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Honda Lab
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The lab studies, from the standpoint of algebraic analysis, the classification of systems of equations with irregular singularities.
AboutAbout the lab
Exploring irregular singularities in higher-dimensional equations.
Prof. Honda works in algebraic analysis, focusing on the classification problem for holonomic systems (maximally overdetermined systems) with irregular singularities.
Algebraic analysis is a field that combines analysis and algebra to approach a wide range of problems, and it was initiated by Japanese researchers.
Holonomic systems are higher-dimensional systems of equations with properties similar to systems of ordinary differential equations in one variable, and they have influenced many areas of mathematics.
For regular singularities, results based on the Riemann-Hilbert correspondence are known, but for irregular singularities, entirely different phenomena such as the Stokes phenomenon occur.
Key terms
- Ordinary differential equation
- An equation expressing the relationship between a function of a single variable and its derivatives (rates of change)
- Irregular singular point
- A singular point where, as one approaches it, solutions of the equation grow or decay violently, like an exponential function
- Stokes phenomenon
- A phenomenon in which the form of the expression approximating a solution switches depending on the direction of approach
ResearchResearch themes
From the standpoint of algebraic analysis, the lab focuses on the classification problem for holonomic systems (maximally overdetermined systems) with irregular singularities. By studying them in higher dimensions, the research aims to find new discoveries and interesting phenomena.
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MembersFaculty
- ProfessorNaofumi Honda
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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: “Essential singularity” Functor Salad / CC BY-SA 3.0 (cropped)
- Classifying Holonomic Systems with Irregular Singularities: “AiryAi Real Surface” Inductiveload / Public domain (cropped)
- Related lab (Geometry Lab (Kobayashi)): “Chen-Gackstatter-Thayer surfaces” Anders Sandberg / CC BY-SA 3.0 (cropped)
- Related lab (Analysis (Kubo) Lab): “Surface waves” Roger McLassus / CC BY-SA 3.0 (cropped)
- Related lab (Nakano Lab): “Hurricane Isabel from ISS” Image courtesy of Mike Trenchard, Earth Sciences & Image Analysis Laboratory, NASA Johnson Space Center. / Public domain (cropped)
- Related lab (Analysis Lab (Takahiro Hasebe)): “Fig sinc” Sergey69 / CC BY-SA 3.0 (cropped)
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