【07月8日】Mini-workshop on Geometric Topology

发布者:王欣发布时间:2023-06-28浏览次数:152



TimeJuly 8, 2023

RoomC1124, 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 )



Time9:00-10:00

SpeakersXujia Chen

TitleKontsevich’s invariants as topological invariants of configuration space bundles

AbstractKontsevich'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.



Time10:30-11:30

SpeakersDong Tan

TitleThe geometry of Horospheres in Teichmuller space

AbstractIn 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.



Time14:00-15:00

SpeakersYouliang Zhong

TitleLocal geometry of Teichmuller space

AbstractThis 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.



Time15:30-16:30

SpeakersGuangming Hu

TitleCircle packings and total geodesic curvatures on hyperbolic metrics

AbstractThis 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.



Time17:00-18:00

SpeakersSicheng Lu

TitleWhat does a general spherical triangle look like?

AbstractIn 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.