YMSC-SIMIS joint workshop on moduli spaces and related topics
Organizers
| Xiang He (YMSC) | xianghe"at"mail.tsinghua.edu.cn |
| Chenglong Yu (SIMIS) | yuchenglong"at"simis.cn |
| Dingxin Zhang (SIMIS) | zhang"at"simis.cn |
| Zhiwei Zheng (YMSC) | zhengzhiwei"at"mail.tsinghua.edu.cn |
| Jie Zhou (YMSC) | jzhou2018"at"mail.tsinghua.edu.cn |
Venue & Time
This workshop will be held in B725, Shuangqing Complex Building , during Nov 1-3, 2025.
Schedule
| Time & Date | Saturday (Nov 1) | Sunday (Nov 2) | Monday (Nov 3) |
| 09: 30-10: 30 | Kang Zuo | Jinxing Xu | Free discussion |
| 11: 00-12: 00 | Caucher Birkar | Zhiyu Tian | Free discussion |
| 12: 00-14: 00 | Lunch |
Lunch |
|
| 14: 00-15: 00 | Tong Zhang | Haohua Deng | |
| 15: 30-16: 30 | Yongqiang Liu | Ruiran Sun | |
| 17: 00-18: 00 | Free discussion |
Mao Sheng |
Title & Abstract
Caucher Birkar (Tsinghua University)
Title: Moduli of minimal models
Abstract: In this talk I will discuss moduli of algebraic varieties of arbitrary non-negative Kodaira dimension via the theory of stable minimal models.
Haohua Deng (Dartmouth College/Zhejiang University)
Title: Recent breakthroughs on completing general period mappings
Abstract: Since Griffiths' question in the 70's, it is a long-standing problem to find a completion of general period mapping with significant geometric and Hodge-theoretic meaning. The classical theories on the compactification of locally symmetric varieties by Satake--Baily--Borel and Mumford et al provide such completions to a very limited set of "classical" cases, while the problem has been almost completely open for non-classical cases until recent years. I will report the latest progress in this direction including several of my papers. Collaborators include Chongyao Chen (IMFP Shanghai), Colleen Robles (Duke), Jacob Tsimerman (Toronto).
Yongqiang Liu (University of Science and Technology of China)
Title: Kahler weighted right-angled Artin group
Abstract: It is a question of Serre to characterize finitely presented groups that can serve as the fundamental group of a compact Kahler manifold, called the Kahler groups. Dimca, Papadima and Suciu classified the Kahler groups in the class of right-angled Artin groups in 2009. We classify the Kahler groups contained in the class of weighted right-angled Artin groups. This class of groups comes from the edge-weighted finite simple graphs and is a natural generalization of the right-angled Artin groups. This talk is based on a joint work with Yuan Liu.
Mao Sheng (Tsinghua University)
Title: Nonabelian one-periodicity theorem
Abstract: In positive characteristic, Ogus-Vologodsky established the following result: Let $f: X\to S$ be a $W_2(k)$-liftable smooth proper morphism over $k$ with its relative dimension $d\leq p=char(k)-1$. Then the relative Frobenius of $f$ induces an isomorphsim of flat connections $C^{-1}Gr_{F_{hod}}(H^d_{dR}(X/S),\nabla_{GM})\cong (H^d_{dR}(X/S),\nabla_{GM})$. This is called one-periodicity theorem in the context of the theory of periodic Higgs-de Rham flows. In this talk, I want to report on our recent work (in progress) on its nonabelian analogue.
Ruiran Sun (Xiamen University)
Title: Rigidity problems on moduli spaces of polarized manifolds
Abstract: A key step of Arakelov and Parshin's proof of the Shafarevich conjecture was establishing the rigidity of families of curves over a base curve (or equivalently, the rigidity of morphisms into the moduli space M_g). In higher dimensions, however, this rigidity often fails, and non-rigid families abound. This talk will survey recent progress on rigidity for moduli spaces of polarized manifolds, addressing two fundamental questions: Under what conditions is a family rigid? And when it is not, how can we describe its space of deformations?
Zhiyu Tian (BICMR, Peking University)
Title: Deformation invariance of some Lawson homology groups
Abstract: Lawson homology is the semitopological analogue of higer Chow groups. It is conjectured that some Lawson homology groups are isomorphic to the homology group. In particular, they should be deformation invariant, in contrast to the usual behaviour of cycle invariants in a family that usually change at countably many subvarieties. I will explain some rather simple observations about the deformation invariance.
Jinxing Xu (University of Science and Technology of China)
Title: Monodromy representations from hyperplane arrangements
Abstract: Given a hyperplane arrangement in general position, one can construct the double cover of the projective space branched along the arrangement. As the hyperplane arrangement varies, this gives rise to a family of projective varieties that generalizes the classical family of hyperelliptic curves. I will discuss the monodromy representations associated with this family, from both the complex and mod l side. This is based on a joint work with Xiaopeng Xia.
Tong Zhang (East China Normal University)
Title: Moduli spaces of threefolds on the Noether line
Abstract: I will talk about the classification of canonical threefolds on the (refined) Noether line by describing their moduli spaces, which includes an explicit stratification, an estimate of the number of irreducible components and the dimension formula for every such moduli space. The key idea behind the proof will also be discussed. This is a joint work with S. Coughlan, Y. Hu and R. Pignatelli.
