International Joint Usage /
Research Center

International Center for Collaborative Study in Mathematical Sciences

On November 13, 2018, RIMS was certified as one of the International Joint Usage/Research Centers by the Ministry of Education, Culture, Sports, Science and Technology (MEXT).

List of RIMS Research Projects

2019
  Cluster algebras were original introduced by Fomin and Zelevinsky around 2000 to generalize a class of commutative algebras appearing in Lie theory in view of the Laurent phenomenon. Nowadays they are recognized as a kind of extension of the theory of root systems, and they are actively studied as an underlying algebraic and combinatorial structure ubiquitously appearing in several areas of mathematics.
  In this research project, we will hold an international workshops series "Cluster Algebras 2019" at RIMS in June, 2019, which is the largest comprehensive program on cluster algebras since the semantic program in KIAS, Korea in 2014. We will also hold a mini course on topics in cluster algebras at RIMS in May, 2019 by the visiting professors Bernard Leclerc (Universitè de Caen) and Michael Gekhtman (Notre Dame).
2019
Discrete Optimization and Related Topics
Discrete optimization occurs frequently in our economic and social activities.
The development of discrete optimization in both theory and application has a major impact on our society, since artificial intelligence (AI), machine learning, and big data receive much attention.
In this project research, we aim to promote theoretical research on discrete optimization. The project focus not only on classical research but also on the one related to big data, such as sublinear or constant time optimization algorithm. For example, we plan to have the following three international workshops

1) Hungarian-Japanese Symposium on Discrete Mathematics and Its Applications

2) International Workshop on Innovative Algorithms for Big Data

3) International Workshop on Combinatorial Optimization and Algorithmic Game Theory
  • Japanese-Hungarian Symposium on Discrete Mathematics and Its Applications (RIMS Project Research 2019)

    Location: Sanjo Conference Hall, The University of Tokyo    Period: 2019-05-27--2019-05-30
    Organizer: Kazuhisa Makino(RIMS, Kyoto University)

  • Discrete Structures in Phylogenetic Networks (RIMS Project Research 2019)(closed)

    Location:    Period: 2019-07-14--2019-07-20
    Organizer: Kazuhisa Makino(RIMS, Kyoto University)

  • International Workshop on Innovative Algorithms for Big Data 2019 (RIMS Project Research 2019)

    Location: Rm 420    Period: 2019-10-30--2019-11-01
    Organizer: Kazuhisa Makino(RIMS, Kyoto University)

  • International Workshop on Combinatorial Optimization and Algorithmic Game Theory (RIMS Project Research 2019)

    Location: Rm 420    Period: 2020-01-13--2020-01-14
    Organizer: Kazuhisa Makino(RIMS, Kyoto University)

  • Combinatorial Optimization and Algorithms (RIMS Project Research 2019)(closed)

    Location:    Period: 2020-01-15--2020-01-20
    Organizer: Kazuhisa Makino(RIMS, Kyoto University)

2020

The elucidation of the way in which the additive and multiplicative structure of the integers are intertwined with one another is one of the most important and central themes in number theory.  In August 2012, Shinichi Mochizuki (the proposer and chief organizer of the present RIMS Research Project) released preprints of a series of papers concerning "Inter-universal Teichmüller Theory", a theory that constitutes an important advance with regard to elucidating this intertwining.  Moreover, the proof of the "ABC Conjecture", which follows as a consequence of the theory, attracted worldwide attention.  In the roughly six and a half years since the release of these preprints:

· The number of researchers who have already acquired a thorough understanding of the theory, as well as advanced learners of the theory, has increased slowly, but steadily.

· Quite a number of surveys and related expositions of the theory (7 of which have been made public, while another 2 are currently in preparation) have been written, not only by the author of the theory, but also by researchers who have already acquired a thorough understanding of the theory.

· Although it is difficult to ascertain the precise number, at least on the order of 30 lectures and small-scale workshops on the theory have been conducted all over the world (in Japan, the UK, Russia, the US, China, Germany, and France).

· At least 4 large-scale workshops (of one to two weeks in length) on the theory have been conducted not only within Japan (in Kyoto, March 2015 and July 2016), but also in China (in Beijing, July 2015) and the UK (in Oxford, December 2015).

As a result of these activities, a sort of "inter-universal Teichmüller theory community", consisting of between ten and twenty researchers, is currently in the process of forming. Moreover, as a result of advances in research, such as combinatorial anabelian geometry, based on ideas closely related to the ideas that underlie inter-universal Teichmüller theory, important links between research on inter-universal Teichmüller theory and research concerning the Grothendieck-Teichmüller group and the absolute Galois group of the rational numbers have begun to form.

In light of these developments, the present RIMS Research Project seeks to bring together various researchers not only from the "inter-universal Teichmüller theory community", but also researchers interested in various forms of mathematics related to inter-universal Teichmüller theory, and to provide all such researchers an opportunity to engage in lively discussions concerning the various developments discussed above in an environment in which interaction for periods on the order of months is possible, that is to say, unlike the situation in the case of a single workshop (i.e., which typically only lasts for roughly a week).

2020
Differential Geometry and Integrable Systems -Mathematics of Symmetry, Stability and Moduli-
2021
 As a part of applied mathematical studies, biofluid mechanics has gathered significant attention from various research communities such as physical and material sciences, engineering, biology and medicine. In particular, novel computational and theoretical techniques, mathematical models and methods are all required to understand complex motions in biological phenomena. In this research project, though a series of workshops, tutorial seminars and symposia, we enthusiastically explore newly-born research topics in collaboration with researchers with various research backgrounds to expand the horizons of fluid mechanics and applied mathematics, in addition to deepening the traditional research topics, aiming at cultivating national and international networks of related researchers.
Past RIMS Research Projects
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