题目摘要 Title & Abstract
陈国度 （上海交通大学）
报告时间： 9月24日 8：30 - 9：30
题目： Boundedness of complements for log Calabi-Yau threefolds
摘要： The theory of complements is introduced by Shokurov when he proved the existence of flips for threefolds. It turns out that complements theory plays an important role in the study of higher dimensional geometry. In this talk, I will introduce some applications of this theory and survey some recent progress towards the boundedness of complements with DCC coefficients. Then we may turn to deal with pairs with [0,1] coefficients and prove the boundedness of complements for Calabi-Yau three-folds. This is a joint work with Jingjun Han and Qingyuan Xue.
胡正宇 （重庆理工大学）
报告时间： 9月22日 9：30 - 10：30
题目： Generic minimal model program
摘要： The theory of generalised pairs plays an important role in higher dimensional algebraic geometry, for example, in the proof of BAB conjecture. In many situations, the minimal model program(MMP) for generalised pairs can be reduced to that for usual pairs, which allows us to apply the classical minimal model theory. In this talk, I will discuss a more general class of geometric objects on which we can run MMP namely generic MMP and some related results. This is joint work with Caucher Birkar.
贾甲 （清华大学丘成桐数学科学中心）
报告时间： 9月23日 14：00 - 15：00
题目： Smooth projective surfaces with pseudo-effective tangent bundles
摘要： Let S be a non-uniruled smooth projective surface.
We show that the tangent bundle T_S is pseudo-effective if and only if
the canonical divisor K_S is nef and the second Chern class c_2(S) vanishes.
I will also talk about the blow-up of a non-rational ruled surface with pseudo-effective tangent bundle.
This is based on a joint project with Yongnam Lee and Guolei Zhong.
李铎 （中山大学）
报告时间： 9月22日 14：00 - 15：00
题目： 范德蒙问题的综述
摘要： 假设X，Y都为射影光滑代数簇且存在从X到Y的满态射。如果X是具有性质P，那么Y是否具有同样的性质P呢？此类问题称为范德蒙问题。我们将综述范德蒙问题的一些结果，比如当X是射影空间时，Y也为射影空间；当X是Mori dream space时，Y也为Mori dream space，……。特别地，Occhetta和Wisniewski 猜测当X是toric variety时，Y也为toric variety，我们将重点综述一下该猜想的进展和相关问题。
李起峰 （山东大学）
报告时间： 9月24日 9：50 - 10：50
题目： Rigidity of wonderful group compactifications under Fano deformations
摘要： For a complex connected semisimple linear algebraic group $G$ of adjoint type and of rank $n$, De Concini and Procesi constructed its wonderful compactification $\bar{G}$, which is a smooth Fano $G \times G$-variety of Picard number $n$ enjoying many interesting properties. In this talk, we will discuss on the rigidity of the wonderful compactification $\bar{G}$ under Fano deformations. It is a joint work with Baohua Fu.
林洁 （杜伊斯堡-埃森大学）
报告时间： 9月22日 16：30 - 17：30
题目： Period Relations for Arithmetic Automorphic Periods on Unitary Groups
摘要： Given an automorphic representation of a unitary group, one can define an arithmetic automorphic period as the Petersson inner product of a deRham rational form. Here the deRham rational structure comes from the cohomology of Shimura varieties. When the form is holomorphic, the period can be related to special values of L-functions and is better understood. In this talk, we formulate a conjecture on relations among general arithmetic periods of representations in the same L-packet and explain a conditional proof.
刘海东 （中山大学）
报告时间： 9月22日 11：00 - 12：00
题目： Boundedness of B-pluricanonical representations and indices of log Calabi–Yau pairs
摘要： The boundedness of B-pluricanonical representations plays an important role in the study of the abundance conjecture in the minimal model program. In this talk, I will discuss about the B-pluricanonical representations of log Calabi–Yau pairs in low dimensions and its relation to index conjecture. This is a joint work with Chen Jiang.
刘杰 （中国科学院数学与系统科学研究院）
报告时间： 9月23日 9：50 - 10：50
题目： Kawamata-Miyaoka type inequality for canonical $\mathbb{Q}$-Fano varieties
摘要： By a recent result of Masataka Iwai, Chen Jiang and Haidong Liu, it is known that the second Chern class of a klt weak Fano variety is always positive. In this talk I will present an effective lower bound of the second Chern class of $\mathbb{Q}$-factorial Fano varieties with canonical singualrities and of Picard number one in terms of its anti-canonical volume. This is a joint work with Haidong Liu.
申屠钧超 （中国科学技术大学）
报告时间： 9月23日 8：30 - 9：30
题目： Kollar's package with coefficients
摘要： Kollar proved in 1986 a package of theorems on the pushforward of dualizing sheaves (torsion freeness, injectivity theorem, vanishing theorem, decomposition theorem). They have been generalized into two directions: 1) Kollar's package for dualizing sheaves twisted by a multiplier ideal sheaf; 2) Kollar's package for Hodge theoretic objects such as Hodge modules. In this talk I will survey the resent progress on this topic and explain how to unify the above results by using L2-analytic method. This is a joint work with C. Zhao.