Kang Zuo (Wuhan University)
Title: Special subvarieties in moduli spaces of Calabi-Yau n-folds
Abstract: We shall discuss on special subvarieties in a moduli space M of CY manifolds appearing as bihomscheme of non-rigid maps into M. We shall discuss on a conjecture claiming that those type special subvarieties can not be Zariski dense in M except M is a Shimura variety. We find many examples of bihomschemes in moduli spaces of CY 3-folds appearing as Shimura subvarieties. We shall also discuss a possible splitting of families over bihomscheme in moduli of hypersurfaces in terms of possible splitting of Jacobian ring. My talk is based on joint works with R.R. Sun and C.L. Yu.
Workshop on multi-zeta values and iterated integrals
Organizers:
| Xiang He | xianghe"at"mail.tsinghua.edu.cn |
| Chenglong Yu | yuchenglong"at"mail.tsinghua.edu.cn |
| Dingxin Zhang | dingxin"at"mail.tsinghua.edu.cn |
| Zhiwei Zheng | zhengzw11"at"163.com |
| Jie Zhou | jzhou2018"at"mail.tsinghua.edu.cn |
Venue&Time:
This workshop will be held in C654, Shuangqing Complex Building, during Nov 11-12, 2023.| Time | Speaker | Title | Abstract |
| Nov 11 9：30-10：30 | Ma Luo |
Iterated integrals of modular forms, I | Iterated integrals was introduced and developed by Kuo-Tsai Chen, to study fundamental groups and higher homotopy groups. This theory has now become an important tool not only in topology, but also in algebraic geometry and in number theory. To illustrate the versatility of iterated integrals, various properties, examples, and applications will be presented in my first talk. In the second talk, we focus on a special class of numbers called multiple zeta values, which appear in number theory, in the study of motives, and in quantum field theory. They can be written as iterated integrals due to Kontsevich's observation. Recently, it was shown that they can be written differently as iterated integrals of modular forms. All of these are subsumed in a program called Galois theory of periods, which we will describe and discuss. |
| Nov 11 11:00-12:00 | Ce Xu |
Alternating Multiple Mixed Values | In this talk we define and study a variant of multiple zeta values (MZVs) of level four, called alternating multiple mixed values (AMMVs), forming a Q[i]-subspace of the colored MZVs of level four. This variant includes the alternating version of Hoffman’s multiple t-values, Kaneko-Tsumura’s multiple T-values, and the multiple S-values studied by the authors previously as special cases. We exhibit nice properties of AMMVs similar to the ordinary MZVs such as the duality, integral shuffle and series stuffle relations and then establish some other explicit relations among them. We will also discuss some conjectures concerning the dimensions of the above-mentioned subspaces of AMMVs. These conjectures hint at a few very rich but previously overlooked algebraic and geometric structures associated with these vector spaces. This is a joint work with Lu Yan and Jianqiang Zhao. |
| Nov 11 14：00-16：00 | Zigang Zhu |
Computer Algebra in the study of Automorphism Groups of Smooth Hypersurfaces | In this talk, we introduce notions of partitionability and characteristic sets of homogeneous polynomials and give a complete classification of groups faithfully acting on smooth cubic fivefolds and fourfolds. The classification is computer-aided with GAP (Groups, Algorithms, Programming), SageMath, and Mathematica. We demonstrate the functionalities of GAP, SageMath, and Mathematica, and discuss their interactions. We illustrate the usage of these mathematical softwares in the classification process through specific examples. This talk is based on a joint work with Song Yang and Xun Yu. |
| Nov 12 9：30-10：30 | Ma Luo |
Iterated integrals of modular forms, II | Iterated integrals was introduced and developed by Kuo-Tsai Chen, to study fundamental groups and higher homotopy groups. This theory has now become an important tool not only in topology, but also in algebraic geometry and in number theory. To illustrate the versatility of iterated integrals, various properties, examples, and applications will be presented in my first talk. In the second talk, we focus on a special class of numbers called multiple zeta values, which appear in number theory, in the study of motives, and in quantum field theory. They can be written as iterated integrals due to Kontsevich's observation. Recently, it was shown that they can be written differently as iterated integrals of modular forms. All of these are subsumed in a program called Galois theory of periods, which we will describe and discuss. |
| Nov 12 11:00-12:00 | Ce Xu |
On Some Unramified Families of Motivic Euler Sums | It is well known that sometimes Euler sums (i.e., alternating multiple zeta values) can be expressed as Q-linear combinations of multiple zeta values (MZVs). In her thesis Glanois presented a criterion for motivic Euler sums (MES) to be unramified, namely, expressible as Q-linear combinations of motivic MZVs. By applying this criterion we present a few families of such unramified MES in two groups. In one such group we can further prove the concrete identities relating the MES to the motivic MZVs, determined up to rational multiple of a motivic Riemann zeta value by a result of Brown. This is a joint work with Jianqiang Zhao. |
| Nov 12 14:00-16:00 | Discussions |