Bannai, Kenichi

写真a

Affiliation

Faculty of Science and Technology, Department of Mathematics ( Yagami )

Position

Professor

Related Websites
Scopus Paper Info  
Paper Count: 20 Citation Count: 101 h-index: 6

Click to view the Scopus page. The data was downloaded from Scopus API in May 24, 2026, via http://api.elsevier.com and http://www.scopus.com .

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Career 【 Display / hide 】

  • 2001.04
    -
    2001.08

    JSPS Post Doctoral Fellow, 特別研究員・PD

  • 2001.09
    -
    2007.03

    Assistant Professor, Graduate School of Mathematics, Nagoya University, 多元数理科学研究科, 助手

  • 2005.04
    -
    2007.03

    JSPS Fellowship Abroad (ENS, Paris), 海外特別研究員（派遣先：パリ高等師範学校）

  • 2007.04
    -
    2008.03

    Nagoya University, Graduate School of Mathematics,, Assistant Professor

  • 2008.04
    -
    2012.03

    University of Keio, Department of Mathematics, Senior Assistant Professor

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Academic Background 【 Display / hide 】

  • 1995.03

    The University of Tokyo, Faculty of Science, Department of Mathematics

    University, Graduated

  • 1997.03

    The University of Tokyo, Graduate School, Division of Mathematical Sciences

    Graduate School, Completed, Master's course

  • 2000.03

    The University of Tokyo, Graduate School, Division of Mathematical Sciences

    Graduate School, Completed, Doctoral course

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Academic Degrees 【 Display / hide 】

  • 博士（数理科学）, 東京大学, Coursework, 2000.03

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Research Areas 【 Display / hide 】

  • Natural Science / Algebra

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Research Keywords 【 Display / hide 】

  • Arithmetic Geometry

  • Number Theory

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Research Themes 【 Display / hide 】

  • 代数多様体の数論幾何的予想の解決に向けた戦略的研究, 

    2009
    -
    2013

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Papers 【 Display / hide 】

  • On Interactions for Large Scale Interacting Systems

    Bannai K., Koriki J., Sasada M., Wachi H., Yamamoto S.

    Journal of Statistical Physics 193 ( 1 )  2026.01

    ISSN  00224715

    　View Summary

    Statistical mechanics explains the properties of macroscopic phenomena based on the movements of microscopic particles such as atoms and molecules. Movements of microscopic particles can be represented by large-scale interacting systems. In this article, we systematically study combinatorial objects which we call interactions, given as symmetric directed graphs representing the possible transitions of states on adjacent sites of large-scale interacting systems. Such interactions underlie various standard stochastic processes such as the exclusion processes, generalized exclusion processes, multi-species exclusion processes, lattice gas with energy processes, and the multi-lane exclusion processes. We introduce the notion of equivalences of interactions using their space of conserved quantities. This allows for the classification of interactions reflecting the expected macroscopic properties. In particular, we prove that when the set of local states consists of two, three or four elements, then the number of equivalence classes of separable interactions are respectively one, two and five. We also define the wedge sums and box products of interactions, which give systematic methods for constructing new interactions from existing ones. Furthermore, we prove that the irreducibly quantified condition for interactions, which implicitly plays an important role in the theory of hydrodynamic limits, is preserved by wedge sums and box products. Our results provide a systematic method to construct and classify interactions, offering abundant examples suitable for considering hydrodynamic limits.

  • On Uniform Functions on Configuration Spaces of Large-Scale Interacting Systems

    Bannai K., Sasada M.

    Alea 23   647 - 662 2026

    ISSN  19800436

    　View Summary

    Stochastic large-scale interacting systems can be studied via the observables, i.e. functions on the underlying configuration space. In our previous article (Bannai et al., 2024), we introduced the concept of uniform functions, which is a suitable class of functions on configuration spaces underlying stochastic systems on infinite graphs. An important consequence is the successful characterization of conserved quantities without introducing the notion of stationary distributions. In this article, we further develop the theory of uniform functions and construct the theory independently of any choice of a base state. Furthermore, we generalize the notion of interactions given in Bannai et al. (2024) to accommodate the case where there are multiple possible state transitions on adjacent vertices. We then prove that if the interaction is exchangeable, then any uniform function which gives a global conserved quantity can be expressed as a sum of local conserved quantities of the interaction. Contrary to our previous article, we do not need to assume that the interaction is irreducibly quantified. This shows that our theory of uniform functions on configuration spaces over infinite graphs with transition structure given by an exchangeable interaction is a natural framework to study general stochastic large-scale interacting systems. While some of the ideas in this article are based on Bannai et al. (2024), the current article is logically independent and self-contained.

