[3/13] The 3rd “AIMR Seminar”



Prof. Ryoko Tomiyasu (Institute of Mathematics for Industry, Kyushu University)


Applications of lattice-basis reduction theory to crystal structure analysis


March 13 (Wed), 2024, 16:00–17:00 on Japan Time


Seminar Room, 2nd floor, AIMR Main Building


This talk concerns the mathematics used for the powder ab-initio indexing software CONOGRAPH we released 10 years ago, which improves the success rate by 20-40% compared to the classical software ITO/TREOR/DICVOL in computation time similar to them. To date, CONOGRAPH's ideas have been applied to ab-initio indexing of electron backscattered diffraction and transmission electron microscopy (TEM) images.

However, it is not widely recognized, even among software users, how rigorous mathematics was utilized for the improvement. In particular, the lattice-basis reduction theory was useful for developing new and efficient methods to solve the following subproblems.

  • (a) ab-initio indexing algorithms using a graph structure called Conway's topograph,
  • (b) error-stable Bravais lattice determination,
  • (c) unit-cell identification to avoid multiple outputs of very close unit-cells represented by the Niggli-reduced parameters.

In crystallography, the Niggli-Eisenstein reduction has been used to uniquely parametrize crystal lattices. As its derivation, (c) has been discussed mainly outside of mathematics because of its cross-disciplinary nature (algebra, geometry, and statistics).

In more recent years, for the purpose of materials design, the use of rigorous mathematics is discussed to obtain efficient methods for identification and parametrization (so called, moduli space in mathematics) of crystal structures and lattices. I will explain how the lattice-basis reduction (such as Minkowski, Selling, Voronoi, Venkov, and Ryskov C-type etc.) can be used for all of the mentioned problems.

AIMR Seminars and Tea Time

We hold AIMR Seminars and Friday Tea Time as part of the initiative to promote fusion research.

Seminars are presented by AIMR researchers and visiting scientists who provide a wide range of hot topics from materials science to mathematics. The aims of the AIMR Seminar are to build up mutual understanding, communication, and discussions of each other’s research fields.

Weekly held Friday Tea Time is where AIMR researchers and staff members can relax and talk freely while drinking coffee. Expectations of stimulating conversation may arise among the researchers and leading to new research.

From 2024, active fusion research through synergistic effects from AIMR Seminars and Friday Tea Time will be promoted.

Past AIMR Seminar
2nd Jan. 26, 2024 Prof. Michael I. Ojovan (Imperial College London, U.K.)
1st Jan. 12, 2024 Dr. William Chuck Witt (University of Cambridge, U.K.)
About Tea Time Talk

As part of an event during Friday Tea Time, AIMR has been hosting lectures by famed researchers and the archives up to 2023 are listed below:

43rd July 21, 2023 Prof. Feral Temelli (University of Alberta, Canada)
42nd June 30, 2023 Dr. Douglas Brumley (The University of Melbourne, Australia)
41st Mar. 28, 2023 Prof. Motomu Tanaka (Physical Chemistry of Biosystems, Institute of Physical Chemistry, Heidelberg University, Germany)
40th Nov. 10, 2022 Prof. Masahiro Yoshimura (National Cheng Kung University, Taiwan)
39th June 17, 2022 Prof. Rana Mohtadi (Toyota Research Institute of North America)
38th June 17, 2022 Prof. Michael Hirscher (Max-Planck-Institute for Intelligent Systems, Germany)
37th June 3, 2022 Prof. Reiko Oda (French National Centre for Scientific Research)
36th May 28, 2021 Prof. Magda Titirici (Imperial College London, U.K.)
35th Mar. 26, 2021 Prof. Yaroslav Blanter (Kavli Institute of Nanoscience, Delft University of Technology)
34th Oct. 23, 2020 Dr. Kazuhito Tsukagoshi (PI:WPI-MANA, NIMS & AIMR)
33rd July 17, 2020 Prof. Kaoru Tamada (IMCE, Kyushu University & AIMR)
32nd Jan. 17, 2020 Prof. Miho Yamauchi (I2CNER / Kyushu University & AIMR)
31st Jan. 17, 2020 Prof. Mickaël Lallart (INSA Lyon, Université de Lyon)
30th Oct. 25, 2019 Assoc. Prof. Frédéric Gillot (Department of Solid Mechanics, Mechanical Eng. and Civil Eng., École Centrale de Lyon)
29th July 12, 2019 Prof. Qian Niu (Department of Physics, The University of Texas at Austin)
28th May 17, 2019 Prof. Damien Fabrègue (INSA Lyon, France / ELyT MaX Lab at Tohoku University)
27th Dec. 14, 2018 Prof. Yukitoshi Motome (Department of Applied Physics, The University of Tokyo, Japan)
26th July 13, 2018 Dr. Shimpei Ono (Central Research Institute of Electric Power Industry, Japan)
25th May 11, 2018 Dr. Pierre-Antoine Geslin (Mateis lab, INSA Lyon/CNRS / ELyTMaX Lab at Tohoku University / Institute for Materials Research, Tohoku University)
24th Apr. 27, 2018 Prof. Masaru Tsukada (AIMR, Tohoku University)
23rd Dec. 8, 2017 Prof. Jean-Yves Cavaillé (INSA Lyon, France / ELyT MaX Lab at Tohoku University)
22nd July 28, 2017 Prof. Nicolas Mary (INSA Lyon, France / ELyT MaX Lab at Tohoku University)
21st July 21, 2017 Prof. Gael Sebald (INSA Lyon, France / ELyT MaX at Tohoku University)
20th July 7, 2017 Prof. Arun Bansil (Northeastern University)
19th June 30, 2017 Dr. Takeshi Nakanishi (AIST-Tohoku U Mathematics for Advanced Materials Open Innovation Laboratory (MathAM-OIL))
18th June 23, 2017 Prof. Denis Arčon (Jožef Stefan Institute, Slovenia)
17th Apr. 28, 2017 Prof. Ayumi Hirano (AIMR, Tohoku University)
16th Nov. 29, 2016 Dr. David Guy Austing (National Research Council Canada, Canada)
15th Sept. 30, 2016 Prof. C. Suryanarayana (University of Central Florida, U.S.A.)
14th June 17, 2016 Prof. Tomoteru Fukumura (AIMR, Tohoku University)
13th May 13, 2016 Prof. Jean-Yves Cavaillé (ELyT MaX (Joint Lab at Tohoku University), University of Lyon, France)
12th June 26, 2015 Dr. B. Muralidharan (Indian Institute of Technology Bombay, India)
11th June 27, 2014 Prof. Michael B. Santos (The University of Oklahoma, U.S.A.)
10th Nov. 19, 2013 Dr. Pawel Hawrylak (National Research Council Canada, Canada)
9th Oct. 1, 2013 Dr. Yuan T. Lee (Nobel laureate in Chemistry, Academia Sinica of Taiwan)
8th June 28, 2013 Dr. Bjorn Mysen (Geophysical Laboratory, Carnegie Institution for Science, U.S.A.)
7th Apr. 12, 2013 Prof. Yiming Li (National Chiao Tung University, Taiwan)
6th Jan. 18, 2013 Prof. Tomasz Dietl (Polish Academy of Sciences, Poland)
5th Aug. 31, 2012 Prof. John H. Perepezko (University of Wisconsin-Madison, U.S.A.)
4th Aug. 17,2012 Prof. Alain Reza Yavari (Grenoble Institute of Technology, France)
3rd Aug. 10, 2012 Prof. Alan Lindsay Greer (University of Cambridge, U.K.)
2nd July 6, 2012 Prof. Winfried Teizer (Texas A&M University, U.S.A.)
1st May 25, 2012 Prof. Thomas P. Russell (The University of Massachusetts Amherst, U.S.A.)


Kazuto Akagi
Deputy Director, Research Support Division, AIMR

E-mail: kazuto.akagi.b5@tohoku.ac.jp