small volumes.

Speaker: Professor Shigeru Mukai (Research Institute for Mathematical Sciences)

Title: Prime Fano threefolds and Leech-like lattices

Date: Dec 23, 2021

Time: 15:30-16:30

Zoom Meeting ID: 849 963 1368

Passcode: YMSC

Zoom link: https://us02web.zoom.us/j/8499631368?pwd=cHpiaXZBdS9abEpBbDZSeHJZNEU2UT09

Abstract: I computed the automorphism groups of certain two models of supersingular K3 surfaces with Artin invariant one in Beijing 2019. One is over the binary and the other over ternary field. Recently I found two more models over the binary and quaternary fields. I will report their relation with prime Fano threefolds classified into 10 deformation types of degree (-K)^3=2g-2 with g=2,…,10 and 12, by Fano-Iskovskih. Our four models are related with g=7, 8, 9, 10 via three Leech-like lattices; Leech, Barnes-Wall and Coxeter-Todd. Another Leech-like lattice is related with g=12 via the regular 4-polytope {3,3,5}.

Note: https://cloud.tsinghua.edu.cn/f/b8396443d2874b5aaaea/?dl=1

Speaker: Professor De-Qi Zhang (National University of Singapore)

Title: Jordan Property for Automorphism Groups of Compact Complex Varieties

Date: Dec 16, 2021

Time: 15:30 - 16:30

Zoom Meeting ID: 849 963 1368

Passcode: YMSC

Zoom link: https://us02web.zoom.us/j/8499631368?pwd=cHpiaXZBdS9abEpBbDZSeHJZNEU2UT09

Abstract: We report some recent progress on the Jordan property of the automorphism group Aut(X) of an algebraic variety X or a compact complex manifold (close to be Kahler), i.e., whether every finite subgroup of it is almost commutative.

Speaker: Professor Jungkai Chen (National Taiwan University)

Title: On recent development of geography of varieties of general type

Date: Dec 9, 2021

Time: 15:30-16:30

Zoom Meeting ID: 849 963 1368

Passcode: YMSC

Zoom link: https://us02web.zoom.us/j/8499631368?pwd=cHpiaXZBdS9abEpBbDZSeHJZNEU2UT09

Abstract: Among varieties of general of fixed dimension, there are some known (or expected) constraints on their birational invariant. It is particularly interesting to study those varieties whose invariants achieve optimal values. In this talk, I am going to introduce some recent developments along this direction. One type of result is about asymptotic behavior of invariants, as dimension approaches infinity.

The other type of result is about explicit description of varieties with extremal invariants. For example, let d_X be the dimension of image of canonical map. If d_X=n, then one has that the canonical volume is greater than or equal to 2(p_g-n). If equality holds, then we call X to be a Horikawa variety. Various geometric properties of Horikawa varieties can be described very explicitly in the joint work with Bangere and Gallego. Various geometric structure of threefolds of general type with extremal invariants will be introduced as well.

Speaker: Professor Victor Batyrev (University of Tuebingen)

Title: On combinatorial and algorithmic aspects of the Minimal Model Program

Date: Dec 2, 2021

Time: 15:30-16:30

Zoom Meeting ID: 849 963 1368

Passcode: YMSC

Zoom link: https://us02web.zoom.us/j/8499631368?pwd=cHpiaXZBdS9abEpBbDZSeHJZNEU2UT09

Abstract: The talk is devoted to a simple combinatorial algorithm for explicit constructing minimal models of complex algebraic varieties defined by Laurent polynomials in algebraic torus of arbitrary dimension d>1. The considered algorithm proposes explicit combinatorial formulas for the Hodge-theoretic topological invariants of obtained minimal models. In the talk I will explain the main ideas of the algorithm and the corresponding combinatorial formulas in a way comprehesible for undergraduate students.

Speaker: Professor Yi Hu, (The University of Arizona)

Title: Local Resolution of Singularities

Date: Nov 25, 2021

Time: 11-12 am

Zoom Meeting ID: 981 9384 1924

Passcode: YMSC

Zoom link: https://zoom.us/j/98193841924?pwd=L2p5cTgxU1ZLUGRucllFSWNlZkl2UT09

Abstract: Mnev's universality theorem asserts that every singularity type over the ring of integers appears in some thin Schubert cell of the Grassmannian Gr(3,E) for some vector space E. We construct sequential blowups of Gr(3,E) such that certain induced birational transforms of all thin Schubert cells become smooth over prime fields. This implies that every singular variety X defined over a prime field admits local resolutions. For a singular variety X over a general perfect field k, we spread it out and deduce that X/k admits local resolution as well.

