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System Information Mathematics I Lab
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The lab studies coding theory, combinatorial designs, and geometry.
AboutAbout the lab
Studying codes, designs, and the geometry of space
The System Information Mathematics I Lab consists of the Harada Lab and the Funano Lab, and studies combinatorial coding theory, combinatorial design theory, Riemannian geometry, and related areas.
The Harada Lab uses combinatorial methods to study error-correcting codes, which convey information efficiently and reliably over communication channels where errors occur, and combinatorial designs, which originated in the design of experiments.
The Funano Lab studies curvature, which describes how a space bends, and the eigenvalues and eigenfunctions of the Laplacian, from the perspectives of Riemannian geometry and spectral geometry.
Key terms
- error-correcting code
- A code used to convey information reliably over a communication channel where errors occur
- combinatorial design
- A combinatorial structure that originated in the design of experiments. The basic problem is to find "good" subsets that approximate the whole well
- Laplacian
- The most fundamental second-order elliptic partial differential operator. It is involved in the structure of solutions to the heat equation and the wave equation
ResearchResearch themes
The System Information Mathematics I Lab conducts research from two sides: combinatorial structures that originated in information and communication and in the design of experiments, and geometry, which investigates the shape of space. The Harada Lab mainly works on codes and designs, and the Funano Lab on curvature and the Laplacian.
*Illustrative imageCombinatorial Coding Theory
The lab studies error-correcting codes using combinatorial methods. It investigates the structure of "good" subspaces of linear spaces over finite fields, with self-dual codes and linear complementary dual (LCD) codes as the main objects.
*Illustrative imageCombinatorial Design Theory
The lab studies combinatorial designs, which originated in the design of experiments. Using combinatorial methods, it works with "good" subsets that approximate the whole well, with symmetric designs and Hadamard matrices as the main objects.
*Illustrative imageComparison Geometry
Imposing a lower bound on curvature amounts to comparing a space with a simpler, better-understood space. The lab investigates the geometric properties of spaces through such comparisons. In recent years, the idea of comparison has been extended to metric spaces.
*Illustrative imageEigenvalues and Eigenfunctions of the Laplacian
To understand the structure of solutions to the heat equation and the wave equation, the lab studies the eigenvalues and eigenfunctions of the Laplacian. These are related to geometric quantities such as curvature and volume, and when treated discretely, they are also related to research on network structure and clustering.
MembersFaculty
The members of the System Information Mathematics I Lab are faculty and master's students.As of 2026
- ProfessorMasaaki Harada
- Associate ProfessorKei Funano
- Assistant ProfessorJunya Takahashi
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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: “Collection of geometry models-CnAM 3824-IMG 6752” Rama / CC BY-SA 3.0 fr (cropped)
- Combinatorial Coding Theory: “QR Code Damaged” QR code for English Wikipedia.svg: brdall. Original uploader was Brdall at en.wikipedia. Later version(s) were uploaded by Sertion, Johndrinkwater, Ke4roh at en.wikipedia. derivative work: Bobmath (talk) / CC0 (cropped)
- Combinatorial Design Theory: “Fano plane (Fano vlak)” Basboschman / CC BY-SA 4.0 (cropped)
- Comparison Geometry: “Hyperbolic orthogonal dodecahedral honeycomb” 作者不詳 / Public domain (cropped)
- Eigenvalues and Eigenfunctions of the Laplacian: “Chladni plate 10” Exhibit made by Estes Objethos Atelier, photo by Rodrigo Tetsuo Argenton / CC BY-SA 4.0 (cropped)
- Related lab (Image Analysis Lab): “Optical Sensor” QueSera4710 / CC BY-SA 3.0 (cropped)
- Related lab (Information Systems Evaluation Lab): “Efficient and Secure Group Messaging Encryption (2020) - page 8” Tyler Weitzman / CC BY-SA 4.0 (cropped)
- Related lab (Higher-Order Visual Information Lab): “Optical Illusion” Ironnail / CC BY-SA 4.0 (cropped)
- Related lab (Intelligent Systems Science Lab): “Data center roof” Rsparks3 / CC0 (cropped)
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