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Kasuya Lab
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Research on complex surfaces and the contact structures that appear on their boundaries.
AboutAbout the lab
Seeing contact structures on the boundaries of complex surfaces
Prof. Kasuya studies complex surfaces and the contact structures that appear on their boundaries.
A typical example is a Stein surface and its strongly pseudoconvex boundary.
Of particular interest are the Milnor fibers and singularity links of complex hypersurface singularities known as cusp singularities.
Building on differential topology, the work also intersects with complex geometry, several complex variables, and singularity theory.
Key terms
- Contact structure
- A structure formed by attaching a suitably twisted hyperplane to each point of an odd-dimensional space
- Complex surface
- A 2-dimensional figure whose coordinates are complex numbers. Counted in real dimensions, it is a 4-dimensional figure
- Milnor fiber
- A figure that appears when the neighborhood of a singularity is shifted slightly. It reflects the properties of the singularity
ResearchResearch themes
The lab mainly studies complex surfaces and the contact structures that appear on their boundaries. Building on differential topology, it deals with the areas where this meets complex geometry, several complex variables, and singularity theory.
*Illustrative imageComplex Surfaces and Contact Structures
The lab investigates complex surfaces and the contact structures that appear on their boundaries. A typical example is a Stein surface and its strongly pseudoconvex boundary.
*Illustrative imageThe Shape Around Cusp Singularities
The lab studies the Milnor fibers and singularity links of complex hypersurface singularities called cusp singularities, using knowledge from differential topology, contact geometry, and symplectic geometry.
*Illustrative imageNon-Kähler Complex Surfaces
The lab is also interested in non-Kähler complex surfaces and in complex surfaces with strongly pseudoconcave boundary. As an application of 4-dimensional topology, it has shown that there is a complex structure on 4-dimensional Euclidean space that has both properties.
MembersFaculty
- Associate ProfessorNaohiko Kasuya
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Report an errorAbout the images
The top and research theme images are illustrative and were not taken at the lab. They are cropped from Wikimedia Commons images. Cropped CC BY-SA images are provided under the same CC BY-SA license as the original (version shown on each line).
- Top image: “Standard contact structure r 3” Pmassot / CC BY-SA 3.0 (cropped)
- Complex Surfaces and Contact Structures: “Togliatti surface” Claudio Rocchini / CC BY-SA 3.0 (cropped)
- The Shape Around Cusp Singularities: “Bowknot” Gene Ward Smith / Public domain (cropped)
- Non-Kähler Complex Surfaces: “Bitrunc tessa schlegel” Claudio Rocchini / CC BY 2.5 (cropped)
- Related lab (幾何系
（川﨑盛通） ): “Chaos Theory & Double Pendulum - 1” Cristian V. / CC BY-SA 4.0 (cropped) - Related lab (代数系
（沼田泰英） ): “Young tableau for partitions of number 10” Unmismoobjetivo / CC BY 4.0 (cropped) - Related lab (幾何系
（野崎雄太） ): “Trefoil knot cgi” Altapedia / CC BY-SA 4.0 (cropped) - Related lab (数理科学系
（黒田紘敏） ): “Newly fallen snow crystals accumulating on a window sill” W.carter / CC0 (cropped)
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