Speaker: Professor Burt Totaro (UCLA)

Title: Varieties of general type with doubly exponential asymptotics

Date: 18 Nov, 2021

Time: 9-10 am

Zoom Meeting ID: 843 5849 9857

Passcode: YMSC

Zoom link: https://us02web.zoom.us/j/84358499857?pwd=NlVoYlZ6TEwzaXVCWmZCaVA4ZjhWQT09

Abstract: We construct smooth projective varieties of general type with the smallest known volume and others with the most known vanishing plurigenera in high dimensions. The optimal volume bound is expected to decay doubly exponentially with dimension, and our examples achieve this decay rate. We also consider the analogous questions for other types of varieties. For example, in every dimension we conjecture the terminal Fano variety of minimal volume, and the canonical Calabi-Yau variety of minimal volume. In each case, our examples exhibit doubly exponential behavior. (Joint work with Louis Esser and Chengxi Wang.)

Speaker: Professor Yuri Prokhorov (Steklov Mathematical Institute & HSE University)

Title：Towards a classification of Q-Fano threefolds

Date：Nov 11, 2021

Time：15：30-16：30

Zoom Meeting ID: 849 963 1368

Passcode: YMSC

Zoom link: https://us02web.zoom.us/j/8499631368?pwd=cHpiaXZBdS9abEpBbDZSeHJZNEU2UT09

Abstract：We survey recent progress in classification of singular Fano threefolds with special emphasis on birational transformations between them.

Speaker: Sean Keel (University of Texas)

Title: Mirror symmetry, analytic disks, and (if time permits) moduli of log CY pairs.

Date: Nov 4, 2021

Time: 22：00-23：00

Zoom Meeting ID：850 5273 8208

Passcode：YMSC

Zoom link: https://us02web.zoom.us/j/85052738208?pwd=VnBaQ2RWVzJBcVJENnRKUEVQNTNvZz09

Abstract: I will explain my recent construction, joint with Tony Yu, of the mirror to an affine log CY variety of an algebra with a canonical Mori theoretic basis and structure constants given by naive counts of Berkovich analytic disks. My main goal will be to convince you of the simplicity of the construction, both conceptually, and in technical detail. I will assume a basic understanding of algebraic geometry, but no background in Berkovich geometry. If time permits, I will explain the connection to our conjecture, joint with Paul Hacking, that very natural moduli spaces of log CY pairs are (up to finite cover) toric varieties.

Videos: https://cloud.tsinghua.edu.cn/f/085194f1f6534ebb8b31/

Speaker: Professor Valery Alexeev (University of Georgia)

Title: Compact moduli spaces of K3 surfaces

Date: October 28, 2021

Time: 9:00-10:00 am

Zoom Meeting ID：228 011 0844

Passcode：YMSC

Abatract: I will explain recent results on modular, geometrically meaningful compactifications of moduli spaces of K3 surfaces, most of which are joint with Philip Engel. A key notion is that of a recognizable divisor: a canonical choice of a divisor in a multiple of the polarization that can be canonically extended to any Kulikov degeneration. For a moduli of lattice-polarized K3s with a recognizable divisor we construct a canonical stable slc pair (KSBA) compactification and prove that it is semi toroidal. We prove that the rational curve divisor is recognizable, and give many other examples.

Speaker: Prof. Yujiro Kawamata, University of Tokyo

Title: Semi-orthogonal decomposition and smoothing

Date: October 21, 2021

Time: 3:30-4:30

Abstract: A sheaf F on a normal projective variety X is called pre-tilting if all higher self-extensions vanish. F generates a subcategory in a bounded derived category of coherent sheaves D(X) which is equivalent to a bounded derived category D(R) of finitely generated modules over a finite dimensional associative algebra R = End(F), and D(X) has a corresponding semi-orthogonal decomposition. I will investigate what happens to F, R and D(X) if X has a deformation to a smooth projective variety Y. I take examples where X is a weighted projective surface which are deformed to a projective plane or a quadric Y by Q-Gorenstein smoothing. Then I will prove in general that a pre-tilting object F arising from a singularity which allows Q-Gorenstein smoothing is deformed to a direct sum of exceptional vector bundles found by Hacking. In particular, R is deformed to a direct product of matrix algebras.

