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Applied Mathematics Division (Kawamura) Lab
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A lab that mathematically explores what can and cannot be computed.
AboutAbout the lab
What can be computed, and what cannot?
The Theory of Computation Lab (Kawamura Lab) studies the foundational theory of the methods, efficiency, and limits of information processing (the theory of computation).
Whether in computer computation or in human mathematical reasoning, information processing is expressed as an algorithm, a procedure made up of finite operations, and the theory of computation explores what can and cannot be done with it.
The lab approaches this from both sides: designing useful computational methods and investigating their limits.
Centering on the theory of computation, it also takes up topics at the boundary of mathematics and computer science, such as computer mathematics and computer-assisted proofs.
Key terms
- Theory of computation
- A theory that explores what can and cannot be done in information processing, whether by computers or by human reasoning
- Computational complexity theory
- A theory that investigates the difficulty inherent in a problem from the amount of time, memory, and other resources needed to solve it
- Computable analysis
- A field that studies, for computation on continuous objects such as real numbers and functions, whether they can be computed and how much effort is required
NewsLab news
Research group proves the "5/6 conjecture" on round-robin allocation using mathematics and computers
Associate Professor Kawamura receives the Information Processing Society of Japan Yamashita SIG Research Award
ResearchResearch themes
The lab studies the foundational theory of the methods, efficiency, and limits of information processing. It approaches this from both sides, designing useful computational methods and clarifying their limits, and is particularly interested in applying these theories to a wide range of mathematical objects.
*Illustrative imageAlgorithm engineering
The lab designs and analyzes algorithms with good performance and efficiency for problems such as computational geometry, resource allocation, and scheduling, using mathematical engineering methods.
*Illustrative imageClarifying limits (computational complexity theory)
The lab explores how far things can be computed under various conditions, aiming to get at the difficulty inherent in problems and the essential limits of intelligent processing.
*Illustrative imageComputable analysis
Even for continuous objects such as real numbers, and for higher-order computation, computational complexity can be studied by focusing on the content of the processing and operations applied to data.
MembersFaculty
- Associate ProfessorAkitoshi Kawamura
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: “Turing Machine” Porao / Public domain (cropped)
- Algorithm engineering: “Convex hull of a union” Saroad / CC0 (cropped)
- Clarifying limits (computational complexity theory): “The relations between various L-related complexity classes” Cosmia Nebula / CC BY-SA 4.0 (cropped)
- Computable analysis: “Machine de Turing pédagogique” Mdtcreator / CC BY-SA 4.0 (cropped)
- Related lab (Applied Mathematics Lab (Kazuhisa Makino)): “B functies 2var versie02” Bob.v.R / CC BY-SA 4.0 (cropped)
- Related lab (Applied Mathematics Division (Kobayashi) Lab): “Graph-matroid” Didia / CC BY-SA 4.0 (cropped)
- Related lab (Applied Mathematics Lab (Masahito Hasegawa)): “Kleisli Category - morphism composition” AugPi / CC BY-SA 4.0 (cropped)
- Related lab (Isono Lab): “Bernoullishift” Andreas Mandl / CC BY-SA 3.0 (cropped)
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