时间： 2017年5月11日——5月14日
地点：览秀楼报告厅
会议日程：
5月 11日 报到
5月 12日 上午 10：00-10：10 开幕式
10：10-11：10 报告一（杜荣）
11：20-12：20 报告二（余讯）
下午 2：00-3：00 报告三 （左怀青）
3：10- 4：10 报告四（顾怡）
4：20- 5：20 报告五（胡勇）
5月13日 上午 9：00- 10：00 报告六（刘文飞）
10：10-11：10 报告 七（张磊）
11：20-12：20 报告八（赵全庭）
下午 2：00-3：00 报告九（于飞）
3：10- 4：10 报告十（朱盛茂）
晚 7：00-9：00 关于代数几何在本科生中开展的讨论 （彭帆，涂玉平）
5月 14日 上午 9：00-10：00 报告十一（吕鑫）
10：10-11：10 报告十二 （许劲松）
11：20-12：20 报告十三（李灵光）
下午 2：00-4：00 关于代数几何研究与教学问题的讨论 （陆俊，谈胜利）
报告与摘要
报告题目：Geometry of ball quotients
报告人：杜荣 （华东师范大学）
摘要：We will introduce Gauss-Schwarz Theory for hypergeometric differential
equations. By using this theory, we will study the geometry of ball quotient
surfaces which are branched covers over complex projective planes with
complete quadrilateral as branch loci.
题目 : On smooth isolated curves in general complete intersection Calabi-Yau threefolds
报告人：余讯(天津大学)
摘要: Let Y be a Calabi-Yau threefold. Then the expected dimension of the deformation
space of a locally complete intersection curve in Y is zero. However, for a given pair (d,g),
it is hard to show the existence of a curve C of degree d and genus g such that C is rigid in Y.Building on results of Clemens and Kley, Knutsen found a powerful method to show existence of smooth isolated curves in general complete intersection Calabi-Yau threefolds. In this talk, we will discuss Knutsen's method and a variant of this method.
题目：A sharp Lower bound for the geometric genus and Zariski multiplicity question
报告人：左怀青（清华大学）
摘要： It is well known that the geometric genus and multiplicity are two important invariants for isolated singularities. In this project we give a sharp lower estimate of the geometric genus in terms of the multiplicity for isolated hypersurface singularities. In 1971, Zariski asked whether the multiplicity of an isolated hypersurface singularity depends only on its embedded topological type. This problem remains unsettled. Recently, we answer positively Zariski's multiplicity question for isolated hypersurface singularity if Milnor number or geometric genus is small.
题目： ON ALGEBRAIC SURFACES OF GENERAL TYPE WITH NEGATIVE c2
报告人：顾怡 （中国科学院）
摘要： Let X be an algebraic surface of general type over C, we have the following Bogomolov-Miayoka-Yau inequality: c1^2 (X) ≤ 3c2(X), or equivalently c1^2(X) ≤ 9χ(OX). As a consequence, both c2(X) and χ(OX) are positive integers. However the same inequality fails in positive characteristics. In fact, we have examples of algebraic surface of general type with negative c2 in positive characteristics. Instead of c2, Shepherd-Barron asked in a paper whether χ > 0 still holds true. In this talk, we shall show there is a positive number κp for each prime p > 2 such that whenever X is an algebraic surface of general type over a field of characteristic p, then χ(OX) ≥ κ_p c_1^2(X). In particular, this answers the question of Shepherd-Barron when p ≠ 2.
题目：On 3-folds of general type with $p_g=1, 2$ or $3$.
报告人：胡勇（复旦大学）
摘要：We classify minimal 3-folds of general type with the geometric genus 1,2 or 3 by characterizing the birationality of /Phi_m (where m is small). This is a joint work with Meng Chen and Matteo Penegini.
题目： The minimal volume of log surfaces of general type with positive geometric genus
报告人：刘文飞（厦门大学）
摘要： A log surface of general type is a smooth projective surface with a normal crossing boundary curve such that the log canonical divisor is big. The volumes of such surfaces satisfy the descending chain condition by a deep result of Alexeev. Thus the set of the volumes of any given class of log surfaces of general type attain a minimum. In this talk, I will provide the minimal volume of log surfaces of general type with positive geometric genus. This extends the Noether type inequality of Shuichiro Tsunoda and De-Qi Zhang. As a consequence, a Noether type inequality for stable log surfaces, normal or non-normal, can be obtained.
