2019流形上的整体分析研讨会
会议时间：2019年7月28日（报到）－8月3日（离会）
会议地点：管理科研楼数学科学学院
7月30日（周二）下午 、8月1日（周四）下午1318教室，其余时间1308教室
会议报告时间安排：
| 7月29日 | 7月30日 | 7月31日 | 8月1日 | 8月2日 |
8:30-10:00 | 8:30-9:30 申述 | 刘冰萧 | 刘冰萧 | 刘冰萧 | 刘冰萧 |
休息 | |||||
| 9:50-11:20 刘冰萧 | 休息 | |||
10:20-11:20 | 申述 | 申述 | 申述 | 申述 | |
2:00-2:45 | 伊泽霖 | 王相生 | 自由 讨论 | 史鹏帅 | 刘宇航 |
2:50-3:35 | 张鑫 | 卢文 | 余世霖 | 苏广想 | |
| 合影、茶歇 | 茶歇 | 茶歇 | ||
4:15- | 戴先哲 | 张野平 | 宋言理 |
| |
会议报告题目：
刘冰萧 马普所(波恩)
An introduction to symmetric spaces
申述 巴黎第六大学
Introduction to the trace formual for GL(2)
伊泽霖 南开大学
The tangent groupoid and rescaled bundle
张鑫 武汉理工大学
Hopf cyclic cohomology for non-compact $G$-manifolds
戴先哲 加州大学（圣芭芭拉）、华东师范大学
TBA
王相生 北京大学
Weyl group actions on geometric objects
卢文 华中科技大学
Bergman kernel for sequence of line bundles on K/"{a}hler manifolds
张野平 日本京都大学
BCOV invariant and ramified cover
史鹏帅 北京大学
The APS index problem for Callias-type operators and the relative eta invariant
余世霖 厦门大学
Deformation quantization of coadjoint orbits
宋言理 华盛顿大学（圣路易斯）
A geometric formula for $K$-type of tempered representations
刘宇航 北京大学
On positively curved 6-manifolds
苏广想 南开大学
Positive scalar curvature on noncompact foliations
会议报告摘要：
刘冰萧 马普所（波恩）
Title: An introduction to symmetric spaces
Abstract: The study of Riemannian symmetric spaces can be reduced tostudy the symmetric pair (G，K), where G is a reductive Lie group and K is a compact subgroup. Here, we give an introduction to the theories of reductive Lie groups and semisimple Lie algebras, then we relate them to the theory of symmetric spaces.
申述 巴黎第六大学
Title: Introduction to the trace formual for GL(2)
Abstract: In these lectures, we give a detail proof for the trace formula on $SL(2，/mathbb{Z})/SL(2, /mathbb{R}) $and we explain its generalisation to $GL_2(/mathbb{Q})/GL_2(A)$. We will cover the following topics.
1. Cusp forms
2. Eisenstein series and the constant terms
3. Arthur’s truncation
4. Orbital integral and weighted orbital integral
5. Ad`ele ring and strong approximation
伊泽霖 南开大学
Title: The tangent groupoid and rescaled bundle
Abstract: The notion of rescaled bundle is an attempt to combine Getzler’s rescaling calculus with Connes’ tangent groupoid construction. In this talk I shall present the construction of rescaled bundle and explain its relation with the localindex theorem. This is a joint work with Nigel Higson.
张鑫 武汉理工大学
Title: Hopf cyclic cohomology for non-compact G-manifolds
Abstract: We introduce differential graded Hopf algebroids associate to non-compact G-manifolds, especially for complex manifolds and smooth manifolds with boundary. When the G-action is proper and cocompact, we prove that the cyclic cohomology groups of the above Hopf algebroids are finite dimensional.
戴先哲 加州大学（圣芭芭拉）、华东师范大学
Title: TBA
王相生 北京大学
Title: Weyl group actions on geometric objects
Abstract: We recall some classical Weyl group actions associated to certain geometric objects, e.g., basic affine spaces, Nakajima quiver varieties etc. Then we outline a new Weyl group action on a kind of varieties, which partially generalizes a recent result about the Weyl group action on the cotangent bundle of basic affine spaces.
