学术报告（1.18）苏州2019几何拓扑研讨会

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报告题目：Knotting probability of a spatial arc

报告人：Akio Kawauchi (Osaka City University)

时间：2019年1月18日（星期五）09:00—09:50

地点：苏州大学本部维格堂113

报告摘要：A (polygonal) spatial arc is considered as models of a linear polymer and a

protein. In this talk, a knotting probability of a spatial arc is introduced by using chord

diagrams of ribbon surface-knots in 4-space. Actually, this probability measures a probability

of a spatial arc to be a non-trivial ribbon surface-knot of genus 2.

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报告题目：Fundamental group and Floer homology of (1; 1) knots

报告人：Jiajun Wang (Peking University)

时间：2019年1月18日（星期五）10:10—11:00

地点：苏州大学本部维格堂113

报告摘要：It is a conjecture that the hat Heegaard Floer homology is determined by

its fundamental group. We study the Heegaard Floer homology of (1; 1) knots and give an

algorithm to read its Floer homology from a particular presentation of its fundamental group.

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报告题目：Quadrisecant approximation of minimal polygonal knots

报告人：Gyo Taek Jin (Korean Advanced Institute of Science and Technology)

时间：2019年1月18日（星期五）11:10—12:00

地点：苏州大学本部维格堂113

报告摘要：We show that there exists a minimal polygonal torus knot of type (n; n + 1)

for each 3 ≤ n ≤ 100, and a minimal polygonal torus knot of type (n + 1; 2n + 1) for each

2 ≤ n ≤ 100, having only finitely many quadrisecants whose quadrisecant approximation is of

the same knot type.

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报告题目：Mapping classes and finite covers

报告人：Yi Liu (Beijing International Center for Mathematical Research)

时间：2019年1月18日（星期五）13:30—14:20

地点：苏州大学本部维格堂113

报告摘要：As topology of 3-manifolds can be studied via their finite covers, dynamics of

surface mapping classes can be studied via their lifted actions. In this talk, I will discuss some

recent work that connect twisted Alexander polynomials with entropy and other dynamical

features of mapping classes.

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报告题目：Counting conjugacy classes in groups with contracting elements

报告人：Wenyuan Yang (Beijing International Center for Mathematical Research)

时间：2019年1月18日（星期五）14:40—15:30

地点：苏州大学本部维格堂113

报告摘要：In this talk, we shall derive an asymptotic formula for the number of conjugacy

classes of elements for a class of statistically convex-cocompact actions with contracting elements. Denote by C(n) (resp. C‘(n)) the set of (resp. primitive) conjugacy classes of stable

length at most n. The main result is an asymptotic formula as follows:

#C(n)  #C’(n)  exp(\omega (G)) / n

As a consequence of the formulae, the conjugacy growth series is transcendental for all

non-elementary relatively hyperbolic groups, graphical small cancellation groups with finite

components. This is a joint work with Ilya Gekhtman (University of Toronto).

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报告题目：Diffeomorphism groups of critical regularity

报告人：Sang-hyun Kim (Seoul National University)

时间：2019年1月18日（星期五）15:40—16:30

地点：苏州大学本部维格堂113

报告摘要：We prove that for each compact connected one-manifold M and for each real

number a≥1, there exists a finitely generated group G inside the C^a-diffeomorphism group

Diff^{a}(M) such that G admits no injective homomorphisms into the group _{b>a} Diff^{b}(M). We also prove the dual result for _{b<a} Diff^{b}(M). (Joint work with Thomas Koberda)