题目: Abundance for 3-folds with non-trivial Albanese maps
报告人：张磊（陕西师范大学）
摘要: Abundance has been proved for non-uniruled 3-folds with non-trivial Albanese maps last year, based on the progresses of Iitaka conjecture for fibrations with smooth geometric generic fiber. Recently we can prove abundance for 3-folds with non-trivial Albanese maps by studying fibrations with singular geometric generic fiber. In this talk I will summarize the ideas of studying Iitaka conjecture to treat different cases. In particular, it is discussed in details how to treat the most difficult case when the base of the fibration is an abelian variety, which involves the theory of sheaves on abelian varieties.
题目： Power series methods in the deformation of complex structures
报告人：赵全庭（华中师范大学）
摘要： we will present power series proofs for Kodaira-Spencer's
classical local stability theorem of compact Kahler manifolds,
which is a problem in the lecture notes by Kodaira-Morrow. Based on this method, we will show the local stability of balanced manifolds under the mild ddbar lemma and the one for p-Kahler manifolds under the ddbar lemma. Several applications of this method and examples
will also be discussed.
题目：Lyapunov Exponents and Holomorphic Subbundles
报告人：于飞（浙江大学）
摘要：Recently Eskin-Kontsevich-Moller-Zorich prove my conjecture that the sum of the top $k$ Lyapunov exponents is always greater or equal to the degree of any rank $k$ holomorphic subbundle(They generalize the original context from Teichmuller curves to any local system over a curve with non-expanding cusp monodromies). Furthermore, they conjecture that equality of Lyapunov exponents and degrees is related to the monodromy group being a thin subgroup of its Zariski closure.
I will introduce some backgrounds on those conjectures and some applications to Teichmuller dynamics and Calabi-Yau type families.
题目: Integrality structures in topological strings
报告人：朱盛茂（浙江大学）
摘要: We briefly review the mathematical structures of topological strings and their applications. In particular, we will discuss the integrality structures in topological (open) strings and the related mathematics.
题目：关于在本科生中代数几何教学开展的讨论
报告人：彭帆 （广西师范大学）涂玉平（武汉大学）
摘要：结合已有经验，讨论如何在本科生中开设基础的代数几何课程。
题目: Family of curves over $/mathbb{P}^1$ with a small number of singular fibers
报告人：吕鑫（美因茨大学）
摘要: Let $f: X /to /mathbb{P}^1$ be a non-isotrivial family of curves of positive genus over $/mathbb{P}^1$. I will talk about the question on determining the minimal number of singular fibers for such a family and some geometric and arithmetic aspects of the family achieving the minimum. This is based on joint works with Cheng Gong, Shengli Tan, Wanyuan Xu and Kang Zuo.
题目: Jordan property of birational automorphism groups
报告人：许劲松（西交利物浦大学）
摘要: Due to recent progress in boundedness conjecture of Fano varieties, Prokhorov and Shramov showed that the Cremona groups have Jordan property. We will discuss a geometric characterization of an algebraic variety whose birational automorphism group is not Jordan.
题目：Frobenius Stratification of Moduli Spaces of Vector Bundles in Positive Characteristic
报告人： 李灵光（同济大学）
摘要：Let $X$ be a smooth projective curve of genus $g(X)/geq 1$ over an algebraically closed field $k$ of characteristic $p>0$ and $F_X:X/rightarrow X$ be the absolute Frobenius morphism. Let $/M^s_X(r,d)$ be the moduli space of stable vector bundles of rank $r$ and degree $d$ on $X$. We study the Frobenius stratification of $/M^s_X(r,d)$ in terms of Harder-Narasimhan polygons of Frobenius pull backs of stable vector bundles and get the irreducibility, smoothness and dimension of Frobenius strata in case $(p,g,r,d)=(3,2,3,0)$.
题目：关于代数几何研究与教学问题的讨论
报告人：陆俊，谈胜利（华东师范大学）
摘要：结合已有经验，讨论如何结合代数几何的研究情况在本科生中开设代数几何课程。