Speaker: 杨森(滁州学院)
Time: 9:30-11:00, Dec 21, 2023
Online: 腾讯会议：505-345-583
Titile: Formal D eformation of Chow groups III
Abstract:
This lecture devotes to exploring the infinitesimal theory of algebraic cycles by Green and Griffiths. K-theory comes into this picture again and involves interesting examples and questions.
Speaker: 杨森(滁州学院)
Time: 9:30-11:30, Dec 12, 2023
Online: Zoom：811 5638 1768（Password：msrc）
Titile: Formal D eformation of Chow groups II
Abstract:
We introduce the concept of Chow groups and use K theory to understand the structure of Chow groups . We plan to recall the well known conjecture by Bloch, which predicted that, for X a complex smooth projective surface with trivial geometric genus, the Albanese map is an isomorphism .
Speaker: 杨森(滁州学院)
Time: 9:30-11:30, Dec 5, 2023
Venue: 数学中心研讨室（至善楼602）
Online: Zoom：811 5638 1768（Password：msrc）
Titile: Formal D eformation of Chow groups I
Abstract:
We explain the deformation theory of Chow groups through algebraic K theory. The details are as follows.In Lecture I, we first introduce Grothendieck group K_0 by mimicking the example of extending natural numbers to integers, then we recall Bass K_1 from the viewpoint of linear algebra. Milnor K_2 is also discussed.
Speaker: Yang Shen (MSRC, CQUT)
Time: 14:30-15:30, Nov 28, 2023
Venue: 数学中心研讨室（至善楼602）
Online: Zoom：811 5638 1768（Password：msrc）
Titile: Illustrating the recent theorems in flag domains with classical examples I
Abstract:
Flag domains in flag manifolds are of great importance to complex geometry, Hodge theory and representation theory. For example, the period domains in Hodge theory for studying the moduli spaces are flag domains in the flag manifolds defined by Sp(n,C) or SO(n,C) quotient by the parabolic subgroups. Recently, tools from complex geometry have revolutionary applications in studying the geometry of the flag domains and the corresponding spaces, e.g. the cycles spaces and the incidence variety. In this series talks, we will introduce the classical examples of flag domains with emphasis on period domain, to illustrate the recent progress on flag domains.
Reference:
Griffiths, Hodge theory, complex geometry and complex geometry.Knapp, Representation theory of semisimple groups. An overview based on examples.Fels, Huckleberry, Wolf, Cycle Spaces of Flag Domains
Speaker: Wei Xia (MSRC, CQUT)
Time: 14:30-15:30, Nov 14, 2023
Venue: 数学中心研讨室（至善楼602）
Titile: Irreducible decompositions of double complex-2
Abstract:
I will discuss the proof of the structure theorem of double complexes due to Stelzig.
Speaker: Wei Xia (MSRC, CQUT)
Time: 14:30-15:30, Nov 7, 2023
Venue: 数学中心研讨室（至善楼602）
Titile: Irreducible decompositions of double complex
Abstract:
I will introduce the structure theorem of double complex due to Stelzig and Qi-Khovanov.
Speaker: Wei Xia (MSRC, CQUT)
Time: 14:30-15:30, Oct 31, 2023
Venue: 数学中心研讨室（至善楼602）
Titile: Extension of modules and Ext-2,
Abstract:
I will show the set of equivalent classes of extensions of A by B is isomorphic to the group Ext^1(A,B).
Speaker: Xueyuan Wan (MSRC, CQUT)
Time: 14:30-16:30, Oct 17, 2023
Venue: 数学中心研讨室（至善楼602）
Titile: Spectral constant rigidity of warped product metrics
Abstract:
In this talk, we will prove a rigidity result for warped product metrics involves spectral constants, which generalized a scalar curvature rigidity theorem of Bar-Brendle-Hanke-Wang and Wang-Xie. This work is joint with Xiaoxiang Chai and Juncheol Pyo.
Speaker: Wei Xia (MSRC, CQUT)
Time: 14:30-15:30, Oct 10, 2023
Venue: 数学中心研讨室（至善楼602）
Titile: Extension of modules and Ext
Abstract:
I will discuss extension of modules and its relationships with the Ext functor.
