Time：July 8, 2023
Room：C1124, Material Science Research Building (Section C), USTC
Organizer
Bin Xu (University of Science and Technology of China )
Sicheng Lu (University of Science and Technology of China )
Sponsor
School of Mathematical Sciences, USTC
Institute of Geometry and Physics, USTC
Contact
Huamin Yu (yuhuamin@ustc.edu.cn)
Speakers
陈旭佳 Xujia Chen ( Harvard University )
胡光明 Guangming Hu ( Jinling Institute of Technology )
陆斯成 Sicheng Lu ( University of Science and Technology of China )
谭 东 Dong Tan ( Guangxi University )
钟友良 Youliang Zhong ( South China University of Technology )
Conference Schedule
Time：9:00-10:00
Speakers：Xujia Chen
Title：Kontsevich's invariants as topological invariants of configuration space bundles
Abstract：Kontsevich's invariants (also called configuration space integrals) are invariants for framed smooth manifolds/fiber bundles. The result of Watanabe('18) showed that Kontsevich’s invariants can distinguish smooth fiber bundles that are isomorphic as topological fiber bundles. I will first give an introduction to Kontsevich's invariants, and state a theorem which provides a perspective on how to understand their ability of detecting exotic smooth structures: real blow up operations essentially depend on the smooth structure, and thus given a space/bundle X, the topological invariants of some spaces/bundles obtained by doing some real blow-ups on X can potentially be different for different smooth structures on X.
Time：10:30-11:30
Speakers：Dong Tan
Title：The geometry of Horospheres in Teichmuller space
Abstract：In this talk, we will discuss some geometric properties of horospheres in Teichmuller space and explain some applications of horoshperes. This work is jointed with Xiaoke Lou and Weixu Su.
Time：14:00-15:00
Speakers：Youliang Zhong
Title：Local geometry of Teichmuller space
Abstract：This talk is on the local geometry of Teichmuller space with respect to the Teichmuller metric. We begin by presenting an overview of Teichmuller metric. By establishing local estimations on Teichmuller distance, we proved non-existence of angle and “non-CAT” of Teichmuller metric.
Time：15:30-16:30
Speakers：Guangming Hu
Title：Circle packings and total geodesic curvatures on hyperbolic metrics
Abstract：This talk focuses on the circle packing on non-compact surfaces. Horocycles and hypercycles are also considered in the packing. We give an existence and rigidity result of the circle packing with conical singularities regarding the total geodesic curvature on each circle. As a consequence, we establish an equivalent condition of the convergence of the combinatorial geodesic curvature flow to the desired circle packing.
Time：17:00-18:00
Speakers：Sicheng Lu
Title：What does a general spherical triangle look like?
Abstract：In the 2-dimension geometric world, Euclidean and hyperbolic triangles are well-studied. However, spherical triangles may have arbitrarily large interior angles and are much more complicated. In this talk, we introduce a method to represent a general spherical triangle via the Farey tessellation. The Teichmuller space of triangles and its natural closure is also studied.
