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.
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Postdoc and Scientist Positions Open
Accepting applications for two Postdoc (2year contract) and two Scientist (flexible, at least 6 months) positions. Seeking highly motivated researchers. No teaching duties. Must have excellent oral and written English, no Japanese is required.