Speaker: Mingchen Xia (Université Paris VI)
Time: 14:30-16:00, August 15, 2023
Venue: 数学中心研讨室（至善楼602）
Online: 腾讯会议：938-3350-3499
Titile: A transcendental approach to non-Archimedean metrics
Abstract:
The pluripotential theory on a normal projective variety is closely related to the pluripotential theory on its Berkovich analytification. In particular, thanks to the celebrated work of Berman-Boucksom-Jonsson, we know that the space of finite energy non-Archimedean metrics associated with an ample line bundle is isomorphic to a subspace of the space of geodesic rays in the space Archimedean potentials. In this talk, I will explain an extension of this point of view to transcendental big classes. We show that Boucksom-Jonsson's envelope conjecture holds in our transcendental theory and our theory coincides with Boucksom-Jonsson's on smooth projective varieties. Part of the talk is based on a joint work with Tamás Darvas and Kewei Zhang.
Speaker: Yang Shen (MSRC, CQUT)
Time: 14:30-16:00, August 8, 2023
Venue: 数学中心研讨室（至善楼602）
Online: 腾讯会议：372-261-498
Titile: Stable compact complex submanifolds of complex manifolds and the existence theorem
Abstract:
In this talk we introduce the classical papers [1] and [2] of Kodaira on the stable compact complex submanifolds. In [2], Kodaira gave the definition of the stable compact complex submanifold V of a complex manifold W that for any deformation W_t of W there exists a deformation V_t of V such that V_t is a complex submanifold of W_t for any t. Then Kodaira proved that H^1(V, N)=0 implies that V is a stable compact complex submanifold of W, where N is the normal bundle of V in W.
References:
[1] Kodaira, A theorem of completeness of characteristic systems for analytic families of compact submanifolds of complex manifolds, Ann. of Math., 75 (1962), 146-162.
[2] Kodaira, On stability of compact submanifolds of complex manifolds, Amer. J. Math., 85 (1963), 79-94.
Speaker: 张攀（安徽大学）
Time: 14:30-16:00, August 1, 2023
Venue: 数学中心研讨室（至善楼602）
Online: 腾讯会议：793-692-902
Titile: Some topics on Yang-Mills equations
Abstract:
In this talk, I will introduce our recent work on Yang-Mills equations. And this talk will be divided into two parts. In the first part, I will review some classical results on the Yang-Mills flow, and then introduce our results on the higher order Yang-Mills-Higgs flow. Under some suitable conditions, we show that the flow admit long-time behavior. In the second part, I will talk about the existence of Hermite-Yang-Mills metric on non-Kaehler manifold. The proof is a combination of continuity method and heat flow method. This talk is based on joint works with Hemanth Saratchandran, Chuanjing Zhang, Jiaogen Zhang and Xi Zhang.
Speaker: 邓亚（CNRS, Institut Élie Cartan de Lorraine, Université de Lorraine）
Time: 14:30-16:00, July 26, 2023
Venue: 数学中心研讨室（至善楼602）
Online: Zoom：81618869022（Password：msrc）
Titile: Green-Griffiths-Lang conjecture for algebraic varieties with big fundamental groups
Abstract:
The Green-Griffiths-Lang (GGL) conjecture asserts that any entire curve in a complex projective variety of general type cannot be Zariski dense. This conjecture fascinates many complex geometers, in part due to its arithmetic analogy with the Bombieri-Lang conjecture for rational points in algebraic varieties over number fields. In this talk, I will report a recent work with Cadorel and Yamanoi, focusing on the proof of the generalized GGL conjecture for quasi-projective varieties admitting a big reductive local system.
Speaker: Xueyuan Wan (MSRC, CQUT)
Time: 14:30-16:00, July 18, 2023
Venue: 数学中心研讨室（至善楼602）
Titile: Deformations of differential forms on compact complex manifolds
Abstract:
In this talk, I will discuss the unobstructed deformations of d-closed forms, logarithmic differential forms, and $\bar{\partial}$-closed forms on compact complex manifolds satisfying some special conditions. These results are based on several joint works with Professors Kefeng Liu, Sheng Rao, Quanting Zhao, and Wei Xia.