Matija Tapušković （University of Oxford）
报告时间： 9月23日 16：30 - 17：30
题目： Feynman integrals and the cosmic Galois group
摘要： The intersection of quantum field theory and arithmetic geometry has been an exciting area of research in the last decade. In this talk we will discuss in particular how the theory of motives and their periods helps us understand the structure of Feynman integrals via an object called the cosmic Galois group.
王龙 （复旦大学）
报告时间： 9月23日 11：00 - 12：00
题目： Around Morrison-Kawamata cone conjecture
摘要： The cone conjecture of Morrison and Kawamata concerns the structure of nef and movable cones of Calabi-Yau varieties. In this talk, I will give an overview of this widely open conjecture. I will also report the joint work with Cécile Gachet and Hsueh-Yung Lin about the cone conjecture for the so-called Schoen varieties.
谢松宴 （中国科学院数学与系统科学研究院）
报告时间： 9月24日 11：00 - 12：00
题目： Entire curves producing distinct Nevanlinna currents
摘要： First, inspired by a question of Sibony, we show that in every compact complex manifold $Y$ with certain Oka property, there exists some entire curve $f: \mathbb{C}\rightarrow Y$ generating all Nevanlinna/Ahlfors currents on $Y$, by holomorphic discs $\{f\restriction_{\mathbb{D}(c, r)}\}_{c\in \mathbb{C}, r>0}$. Next, we answer positively a question of Yau, by constructing some entire curve $g: \mathbb{C}\rightarrow X$ in the product $X:=E_1\times E_2$ of two elliptic curves $E_1$ and $E_2$, such that by using concentric holomorphic discs $\{g\restriction_{\mathbb{D}_{ r}}\}_{r>0}$ we can obtain infinitely many distinct Nevanlinna/Ahlfors currents proportional to the extremal currents of integration along curves $[\{e_1\}\times E_2]$, $[E_1\times \{e_2\}]$ for all $e_1\in E_1, e_2\in E_2$ simultaneously. This phenomenon is new, and it shows tremendous holomorphic flexibility of entire curves in large scale geometry.
张子宇 （上海科技大学）
报告时间： 9月22日 15：20 - 16：20
题目： Examples of stable bundles on hyperkähler manifolds of higher dimensions
摘要： Stable sheaves on K3 surfaces have been extensively studied. However, it is a challenging question to construct non-trivial examples of stable sheaves on hyperkähler manifolds of higher dimensions. In this talk I will present several constructions, which produce irreducible components of the moduli spaces of such sheaves. Based on joint work with Fabian Reede.
周海港 （同济大学）
报告时间： 9月23日 15：20 - 16：20
题目： The classification and representations of ternary quadratic forms of level 4N
摘要： Classifications and representations are two main topics in the theory of quadratic forms. In this talk, we consider these topics of ternary quadratic forms. For a given squarefree integer $N$, firstly we give the classification of positive definite ternary quadratic forms of level $4N$ explicitly. Secondly, we give the weighted sum of representations over each class in every genus of ternary quadratic forms of level $4N$ by using quaternion algebras and Jacobi forms. The formulas are involved with modified Hurwitz class number. As a corollary, we get a formula for the class number of ternary quadratic forms of level $4N$. As applications, we give an explicit base of Eisenstein series space of modular forms of weight $3/2$ of level $4N$, and give new proofs of some interesting identities involving representation number of ternary quadratic forms.
住宿信息 Accommodation
住宿酒店为华东师范大学闵行校区旁边的宝龙艺悦酒店(地址: 上海市闵行区吴泾尚义路39弄1号, 电话: 021-33880888)。
从机场/火车站至酒店 From Airports/Stations to Hotel
上海浦东机场至酒店:
从浦东机场站乘坐地铁2号线，至世纪大道站换乘地铁9号线，至桂林路站换乘地铁15号线，至永德路站下车，步行约1.2公里到达宝龙艺悦酒店(步行导航请参考下图)，总耗时约2小时40分钟。
乘坐出租车约需1小时(非高峰时段)，费用约200元。
上海火车站至酒店:
从上海火车站乘坐地铁1号线或3号线，至上海南站换乘地铁15号线，至永德路站下车，步行约1.2公里到达宝龙艺悦酒店(步行导航请参考下图)，总耗时约1小时30分钟。
乘坐出租车约需50分钟(非高峰时段)，费用约140元。
上海虹桥机场/上海虹桥火车站至酒店:
从虹桥站乘坐地铁2号线，至娄山关路站换乘地铁15号线，至永德路站下车，步行约1.2公里到达宝龙艺悦酒店(步行导航请参考下图)，总耗时约1小时40分钟。
乘坐出租车约需40分钟(非高峰时段)，费用约120元。
上海南站至酒店:
从上海南站乘坐地铁15号线，至永德路站下车，步行约1.2公里到达宝龙艺悦酒店(步行导航请参考下图)，总耗时约50分钟。
乘坐出租车约需30分钟(非高峰时段)，费用约60元。
永德路地铁站至宝龙艺悦酒店步行导航图
从酒店至数学楼 From Hotel to Math Building
从宝龙艺悦酒店步行至数学楼路程约1.5公里，用时约20分钟，步行导航请参考下图。
宝龙艺悦酒店至数学楼步行导航图
