Updated on 2022/11/28

写真a

 
GUEST, Martin
 
Scopus Paper Info  
Paper Count: 0  Citation Count: 0  h-index: 4

Citation count denotes the number of citations in papers published for a particular year.

Affiliation
Faculty of Science and Engineering, School of Fundamental Science and Engineering
Job title
Professor

Concurrent Post

  • Faculty of Science and Engineering   Graduate School of Fundamental Science and Engineering

Research Institute

  • 2020
    -
    2022

    理工学術院総合研究所   兼任研究員

Education

  •  
     
     

    Oxford University   数学研究科  

  •  
     
     

    Oxford University  

Degree

  • Oxford   D.Phil

Research Experience

  • 2012
    -
     

    Waseda University Faculty of Science and Engineering   Professor

  • 1999
    -
    2012

    - Professor,Tokyo Metropolitan University

  • 1999
    -
     

    Tokyo Metropolitan University

  • 1997
    -
    1999

    Tokyo Metropolitan University

  • 1997
    -
    1999

    Associate Professor, Tokyo Metropolitan University

Professional Memberships

  •  
     
     

    Mathematical Society of London

  •  
     
     

    Mathematical Society of Japan

  •  
     
     

    Mathematical Society of London

  •  
     
     

    Mathematical Society of Japan

 

Research Areas

  • Geometry

  • Geometry

Research Interests

  • 量子コホモロジー

  • トポロジー

  • 微分幾何学

  • 可積分系

  • 幾何学

  • Geometry

▼display all

Papers

  • Isomonodromy aspects of the tt* equations of Cecotti and Vafa III. Iwasawa factorization and asymptotics

    Martin Guest, Alexander Its, Chang-Shou Lin

    Commun. Math. Phys.    2019.09  [Refereed]

  • Kostant, Steinberg, and the Stokes matrices of the tt*-Toda equations

    Martin Guest, Nan-Kuo Ho

    Selecta Math.    2019.08  [Refereed]

  • A Lie-theoretic description of the solution space of the tt*-Toda equations

    Martin Guest, Nan-Kuo Ho

    Math. Phys. Anal. Geom.    2017.12  [Refereed]

  • Isomonodromy Aspects of the tt* Equations of Cecotti and Vafa II: Riemann-Hilbert Problem

    Martin A. Guest, Alexander R. Its, Chang-Shou Lin

    COMMUNICATIONS IN MATHEMATICAL PHYSICS   336 ( 1 ) 337 - 380  2015.05  [Refereed]

     View Summary

    In Guest et al. arXiv:1209.2045(part I) we computed the Stokes data for the smooth solutions of the tt*-Toda equations whose existence we had previously established by p.d.e. methods. Here we formulate the existence problem as a Riemann-Hilbert problem, based on this Stokes data, and solve it under certain conditions (Theorem 5.4). In the process, we compute the connection matrix for all smooth solutions, thus completing the computation of the monodromy data (Theorem 5.5). We also give connection formulae relating the asymptotics at zero and infinity of all smooth solutions (Theorem 4.1), clarifying the region of validity of the formulae established earlier by Tracy and Widom. Finally, we resolve some conjectures of Cecotti and Vafa concerning the positivity of S + S (t) (where S is the Stokes matrix) and the unimodularity of the eigenvalues of the monodromy matrix (Theorem 5.6). In particular, we show that "unitarity implies regularity" for the tt*-Toda equations.

    DOI

    Scopus

    8
    Citation
    (Scopus)
  • Isomonodromy Aspects of the tt* Equations of Cecotti and Vafa I. Stokes Data

    Martin A. Guest, Alexander R. Its, Chang-Shou Lin

    INTERNATIONAL MATHEMATICS RESEARCH NOTICES   2015 ( 22 ) 11745 - 11784  2015  [Refereed]

     View Summary

    We describe all smooth solutions of the two-function tt*-Toda equations (a version of the tt* equations or equations for harmonic maps into SLnR/SOn) in terms of (1) asymptotic data, (2) holomorphic data, and (3) monodromy data, and we compute all of this data explicitly. This allows us, in particular, to find all solutions with integral Stokes data. These include solutions associated to non-linear sigma models (quantum cohomology) or Landau-Ginzburg models (unfoldings of singularities), as conjectured by Cecotti and Vafa in the 1990s.

    DOI

    Scopus

    7
    Citation
    (Scopus)
  • Orbifold quantum D-modules associated to weighted projective spaces

    Martin A. Guest, Hironori Sakai

    COMMENTARII MATHEMATICI HELVETICI   89 ( 2 ) 273 - 297  2014  [Refereed]

     View Summary

    We construct in an abstract fashion (without using Gromov-Witten invariants) the orbifold quantum cohomology of weighted projective space, starting from a certain differential operator. We obtain the product, grading, and intersection form by making use of the associated self-adjoint D-module and the Birkhoff factorization procedure. The method extends in principle to the more difficult case of Fano hypersurfaces in weighted projective space, where Gromov-Witten invariants have not yet been computed, and we illustrate this by means of an example originally studied by A. Corti. In contrast to the case of weighted projective space itself or the case of a Fano hypersurface in projective space, a "small cell" of the Birkhoff decomposition plays a role in the calculation.

    DOI

    Scopus

    4
    Citation
    (Scopus)
  • Some tt* structures and their integral Stokes data

    Martin A. Guest, Chang-Shou Lin

    COMMUNICATIONS IN NUMBER THEORY AND PHYSICS   6 ( 4 ) 785 - 803  2013  [Refereed]

     View Summary

    In [16], a description was given of all smooth solutions of the two-function tt*-Toda equations in terms of asymptotic data, holomorphic data and monodromy data. In this supplementary paper, we focus on the holomorphic data and its interpretation in quantum cohomology, and enumerate those solutions with integral Stokes data. This leads to a characterization of quantum D-modules for certain complete intersections of Fano type in weighted projective spaces.

