LAB LOGA page on LabLog, a review site (not the lab's official page)
Applied Algebra and Mathematical Crystallography Lab
Machine-translated · View original
The lab handles lattices and point configurations mathematically and also works on crystal analysis.
AboutAbout the lab
Developing algorithms for discrete structures.
Prof. Tomiyasu's lab develops algorithms and applications for discrete structures such as lattices, integer rings, and point configurations in Euclidean space and on manifolds.
Its main tools are the theories of geometry of numbers, algebraic number theory, discrete mathematics, and convex optimization, together with analytic methods related to the diffraction theory of crystals.
In addition to activities in mathematical crystallography, including interdisciplinary collaboration, the lab also addresses problems with concrete applications in numerical analysis and in materials science dealing with atomic structures.
The lab also conducts joint research in scientific fields as a place to find new problems in mathematics.
Key terms
- Lattice
- A set of points arranged regularly in space. It is the object dealt with in analyzing crystal lattices
- Mathematical crystallography
- A field that treats problems of crystallography, the study of crystal structure, using mathematical methods
- Semidefinite programming relaxation
- A method for finding the globally best solution of an optimization problem that can be expressed with quadratic polynomials. It is a type of convex optimization
NewsLab news
A paper generalizing the golden angle method was published in Constructive Approximation
A paper explaining lattice basis reduction theory was published in Acta Crystallographica Section A
An explanatory article on indexing using topographs was published in the Journal of the Crystallographic Society of Japan
ResearchResearch themes
The lab develops algorithms using theories of geometry of numbers and algebra, targeting discrete structures such as lattices and point configurations. It also conducts research applying mathematics to materials science problems, such as handling data with observation error and analyzing crystal structures.
*Illustrative imageGenerating Packings on Surfaces and Manifolds
Recent research has extended the golden angle method, known since the 18th century, to general surfaces and general dimensions. The resulting theory has interdisciplinary applications and is also relevant across problems in algebra, geometry, and analysis.
*Illustrative imageAlgebraic Computation and Fourier Analysis with Noise
Because algebraic computation deals with exact values, data containing noise requires new theories and algorithms. The lab addresses determining lattice symmetry in the presence of noise, determining lattices from diffraction data, and estimating truncation error in Fourier transforms of finite data.
*Illustrative imageMathematics of Crystal and Magnetic Structure Analysis
The lab uses semidefinite programming relaxation, a convex optimization technique, to obtain globally optimal solutions in crystal and magnetic structure analysis. In joint research with experimental researchers, it has shown that this method can provide guarantees in determining magnetic moments, atomic occupancies, and atomic species.
MembersFaculty
- ProfessorRyoko Tomiyasu
VoicesStudent voices
Ratings and reviews reflect the experiences of individual current or former students, not the lab's official views. Whether a lab has reviews, or how many, says nothing about the lab itself.
Students who take part in an interview may receive a thank-you gift worth ¥1,000, regardless of what they say.
Student ratings (0 students)
--
--
--
--
--
--
Student voices answer questions like these
- What's great about this lab?
- What did you learn after joining?
- What's the vibe, and what is the professor like?
- Who is this lab for?
- Where do graduates go?
Your experience can help younger students choose their lab. Your name won't be shown.
Write a lab reviewAnonymous · Your draft is saved if you stopRelatedLabs similar to Applied Algebra and Mathematical Crystallography Lab
Applied Algebra and Mathematical Crystallography LabInstitute of Mathematics for Industry, Division of Fundamental Theory ResearchApplied algebra, number theory, and mathematical crystallogr…
Topology and Singularity Theory LabInstitute of Mathematics for Industry, Division of Fundamental Theory ResearchTopology, singularity theory, differential topology, and DNA…
Topology and Singularity Theory LabInstitute of Mathematics for Industry, Division of Fundamental Theory ResearchTopology, singularity theory, differential topology, and DNA…
Probability Theory and Random Point Processes LabInstitute of Mathematics for Industry, Division of Fundamental Theory ResearchProbability theory, random point processes, and random topol…The information on this page is compiled by the LabLog team from the lab's public information and interviews. For corrections or removal requests, please contact LabLog, not the lab.
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: “Simple Cubic Lattice (Brillouin zone)” Auro69 at en.wikipedia / Public domain (cropped)
- Generating Packings on Surfaces and Manifolds: “Trasformazione madre” Hasanisawi / CC BY-SA 4.0 (cropped)
- Algebraic Computation and Fourier Analysis with Noise: “Optical diffraction pattern ( laser), (analogous to X-ray crystallography)” Natural Philo / CC BY-SA 3.0 (cropped)
- Mathematics of Crystal and Magnetic Structure Analysis: “Penroseite crystal structure (Furuseth-Kjekshus-Andresen 1969) along a axis” Ra'ike (Wikipedia) / CC0 (cropped)
- Related lab (Applied Algebra and Mathematical Crystallography Lab): “Rendering of quasicrystal structure” LinKayser / CC BY-SA 4.0 (cropped)
- Related lab (Topology and Singularity Theory Lab): “Linkedin maps data visualization” Luc Legay / CC BY-SA 4.0 (cropped)
- Related lab (Topology and Singularity Theory Lab): “Bastard Weaver s Knot diagram-removebg-preview” Zaripov999 / CC BY-SA 4.0 (cropped)
- Related lab (Probability Theory and Random Point Processes Lab): “A boolean model” Tensorproduct / CC BY-SA 4.0 (cropped)
About LabLog
LabLog is a lab review app for students only. Student members at each university interview students in labs and publish what they say. Student voices can only be read by students who sign up with a university email address. Operated by bestiee Inc.
Learn more about LabLog ↗Search engines and AI may reference the basic lab info and rating summaries on this page and the description of LabLog. Student voices are for student members only. Automated collection by programs (scraping, or input to or training of AI) is prohibited under Article 8 of the Terms of Service. If you need data for research or analysis, please contact us.