学术会议

当前位置:学术交流 >> 学术会议 >> 浏览文章

学术会议:Workshop on Algebraic Geometry

发布时间:2017年01月03日 浏览次数:发布者:mathky

会议名称:Workshop on Algebraic Geometry

会议时间:1月4日-1月6日

会议地点:海韵园实验楼105报告厅

日程表

1月4日,海韵园实验楼105报告厅

7:50

金沙湾宾馆大堂集合,统一乘车去会场

8:00-8:20

签到,领取会议资料

8:20-8:30

开幕式,致辞

8:30-9:30

许阳晨

Stability on valuations of a singularity

9:30-9:50

休息

9:50-10:50

张  磊

Iitaka conjecture and abundance for 3-folds in char p

11:00-12:00

江  智

Some results on the eventual paracanonical maps

12:00-14:00

午餐、休息(海韵大丰园二楼)

14:00-15:00

谈胜利

Poincaré problem and birational invariants of a differential equation

15:10-16:10

龚  成

Classification of Belyi families of curves with two singular fibers  

16:10-16:30

茶歇、合影

16:30-17:30

李长征

On the conjecture O of GGI

18:00

晚餐(海韵大丰园二楼)

19:30

统一乘车返回会场

 


1月5日,海韵园实验楼105报告厅

8:15

金沙湾宾馆大堂集合,统一乘车去会场

8:30-9:30

李志远

Cycles on moduli space of irreducible symplectic varieties

9:30-9:50

茶歇

9:50-10:50

誾琪峥

Cycles on the universal K3 surface

11:00-12:00

余  讯

Elliptic fibrations on K3 surfaces and Salem numbers of maximal degree

12:00-14:00

午餐(海韵大丰园二楼)

14:00-15:00

江  辰

Remarks on Kawamata's effective non-vanishing conjecture

15:10-16:10

许金兴

Monodromy and period mapping around hyperplane arrangements

16:10-16:30

茶歇

16:30-17:30

孙  浩

Bridgeland stability of stable sheaves and its applications

18:00

晚餐(大丰苑二层)

19:00

大丰苑门口统一乘车返回酒店

1月6日,海韵园实验楼105报告厅

8:15

金沙湾宾馆大堂集合,统一乘车去会场

8:30-9:30

孙笑涛

D-modules and étale fundamental group in char. p > 0

9:30-9:50

茶歇

9:50-10:50

瞿  枫

The virtual pullbacks formalism

11:00-12:00

孙  鹏

On generalized cohomology theories and algebraic cobordism

12:00-13:00

午餐(海韵大丰园二楼)

13:00

大丰苑门口统一乘车返回金沙湾宾馆

 


学术报告题目和摘要

Classification of Belyi families of curves with two singular fibers

GONG Cheng (Suzhou U)

Abstract: A relatively minimal family of curves  with 2 or 3 singular fibers is called a Belyi family or fibration, which has some interesting arithmetic and geometric properties. We classify all Belyi families  of curves of genus  with two singular fibers. We compute all sections of  and its

Mordell-Weil group. As an application, we prove that any periodic fiber can be realized as a fiber of a Belyi fibration with two singular fibers.

 

Remarks on Kawamata's effective non-vanishing conjecture

JIANG Chen (Kavli IPMU, U Tokyo)

Abstract: Kawamata proposed a conjecture concerning when a nef divisor has global sections. In particular, this conjecture predicts that, every ample line bundle on a Calabi-Yau manifold has a non-trivial global section. I will discuss some progress on this conjecture, base on a joint work with Yalong Cao. 

 

Some results on the eventual paracanonical maps

JIANG Zhi (SCMS, Fudan U)

Abstract: The eventual paracanonical map was introduced by Barja, Pardini, and Stoppino to prove Severi-type inequalities. We will explain that the eventual paracanonical maps have bounded degrees in low dimensions.

 

On the conjecture O of GGI

LI Changzheng (Sun Yat-Sen U)

Abstract: In this talk, we will discuss the Conjecture O of Galkin, Golyshev and Iritani, which ‘underlies’ Gamma conjectures I and II of them. Conjecture O is concerned with the eigenvalues of the operator on the small quantum cohomology of a Fano manifold X given by the quantum multiplication of the first Chern class of X. We will prove the conjecture for homogeneous varieties G/P and odd symplectic Grassmannians. This is my joint works with Daewoong Cheong, Leonardo Mihalcea, and Ryan Shifler.

 

Cycles on moduli space of irreducible symplectic varieties.

LI Zhiyuan (SCMS, Fudan U)

Abstract: In this talk, I will review the recent work on cycle theory of moduli spaces of irreducible symplectic varieties. It includes the O’Grady’s generalized Franchetta conjecture and Marian-Oprea-Pandharipande’s tautological conjecture. Moreover, we give a proof of the cohomological version of these conjectures. This is a joint work with N.Bergeron. 