  • Topological structures of large-scale interacting systems via uniform functions and forms

    Bannai K., Kametani Y., Sasada M.

    Forum of Mathematics Sigma 12 2024.11

    　View Summary

    In this article, we investigate the topological structure of large-scale interacting systems on infinite graphs, by constructing a suitable cohomology which we call the uniform cohomology. The central idea for the construction is the introduction of a class of functions called uniform functions. Uniform cohomology provides a new perspective for the identification of macroscopic observables from the microscopic system. As a straightforward application of our theory when the underlying graph has a free action of a group, we prove a certain decomposition theorem for shift-invariant closed uniform forms. This result is a uniform version in a very general setting of the decomposition result for shift-invariant closed-forms originally proposed by Varadhan, which has repeatedly played a key role in the proof of the hydrodynamic limits of nongradient large-scale interacting systems. In a subsequent article, we use this result as a key to prove Varadhan's decomposition theorem for a general class of large-scale interacting systems.

  • The Hodge realization of the polylogarithm and the Shintani generating class for totally real fields

    Bannai K., Bekki H., Hagihara K., Ohshita T., Yamada K., Yamamoto S.

    Advances in Mathematics 448 2024.06

    ISSN  00018708

    　View Summary

    In this article, we construct the Hodge realization of the polylogarithm class in the equivariant Deligne–Beilinson cohomology of a certain algebraic torus associated to a totally real field. We then prove that the de Rham realization of this polylogarithm gives the Shintani generating class, a cohomology class generating the values of the Lerch zeta functions of the totally real field at nonpositive integers. Inspired by this result, we give a conjecture concerning the specialization of this polylogarithm class at torsion points, and discuss its relation to the Beilinson conjecture for Hecke characters of totally real fields.

  • CANONICAL EQUIVARIANT COHOMOLOGY CLASSES GENERATING ZETA VALUES OF TOTALLY REAL FIELDS

    Bannai K., Hagihara K., Yamada K., Yamamoto S.

    Transactions of the American Mathematical Society Series B 10   613 - 635 2023

    　View Summary

    It is known that the special values at nonpositive integers of a Dirichlet L-function may be expressed using the generalized Bernoulli numbers, which are defined by a generating function. The purpose of this article is to consider the generalization of this classical result to the case of Hecke L- functions of totally real fields. Hecke L-functions may be expressed canonically as a finite sum of zeta functions of Lerch type. By combining the non-canonical multivariable generating functions constructed by Shintani [J. Fac. Sci. Univ. Tokyo Sect. IA Math. 23 (1976), pp. 393—417], we newly construct a canonical class, which we call the Shintani generating class, in the equivariant cohomology of an algebraic torus associated to the totally real field. Our main result states that the specializations at torsion points of the derivatives of the Shin- tani generating class give values at nonpositive integers of the zeta functions of Lerch type. This result gives the insight that the correct framework in the higher dimensional case is to consider higher equivariant cohomology classes instead of functions.References

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Papers, etc., Registered in KOARA 【 Display / hide 】

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Presentations 【 Display / hide 】

  • Syntomic realization of the polylogarithm for the algebraic torus associated to a totally real field

    Kenichi Bannai

    [International presentation]  Motives, L-values and Eisenstein series (Regensburg University) , 

    2025.09
    , 

    Oral presentation (invited, special)

    　View Summary

    The Beilinson conjecture for algebraic varieties and more general motives defined over algebraic number fields is a conjecture relating the non-critical values of Hasse-Weil L-functions to regulator of certain elements in motivic cohomology. For the case of the Dirichlet L-function for the rational number field Q, the special value is related to the regulator of the cyclotomic element -- which may be constructed as the specialization to torsion points of the motivic polylogarithm in this case. In order to prospect p-adic analogues of such results in the case of totally real fields, we consider the syntomic realization of the polylogarithm for the algebraic torus associated to a totally real field, and its relation to special values of p-adic L-functions associated to Hecke characters of the totally real field. This is a work in process, and includes results of work with H. Bekki, K. Hagihara, T. Oshita, K. Yamada, and S. Yamamoto.

