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Geometry (Nozaki) Lab
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Research that uses quantum topology to understand the shapes of knots and manifolds.
AboutAbout the lab
Shapes that can be seen, yet are hard to understand.
Prof. Nozaki studies the global properties of shapes and spaces.
Specifically, Prof. Nozaki is interested in surfaces, knots, and 3- and 4-dimensional manifolds.
These are objects that can, in an appropriate sense, be made visible as shapes, but uncovering their geometric essence is not easy.
Prof. Nozaki is also interested in interdisciplinary research and is engaged in collaborations related to, for example, computer science and physics.
Key terms
- Knot
- A closed loop made by joining the two ends of a piece of string. It is studied as a mathematical object, for example by asking whether it can be untangled.
- Manifold
- A shape that looks like ordinary flat space when viewed up close at any point.
- Quantum topology
- A field that grew out of ideas from quantum theory in physics, in which quantities are constructed to distinguish knots and manifolds.
ResearchResearch themes
The lab studies the global properties of shapes and spaces. The main objects are surfaces, knots, and 3- and 4-dimensional manifolds, which are investigated using a wide range of tools.
*Illustrative imageSurfaces and Knots
The lab investigates the global properties of surfaces and knots. These are objects that can, in an appropriate sense, be made visible as shapes, but uncovering their geometric essence is not easy.
*Illustrative image3- and 4-Dimensional Manifolds
The lab is also interested in 3- and 4-dimensional manifolds. As with surfaces and knots, the aim is to understand what shape they have as a whole.
*Illustrative imageMethods from Quantum Topology
In practice, the research draws on a wide range of tools, and methods from quantum topology are among those used most often.
MembersFaculty
- Associate ProfessorYuta Nozaki
VoicesStudent voices
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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: “Trefoil knot cgi” Altapedia / CC BY-SA 4.0 (cropped)
- Surfaces and Knots: “Borromean Seifert surface” Accelerometer / CC BY-SA 3.0 (cropped)
- 3- and 4-Dimensional Manifolds: “Order 5 dodecahedral honeycomb” Claudio Rocchini / CC BY-SA 3.0 (cropped)
- Methods from Quantum Topology: “JonesLink” ProfKnots / CC BY-SA 4.0 (cropped)
- Related lab (Algebra (Ouchi) Lab): “CalabiYau5” Andrew J. Hanson / CC BY-SA 3.0 (cropped)
- Related lab (Geometry Lab (Inoguchi)): “Hopf Fibration” Niles Johnson / CC BY 4.0 (cropped)
- Related lab (Analysis Lab (Yuhei Suzuki)): “AnimSun 13” PrzemekMajewski / CC BY-SA 4.0 (cropped)
- Related lab (Algebra (Numata) Lab): “Young tableau for partitions of number 10” Unmismoobjetivo / CC BY 4.0 (cropped)
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