天元代数上几何研讨会由国家自然科学基金委 NSFC资助. 研讨会围绕Hodge理论主题，时间是2020年12月，包括线下和线上活动两部分， 线下活动于12月5-7日在科大东区举办。
报告包括短课程和学术报告，邀请报告持续更新中，报告题目和摘要在网页末端，也可参阅附件。
线下活动系列：12月 5-7日，建议4日到达，5日会场报到。
我们将报销参会者的差旅费、住宿费和参会期间的用餐费用，住宿预订请把自己的行程信息、身份证、手机号、邮箱信息告诉慕苗苗同学（邮箱：mumm@mail.ustc.edu.cn，紧急情况可拨打手机：18612516028）。身份证和手机号需要报送保卫处申请入校，为了报销便利请尽量提前打印好车票，飞机票发票抬头是：中国科学技术大学，纳税人识别号：12100000485001086E。
地点：科大东区5教5301,5206
邀请报告人：
短课程系列：
余讯（天津大学）：Calabi-Yau varieties and automorphisms groups
宋雷（中山大学）：Quotient Scheme
江智（复旦大学）：Syzygies of abelian varieties
沈洋（南京大学）：Canonical sections of Hodge bundles
学术报告：
周明铄（天津大学）：Frobenius splitting and moduli of vector bundles
曹阳（中科大）：Arithemetic purity of local-global principle
申屠钧超（中科大） *
会议安排：
周六（12-05）：东区五教5301
09:00-10:30： 宋雷 Quot Schemes （I-II）
10:45-11:45：余讯 Automorphism groups of Calabi-Yau manifolds (I)
14:00-15:30：余讯 Automorphism groups of Calabi-Yau manifolds (II,III)
16:00-17:00：曹阳 Arithemetic purity of local-global principle
周日（12-06）：东区五教5301
09:00-10:30：沈洋 Canonical sections of Hodge bundles (I, II)
10:45-11:45：宋雷 Quot Schemes （III）
14:00-15:30: 江智 Syzygies of abelian varieties
16:00-17:30：沈洋 Canonical sections of Hodge bundles (III, IV)
周一（12-07）：东区五教5206
09:00-10:00： 周明铄 Frobenius splitting and moduli of vector bundles
10:15-11:15：申屠钧超 Analytic Perspective of Perverse Sheaf
Online Series:
Invited Speakers: Osamu Fujino (Osaka University) ，Lei Wu (University of Utah) ,
Talk information:
Osamu Fujino (Osaka University) : On mixed-$\omega$-sheaves
ZoomMeeting id: 63193349493; Time 2020-12-02 09:40 (Chinese Zone) = 10:40 (Japanese Zone); Password: 341282
ZoomMeeting id: 64635264757; Time 2020-12-09 09:40 (Chinese Zone) = 10:40 (Japanese Zone);
Password: 178142
ZoomMeeting id: 68285908628; Time: 2020-12-16 09:40 (Chinese Zone) = 10:40 (Japanese Zone); Password: 900562
吴磊 (University of Utah ): V-filtrations, nearby and vanishing cycles, Hodge modules and vanishing theorems
会议时间：2020/12/13, 20（周日） ， 30（周三）， 2021/01/06（周三）1 0:00-11:30
腾讯会议 ID：499 9682 0391
会议密码：2020
报告信息：
余讯，天津大学
Title: Automorphism groups of Calabi-Yau manifolds
Abstract: I will start with some basic results for automorphism groups of Calabi-Yau manifolds of arbitrary dimensions. Then I will talk about automorphism groups of K3 surfaces (i.e., two-dimensional Calabi-Yau manifolds). In particular, I will recall global Torelli theorem and surjectivity of the period map for K3 surfaces and explain how to reduce problems about automorphism groups of K3 surfaces to lattice theoretical problems. Finally, I will discuss automorphism groups of Calabi-Yau manifolds of higher dimensions.
宋雷，中山大学
Title: Quot schemes: Construction and applications
Abstract: Quot schemes is an important tool in algebraic geometry. In the first part of talks, I will talk about Grothendieck's construction of quot schemes, following N. Nitsures's notes arXiv:math/0504590v1. In the second part, as an application, I will discuss a theorem of Mukai-Sakai, which gives a lower bound on the slope of maximal subbundles of a vector bundle over a smooth projective curve.
江智，复旦大学
Title: Syzygies of abelian varieties
Abstract: Syzygies of powers of ample line bundles are relatively well-understood due to the work of Lazarsfeld, Kempf, Pareschi. I will report some recent progress of syzygies of primitive ample line bundles and focus on the relations of syzygies with Fujita's conjecture and cohomological rank functions.
沈洋
题目：Canonical sections of Hodge bundles
摘要: In this talk, we introduce our recent work on the canonical sections of Hodge bundles. First, we review the work of the sections of Hodge bundles for Calabi-Yau manifolds, which uses the method of deformation theory. Then we generalize it to the Calabi-Yau type case, using the method of Hodge theory. Finally, we introduce the applications to characterizing the moduli spaces of certain polarized manifolds as ball quotients.
Osamu Fujino, Osaka University
Title: On mixed-$\omega$-sheaves
Abstract: It is well known that the Fujita--Zucker--Kawamata semipositivity theorem is a very important tool for the study of higher-dimensional complex algebraic varieties.Viehweg introduced the notion of weakly positive sheaves in order to study the Iitaka conjecture based on the Fujita--Zucker--Kawamata semipositivity theorem. On the other hand, Nakayama introduced the notion of $\omega$-sheaves to treat subadditivities of numerical Kodaira dimensions. Nakayama's theory gives a powerful framework for the study of pluricanonical bundles and is based on the theory of pure Hodge structures. In this series of lectures, I would like to explain the theory ofmixed-$\omega$-sheaves, which is a kind of generalizations of Nakayama's theory from the mixed Hodge theoretic viewpoint.
Lei Wu, University of Utah
Title: V-filtrations, nearby and vanishing cycles, Hodge modules and vanishing theorems
Abstratc: I will give a brief introduction on the theory of D-modules and Hodge modules. More precisely, it will cover
1. General properties for D-modules and (regular) holonomic D-modules on curves.
2. Relative D-modules and Kashiwara-Malgrange filtrations on holonomic D-modules.
3. The construction of nearby and vanishing cycles for both perverse sheaves and D-modules and their comparison.
4. Bernstein-Sato polynomials.
5. Inductive definition/construction of pure Hodge modules.
6. Applications of pure Hodge modules on vanishing theorems in algebraic geometry.