  • On the Hodge Periods of Large-Scale Interacting Systems and the Diffusion Matrices of Hydrodynamic Limits

    Kenichi Bannai

    [Domestic presentation]  RIMS Workshop Algebraic Number Theory and Related Topics 2024, 

    2025.01
    -
    2025.06
    , 

    Oral presentation (general)

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    Joint work with Makiko Sasada. Hydrodynamic limit is a rigorous method to derive macroscopic partial differential equations as limits from microscopic stochastic large-scale interacting systems. The macroscopic diffusion equations that appear as limits are described via the “diffusion matrices”, and determining these matrices is the first crucial step in proving the hydrodynamic limit. In this talk, we will construct discrete harmonic theory for configuration spaces of microscopic large-scale interacting systems, and we define the Hodge period matrices for these configuration spaces. These period matrices
    are expected to coincide with the diffusion matrices of the hydrodynamic limits. If this expectation is valid, our result provides an interpretation of the diffusion matrices as period matrices of the configuration spaces.

  • Inverse harmonic periods and the diffusion matrices associated to large scale interacting systems

    Kenichi Bannai

    [International presentation]  , The 22nd Symposium Stochastic Analysis on Large Scale Interacting Systems, 

    2024.11
    , 

    Oral presentation (invited, special)

  • On the Shintani Generating Class and the p-adic polylogarithm for totally real fields

    Kenichi Bannai

    [International presentation]  Arithmetic Geometry, Algebraic Geometry and Analytic Geometry -- celebrating Kazuhiro Fujiwara's 60th birthday, 

    2024.07
    , 

    Oral presentation (invited, special)

  • On the Algebraic Torus associated to Totally Real Fields and the Shintani Generating Class

    Kenichi Bannai

    [International presentation]  Vista in Number Theory, 

    2024.06

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Research Projects of Competitive Funds, etc. 【 Display / hide 】

  • 総実代数体に付随する同変ポリログのp進実現と特殊化予想

    2026.04
    -
    2030.03

    Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), No Setting

  • Construction of a universal theory of hydrodynamic limits by developing a new geometry on infinite product spaces

    2024.06
    -
    2027.03

    Grants-in-Aid for Scientific Research, Grant-in-Aid for Challenging Research (Exploratory), No Setting

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    流体力学極限は、膨大な自由度を持ち確率的に振る舞う相互作用粒子系から、時空間変数に関する適切なスケール極限を用いて、その保存量が従う決定論的な偏微分方程式を導出する手法である。非平衡統計力学を基礎付ける方法として長年盛んに研究され続け、個々のモデルに対する定理の積み重ねとして発展してきたが、既存の流体力学極限の証明は、個々のモデルの詳細に依存しており、物理的に期待されるようなロバストで普遍的な理論には程遠い。本研究は、非平衡統計力学を基礎づける重要な手法である流体力学極限の普遍的理論体系の構築を、無限直積空間上の新しい幾何学の創出によって、実現することを目指すものである。

  • Strategic research to construct motivic units using new symmetry

    2018.06
    -
    2023.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, Bannai Kenichi, Grant-in-Aid for Scientific Research (S), Principal investigator

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    Our aim was to prospect the construction of motivic units applicable to the proof of conjectures in arithmetic geometry via a motivic object called the polylogarithm. As a concrete objective, we studied the polyogarithm on an algebraic torus associated to a totally real field with equivariant action of the unit group. We discovered the Shintani generating class which universally generates the special balues of the Hecke L-functions of the totally real field. Using a conjectural structure called a plectic structure, we formulate a precise conjecture concerning the equivariant polylogarithm and its relation to the Beilinson conjecture for the Hecke L-function of totally real fields.

  • Strategic Reseach using Eisensterin classes to prove Conjectures in Arithmetic Geometry

    2014.04
    -
    2019.03

    MEXT,JSPS, Grant-in-Aid for Scientific Research, Bannai Kenichi, TAKAI Yuuki, OTA Kazuto, ONO Masataka, KIRAL Erin Mehmet, Grant-in-Aid for Scientific Research (A) , Principal investigator

    　View Summary

    Our original goal was to study the polylogarithm in the case of totally real fields. Our original goal was to study the polylogarithm via the Eisenstein class, but in course of our research, we realized the importance of a certain algebraic torus associated to a totally real field, and using the ideas from plectic structures proposed by Nekovar and Scholl, we succeeded in proving that the Shintani generating function which generates special values of Shintani zeta functions, defines a canonical class on the algebraic torus.

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Courses Taught 【 Display / hide 】

  • TOPICS IN MATHEMATICAL STRUCTURE

    2026

  • GRADUATE RESEARCH ON INFORMATICS, MANAGEMENT, AND HUMAN SCIENCES A1

    2026

  • DOCTORAL RESEARCH ON MATHEMATICAL AND PHYSICAL SCIENCES

    2026

  • TOPICS IN INTEGRATED MATHEMATICAL SCIENCES 1

    2026

  • MATHEMATICAL SCIENCES PRACTICAL RESEARCH ACTIVITY A

    2026

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