Professor Shuji Yamada
|Area and Subject Taught||Low-Dimensional Topology|
|Research Theme(s)||Knot Theory and Theory of Three-Dimensional Manifolds|
|Academic Degrees||Doctor of Science, Osaka University|
|Keywords for Research Field||Knots, Three-Dimensional Manifolds, Invariants|
|Office Phone Number||81-75-705-1760|
Topology in two, three and four dimensions is called low-dimensional topology.
Phenomena specific to lower dimensions that occur there differ from general dimensions(higher dimensions).
The primary subjects of research in low-dimensional topology are topological classification of low-dimensional manifolds, and classification of the topological positions of submanifolds within lower-dimensional manifolds.
My main research interests are three-dimensional manifolds, one-dimensional submanifolds within three-dimensional manifolds (i.e., knots), and one-dimensional complexes within three-dimensional manifolds (i.e., spatial graphs, which are a generalization of knots).
"Invariants" are tools for researching these subjects, and in our research we are using a recently discovered type of invariant called a "quantum invariant." Our particular focus is Jones polynomials and Vassiliev invariants, and we are studying spatial graphs, which are an extension of knots, using Yamada polynomials defined based on Jones polynomials.
In addition, the study to perform computer simulation using the knowledge of the knot theory reaches to check an aspect of DNA in the nucleus.
Notable Publications and Works in the Last Three Years
Kimura H, Shimooka Y, Nishikawa J, Miura O, Sugiyama S, Yamada S, Ohyama T : The genome folding mechanism in yeast. J Biochem, 2013 Aug,154(2) pp. 137-47
Yoshiyuki Ohyama, Kouki Taniyama, Shuji Yamada: Realization of Vassiliev invariants by unknotting number one knots. Tokyo Journal of Mathematics, Vol. 25, No. 1（ 2001）pp. 17-31