卢文 华中科技大学
Title: Bergman kernel for sequence of line bundles on K/"{a}hler manifolds
Abstract: Given a sequence of holomorphic Hermitian line bundles $L_p$ on K/"{a}hler manifold $X$, we establish the asymptotic expansion of the Bergman kernel of the holomorphic space $H^0(X,L_p)$ under a natural approximate assumption on the curvature of the positive line bundle $L_p$. This is a joint work with Professors Dan Coman, Xiaonan Ma and George Marinescu.
张野平 日本京都大学
Title: BCOV invariant and ramified cover
Abstract: Bershadsky, Cecotti, Ooguri and Vafa constructed a real valued invariant for Calabi-Yau manifolds, which is now called the BCOV invariant. Now we consider a pair $(X,Y)$, where $X$ is a compact Kaehler manifold and $Y/subseteq X$ is a $m$-canonical divisor with $m/neq 0,-1$. In this talk, we extend the BCOV invariant to such pairs. If $m=-2$, then $X$ admits a ramified 2-cover $f: X'/to X$ with branch locus $Y$. Moreover, $X'$ is a K3 surface. Let $/iota$ be the involution on $X'$ commuting with $f$. We will show that the BCOV invariant of $(X,Y)$ and the equivariant BCOV invariant of $(X',/iota)$ coincide under the assumption that $X$ is a rigid del Pezzo surface.
史鹏帅 北京大学
Title: The APS index problem for Callias-type operators and the relative eta invariant
Abstract: Callias-type operators are a class of perturbed Dirac operators on non-compact manifolds first studied by C. Callias. We introduce the classical Callias index theorem and generalize it to manifolds with boundary. In particular, we study the index problem under Atiyah-Patodi-Singer boundary condition for such operators on manifolds with non-compact boundary. This gives rise to a boundary invariant which we call relative eta invariant. We show its properties indicating that it can be seen as a generalization of the eta invariant to non-compact manifolds. Joint work with Maxim Braverman.
余世霖 厦门大学
Title: Deformation quantization of coadjoint orbits
Abstract: The coadjoint orbit method/philosophy suggests that irreducible unitary representations of a Lie group can be constructed as quantization of coadjoint orbits of the group. In this talk, I will propose a geometric way tounderstand orbit method using deformation quantization, in the case of noncompact real reductive Lie groups. This approach combines recent results on quantization of symplectic singularities and Lagrangian subvarieties. This is joint work with Conan Leung.
宋言理 华盛顿大学（圣路易斯）
Title: A geometric formula for K-type of tempered representations
Abstract: I will talk about how to realize K-types of any tempered representation of a non-compact Lie group as geometric quantization of coadjoint orbits. I will also talk about some application of the Ma-Zhang's theorem on geometric quantization in representation theory. This is a joint work with Peter Hochs and Shilin Yu.
刘宇航 北京大学
Title: On positively curved 6-manifolds
Abstract: Closed Riemannian manifolds with positive sectional curvature are a class of fundamental objects in Riemannian geometry. There are few known examples of such manifolds, each of which possesses interesting geometric properties. For example, they usually have large symmetry groups. In this talk, I will review a few classical results in positive curvature, including Bonnet-Myers theorem and Synge theorem. Then I will move to the special case of dim 6, talking about the classification problem of positively curved 6-manifolds with certain non-Abelian symmetry conditions. I showed that such manifolds have Euler characteristic 2,4, or 6, and obtained topological classification after imposing certain restrictions on the action.
苏广想 南开大学
Title: Positive scalar curvature on noncompact foliations
Abstract: Let $(M,g^{TM})$ be a noncompact enlargeable Riemannian manifold in the sense of Gromov-Lawson and $F$ an integrable subbundle of $TM$. Let $k^F$ be the leafwise scalar curvature associated to $g^F=g^{TM}|_F$. We show that if either $TM$ or $F$ is spin, then $/inf(k^F)/leq 0$. This is a joint work with Prof. Weiping Zhang.
会议主办单位：中国科学技术大学数学科学学院
会议组织者：麻小南（巴黎第七大学、中国科学技术大学）
俞建青（中国科学技术大学）
