People

→ Japanese

Xiaobing Sheng

Email sheng.xiaobing.yke(@osaka-u.ac.jp)
Research
 low dimensional topology, geometric group theory, knot theory
Keywords Thompson's groups, quasi-isometries
URL https://orcid.org/0009-0001-7619-3553

My research interests lie in low dimensional topology, geometric group theory. In the past few years, my research focused particularly on combinatorial and geometric aspects of the so-called Thompson's groups and their generalisations.

Thompson's groups $F$, $T$, $V$ were first constructed from a logic point of view while later found to have connections with many other branches of mathematics such as string rewriting system, homotopy theory, combinatorics and dynamical systems. They are becoming intuiging examples in the geometric group theory in the recent years.

On the other hand, Vaughan Jones introduced this connection between Thompson’s groups and conformal field theory (CFT) motivated by the construction of unitary representation of Thompson’s groups (or more generally Thompson-like groups) that related again to coarse geometric properties of the groups. As an analogue of the braid groups, a concrete method of constructing knots and links from elements of Thompson’s group $F$ is found which provides applications to knot theory.