Speaker: Wei Xia (MSRC, CQUT)
Time: 14:30-16:00, July 4, 2023
Venue: 数学中心研讨室（至善楼602）
Titile: Degeneration of the Frölicher spectral sequence and small deformations - 2
Abstract:
I will report Maschio's work on deformation stabilty of degeneration of the Frölicher spectral sequence. It is proved that if all the Hodge numbers are deformation invariant then the Frölicher spectral sequence degenerate at the second page is a deformation stable property. I will discuss some details of the proof this time.
Reference:
Michele Maschio, On the degeneration of the Frölicher spectral sequence and small deformations, arXiv:1811.12877
Speaker: Wei Xia (MSRC, CQUT)
Time: 14:30-16:00, June 13, 2023
Venue: 数学中心研讨室（至善楼602）
Titile: Degeneration of the Frölicher spectral sequence and small deformations
Abstract:
I will report Maschio's work on deformation stabilty of degeneration of the Frölicher spectral sequence. It is proved that if all the Hodge numbers are deformation invariant then the Frölicher spectral sequence degenerate at the second page is a deformation stable property.
Reference:
Michele Maschio, On the degeneration of the Frölicher spectral sequence and small deformations, arXiv:1811.12877
Speaker: Yang Shen (MSRC, CQUT)
Time: 14:30-16:00, June 6, 2023
Venue: 数学中心研讨室（至善楼602）
Titile: Quotients of non-classical period domains are not algebraic II
Abstract:
In this talk, we introduce the work of Griffiths, Robles and Toledo on the non-algebraicity of the quotient space Γ\D of the non-classical period domain D. First we construct the geometric structures of the period domain D from Lie theory. Then we prove that any two points of D can be connected by a chain of compact subvarieties of D, which are parametrized by the cycle space of D. The proof relies on the Lie algebra descriptions of the bundles on the double filtration of D and a standard theorem in Control Theory. Finally we get a contradiction using the Shafarevich map if the quotient space Γ\D is algebraic.
Reference:
Phillip Griffiths, Colleen Robles and Domingo Toledo, Quotients of non-classical flag domains are not algebraic, doi:10.14231
James A. Carlson and Domingo Toledo, Compact quotients of non-classical domains are not Kahler, Contemporary Mathematics Vol. 608, 2014
Speaker: Yang Shen (MSRC, CQUT)
Time: 14:30-16:00, May 30, 2023
Venue: 数学中心研讨室（至善楼602）
Titile: Quotients of non-classical period domains are not algebraic I
Abstract:
In this talk, we introduce the work of Griffiths, Robles and Toledo on the non-algebraicity of the quotient space Γ\D of the period domain D. First we construct the geometric structures of the period domain D from Lie theory. Then we prove that any two points of D can be connected by a chain of compact subvarieties of D, which are parametrized by the cycle space of D. The proof relies on the Lie algebra descriptions of the bundles on the double filtration of D and a standard theorem in Control Theory. Finally we get a contradiction using the Shafarevich map if the quotient space Γ\D is algebraic.
Reference:
Phillip Griffiths, Colleen Robles and Domingo Toledo, Quotients of non-classical flag domains are not algebraic, doi:10.14231
James A. Carlson and Domingo Toledo, Compact quotients of non-classical domains are not Kahler, Contemporary Mathematics Vol. 608, 2014
Speaker: Xueyuan Wan (MSRC, CQUT)
Time: 14:30-16:00, May 23, 2023
Venue: 数学中心研讨室（至善楼602）
Title: Positivity of Schur forms for strongly decomposably positive vector bundles
Abstract:
In this talk, we discuss two types of strongly decomposable positivity, expanding on (dual) Nakano positivity and exceeding S. Finski's concept. We outline criteria for type I and II, proving type I's Schur forms are weakly positive and type II's are positive. We provide an algebraic proof for Schur form positivity in (dual) Nakano positive vector bundles, initially proven by S. Finski.