 

The virtual pullbacks formalism

QU Feng (BICMR, Peking U)

Abstract: Based on deformation to the normal cone, the virtual pullbacks formalism provides a unifying framework to understand properties of virtual fundamental classes and virtual structure sheaves. In this talk, I will explain this formalism, and outline K-theoretic virtual pullbacks in curve-counting theories.

 

Bridgeland stability of stable sheaves and its applications

SUN Hao (Shanghai Normal U)

Abstract: In this talk, we will show the tilt-stability of stable sheaves on  projective varieties with respect to certain tilt-stability conditions depends on two parameters.  It gives applications to effective Serre vanishing theorem, Castelnuovo-Mumford regularity of torsion free sheaves and stable sheaves on .

 

On generalized cohomology theories and algebraic cobordism

SUN Peng (BICMR, Peking U)

Abstract: Following the approach of Levine-Morel,  we will briefly discuss various aspects of generalized cohomology theories from schemes to stacks. Chow groups and Grothendieck groups of vector bundles are examples of such theories coming from geometry. In particular, we put our emphasis on the theory of algebraic cobordism, viewed as the universal theory among all such theories and a generalization of Grothendieck-Riemann-Roch. Surprisingly, algebraic cobordism finds important applications both in the theory of mixed motives and counting curves.

 

D-modules and étale fundamental group in char. p > 0

SUN Xiaotao (CAS /CAM, Tianjin U)

 

Poincaré problem and birational invariants of a differential equation

TAN Sheng-Li Tan (East China Normal U)

Abstarct: In the 19th century, Darboux, Painlevé and Poincaré studied differential equations of the first order by using complex algebraic geometry. More precisely, the theory of integrable curves defined by complex differential equations is similar to the theory of families of algebraic curves, i.e., fibrations on an algebraic surface.  Poincaré proposed the following research program. 

Study the (topological) properties of families of algebraic curves on a complex algebraic surface, and check if they are the properties of differential equations.

Find numerical invariants of complex differential equations.

Classify complex differential equations according to their invariants.

Characterize those complex differential equations which are algebraically integrable.

Apply to some problems on real differential equations.

I will talk about some recent progress in Poincaré Program.

 

Stability on valuations of a singularity

XU Chenyang (BICMR, Peking U)

Abstract:  In higher dimensional geometry, it has been known that from many perspectives a log terminal singularity is a local analogue of Fano varieties. Many statements of Fano varieties have a counterpart for log terminal singularities. One central topic on the geometry of a Fano variety is its stability which for instance reflects whether the Fano variety carries a canonical metric. In this talk, we will discuss a recent joint work with Chi Li (some part still in progress) in which we want to establish a local stability theory of a fixed log terminal singularity. Inspired by the study from differential geometry, (e.g. tangent cone, Sasakian-Einstein metric), for any log terminal singularity, we investigate the valuation which has the minimal normalized volume. Our goal is to prove various properties of this valuation which enable us to canonically degenerate the singularity to a T-singularity (with a torus action) with ’stability’.

 

Monodromy and period mapping around hyperplane arrangements

XU Jinxing (USTC)

Abstract: Given a hyperplane arrangement on a projective space, consider the cyclic cover of the projective space branched along this hyperplane arrangement. Varying the hyperplane arrangements, one gets some  families of projective varieties. I will talk about  some Hodge theoretic aspects about these families, focusing on properties of the monodromy groups and a Torelli type theorem in a special case. Parts of this talk  are based on joint works with Mao Sheng and Kang Zuo.

 

Cycles on the universal K3 surface

YIN Qizhen (BICMR, Peking U)

Abstract: We first review Beauville-Voisin’s work on the Chow ring of a K3 surface. Then, via stable maps and virtual class techniques, we generalize the Beauville-Voisin result to the universal setting. Noether-Lefschetz theory naturally shows up in the picture. As a consequence, we prove the Marian-Oprea-Pandharipande conjecture: the tautological ring of the moduli space of K3 surfaces is generated by the Noether-Lefschetz loci. Joint work with Rahul Pandharipande.

 

 

 

Elliptic fibrations on K3 surfaces and Salem numbers of maximal degree

YU Xun (CAM, Tianjin U)

Abstract: We explain a characterization of the maximal Salem degree of automorphisms of K3 surfaces in terms of elliptic fibrations with infinite automorphism groups. As an application, we show that any supersingular K3 surface in odd characteristic has an automorphism the entropy of which is the natural logarithm of a Salem number of degree 22. In particular, such automorphisms are not geometrically liftable to characteristic 0.

 

Iitaka conjecture and abundance for 3-folds in char p

ZHANG Lei (Shaanxi Normal U)

 

Abstract: Recently, Birkar, Hacon and Xu have proved existence of minimal model of 3-folds in char p >5. It remains to prove abundance. In this talk, we will discuss some related topics, and introduce the recent progresses in Iitaka conjecture and abundance for 3-folds in positive characteristic p >5. If time permitting, we will explain the proof of abundance for 3-folds with non-trivial Albanese maps.