Topology and Geometry of Manifolds Unit (Anastasiia Tsvietkova)
The interests of the group are centered around topology, geometry and complexity of lowdimensional manifolds. Informally, a manifold is a topological space that locally resembles Euclidean space near each point. It has been one of the main objects of study in topology since the beginning of 20th century. However only in 1970's it was noticed by several mathematicians that 3dimensional manifolds can be studied from a new perspective: using geometry.
On a large scale, the geometric picture is now wellunderstood for 3manifolds due to the Geometrization Theorem involving work of Hamilton, Perelman, Thurston, and many others. In particular, many 3manifolds have hyperbolic metric or can be decomposed into pieces with hyperbolic metric. However, on a small scale, i.e. for a particular manifold, the intrinsic connections between its combinatorial, topological and geometric properties are still often a mystery. This is one of the main topics of our research. While the questions lie in the area of pure mathematics, many of them are wellsuited for a computer study, and often lead to open problems concerning complexity or existence of certain algorithms.
Additionally, we are interested in establishing the connections between geometric invariants of 3manifolds and invariants coming from other areas of mathematics, such as quantum topology, number theory or representation theory.
Latest Posts

Faculty positions in Pure Math (tenure and tenuretrack)
Starting in summer 2019 or later, PhD in math and research in pure math is a prerequisite. More info:
https://www.mathjobs.org/jobs/jobs/12066

Temporary positions for 20182019 academic year
Lastmoment positions in lowdimensional topology and geometry, the applications are still being considered. The start date and term are somewhat flexible (at least 6 months). More info:
https://www.mathjobs.org/jobs/jobs/12027

OIST Welcomes Four New Faculty
https://www.oist.jp/newscenter/news/2017/3/1/oistwelcomesfournewfaculty