Topology and Geometry Laboratory
Mathematics of shapes: geometry, topology and singularity theory
Topology is the area of mathematics to study the properties of shapes that do not change even when drastically deformed. In topology, triangles, squares and circumferences are regarded as the same. Also a coffer cup and donut are the same. Complicated train networks are shown as route maps at stations, which is indeed an approach taken by topology. We are examining the hidden properties of shapes, which are more abstract than curbed lines and surface we see, from the perspectives of topology and various geometry aspects.
Affiliation

Architecture (AP,SA,UA) 
Faculty Name

KUROKAWA, Yasuhiro 
Academic Society

Mathematical Society of Japan 
Keyword

Topology, Geometry, Singularity theory, Differential geometry, Architectural geometry 
Study Fields
 Mathematics
 Mathematical sciences
For Society
Topology and singularity theory are relatively new fields. Analysis of how shapes are formed and analyzing how they are joined will relate to various other fields. The analysis of curved lines and surfaces are applied to architectural designs.
Research Themes
 Research on the topology of various geometric structures
 Research on singularity theory related to mapping
 Research on architectural geometry