Speaker: Yitwah Cheung, Tsinghua University

Date: September 30, 2021

Time: 3:30-4:30

Abstract: The Hodge bundle of a Riemann surface of genus g is a complex vector bundle of rank g over the moduli space of closed Riemann surfaces of genus g. On this space, there is an action by SL(2,R) that is poorly understood in algebraic geometric terms. The recent work of Eskin and Mirzakhani completed the (initial phase of the) classification of all orbit closures and invariant probability measures of this action using methods of ergodic theory. It would be desirable to extend the Teichmuller action to one on an appropriate bundle over the moduli space of a higher dimensional complex manifold, which would then allow the methods of ergodic theory to bear fruit. In this talk, my goal is to give an idea of the new area of research that would open up, should this extension be possible.

Videos：https://cloud.tsinghua.edu.cn/f/c40a31744a3e472dacc8/

Title: Kohn-Rossi cohomology, complex Plateau problem and Rigidity of CR morphisms

Speaker: Stephen Yau (Tsinghua University)

Date: 2021-9-23

Abstract: In this talk, we investigate the relationship between compact strongly pseudoconvex CR manifolds and the singularities of their Stein fillings. We first compute the dimensions of Kohn-Rossi cohomology groups with values in holomorphic vector bundles in terms of local cohomology groups. As an application, we solve the classical complex Plateau problem for compact strongly pseudoconvex CR manifolds when its Stein fillings has only isolated complete intersection singularities. Finally, using Kohn-Rossi cohomology, we obtain some sufficient conditions for the non-existence of CR morphisms between the links of isolated complete intersection singularities with different embedding codimensions. This is a joint work with Xiankui Meng.

Title: Hodge ideals and roots of the Bernstein-Sato polynomial

Speaker: Bingyi Chen (Tsinghua University)

Date: 2021-9-16

Abstract: Hodge ideals, which are developed by Mustata and Popa, are important invariants of hypersurface singularities that arise naturally from Saito's theory of mixed Hodge modules. There are two diffierent approaches to study Hodge ideals: birational geomerty method by means of log resolution and D-module method by means of V-filtration. The theory of Hodge ideals connects these two diffierent fields and leads to a number of striking applications. In this talk, I will introduce the theory of Hodge ideals and talk about its application on the bound of roots of reduced Bernstein-Sato polynomial.

Title: Measure the positivity of tangent bundles of Fano varieties

Speaker: Jie Liu (Chinese Academy of Sciences)

Date: 2021-9-09

Abstract: While the properties of the anticanonical divisor $-K_X$ of a Fano variety $X$ and its multiples have been studied by many authors, the positivity of the tangent bundle $T_X$ is much more elusive. In this talk, I will introduce some invariants to measure the positivity of the tangent bundles of Fano varieties via their anti-canonical bundles and then I will discuss various interesting examples to illustrate the general situations. This is based on joint works with Baohua Fu, Andreas Höring and Feng Shao.

Title: Explicit boundedness of canonical Fano 3-folds: known results and open problems

Speaker: Chen Jiang (Fudan University)

Date：2021-9-02

Abstract: Motivated by the classification of canonical Fano 3-folds, we are interested in boundedness results on diffrent kinds of canonical Fano 3-folds, such as anticanonical systems, indices, degrees, and so on. I will summarize known results with some progress (based on joint works with Meng Chen and Yu Zou) and open problems in this area.

Title: Recent progress towards Shokurov’s ACC conjecture for mld

Speaker: Dr. Jihao Liu, Northwest Univ

Date：2021-8-19

Abstract: Shokurov's ascending chain condition (ACC) conjecture for minimal log discrepancies (mlds) is a core conjecture in birational geometry and has a deep relationship with the minimal model program. In particular, in 2004, Shokurov shows that the ACC conjecture and the lower-semicontinuity conjecture for mlds will imply the termination of flips and will thus complete the minimal model program. In this talk, I will discuss some recent progress towards Shokurov's ACC conjecture and some related questions. Some parts of this talk are joint works with Jingjun Han, V.V. Shokurov, Liudan Xiao, and Lingyao Xie.

Title: Sarkisov program and automorphism of affine spaces

Speaker: Yifei Chen (Chinese Academy of Sciences)

Date：2021-8-12

Abstract: Sarkisov program roughly says that birational maps of Mori fiber spaces can be factored through four basic links. In the talk, I will briefly introduce Sarkisov program, as well as its application for Cremona groups of rank 2 and automophisms of affine plane.