  • Nonlinear PDE aspects of the tt* equations of Cecotti and Vafa

    Guest Martin, Lin Chang-Shou

    Journal für die reine und angewandte Mathematik    2012.07  [Refereed]

  • Introduction to homological geometry Ⅰ,Ⅱ

    Guest Martin

    AMS/IP Stud. Adv. Math   36   83-121 - 123-150  2006  [Refereed]

  • Gromov-Witten invariants of flag manifolds, via D-modules

    A Amarzaya, MA Guest

    JOURNAL OF THE LONDON MATHEMATICAL SOCIETY-SECOND SERIES   72   121 - 136  2005.08  [Refereed]

    DOI

    Scopus

    7
    Citation
    (Scopus)
  • Quantum cohomology via D-modules

    MA Guest

    TOPOLOGY   44 ( 2 ) 263 - 281  2005.03  [Refereed]

     View Summary

    We propose a new point of view on quantum cohomology, motivated by the work of Givental and Dubrovin, but closer to differential geometry than the existing approaches. The central object is a D-module which "quantizes" a commutative algebra associated to the (uncompactified) space of rational curves. Under appropriate conditions, we show that the associated flat connection may be gauged to the flat connection underlying quantum cohomology. This method clarifies the role of the Birkhoff factorization in the "mirror transformation", and it gives a new algorithm (requiring construction of a Groebner basis and solution of a system of o.d.e.) for computation of the quantum product. (C) 2004 Elsevier Ltd. All rights reserved.

    DOI

    Scopus

    20
    Citation
    (Scopus)
  • An Update on harmonic maps of finite uniton number via the zero curvature equations, Contemporary Mathematics 309

    American Mathematical Society     85 - 113  2002  [Refereed]

  • Morse Theory in the 1990's

    Guest Martin

    Oxford University Press     146 - 207  2002  [Refereed]  [Invited]

  • Quantum cohomology and the perodic Toda lattice, Commun.

    Guest Martin, Otofuji Takashi

    Comm. Math.Phys.   217   475 - 487  2000  [Refereed]

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Books and Other Publications

  • From quantum cohomology to integrable systems

    Guest Martin(305)

    Oxford University Press  2008

  • Harmonic Maps, Loop Groups, and Integrable Systems

    Martin Guest( Part: Sole author)

    Cambridge University Press  1997

Misc

  • Integrable systems,Topology,and Physics

    Martin Guest, Reiko Miyaoka, Yoshihiro Ohnita

    Contemp. Math 309, Amer.Math Soc    2002

Research Projects

  • 可積分系の幾何学と可視化および量子場の理論と脳神経科学への応用

    文部科学省  科学研究費補助金(挑戦的萌芽研究)

    Project Year :

    2010
    -
    2011
     

    MartinGuest

  • 可積分系を用いた微分幾何学と量子コホモロジーの新しい関係の構築

    文部科学省  科学研究費補助金(基盤研究(A))

    Project Year :

    2009
    -
    2011
     

    MartinGuest

  • Research on quantum cohomology, Frobenius manifolds, and harmonic maps related to integrable systems

    Ministry of Education, Culture, Sports, Science and Technology  Grants-in-Aid for Scientific Research(基盤研究(A))

    Project Year :

    2006
    -
    2008
     

    Guest MARTIN, 大仁田義裕, 宮岡礼子, 乙藤隆史, 前田吉昭, 徳永浩雄, 中村憲, 小林正典, V. SERGEI, 赤穂まなぶ, 前田吉昭, 宮岡礼子, 河野俊丈, 大仁田義裕, 寺尾宏明, 菅野浩明, 乙藤隆史, 小林真平, 酒井高司

  • Geometry and topology of integrable systems, with computer-aided experimentation and visualization

    Ministry of Education, Culture, Sports, Science and Technology  Grants-in-Aid for Scientific Research(基盤研究(A))

    Project Year :

    2002
    -
    2005
     

    Martin GUEST, WayneRossman, 宮岡礼子, 大仁田義裕, 濱田龍義, 乙藤隆史

     View Summary

    Research problems in geometry and topology were investigated using methods from the theory of integrable systems. These included research on the classification of constant mean curvature (CMC) surfaces, isoparametric manifolds, Lagrangian submanifolds, harmonic maps, and quantum cohomology. The principal investigator obtained results on the D-module structure of quantum cohomology, and began a systematic study of relations between quantum cohomology and integrable systems.Computer experiments played an important role in this project. MAPLE was used for computations with differential operato...

  • Applications of integrable systems in geometry and topology

    Ministry of Education, Culture, Sports, Science and Technology  Grants-in-Aid for Scientific Research(基盤研究(C))

    Project Year :

    2000
    -
    2001
     

    Martin GUEST, 神島芳宣, 岡睦雄, 大仁田義裕, 井ノ口順一, 宇田川誠一

     View Summary

    Results were obtained on the geometry and topology of harmonic maps and spaces of harmonic maps, especially in the case where the domain is a Riemann surface and the target space is a compact Lie group or symmetric space. Guest used a generalization of the Weierstrass representation for minimal surfaces to study harmonic maps from the two-dimensional sphere (or, more generally, harmonic maps of finite uniton number, from any Riemann surface) to the unitary group. Earlier results of Uhlenbeck, Segal, Dorfmeister-Pedit-Wu, Burstall-Guest were developed into an effective tool for describing su...

  • Geometry

  • Topology

  • Integrable System

  • Geometry

  • Topology

  • Integrable System

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Specific Research

  • 微分幾何と可積分系理論の境界領域における研究の深化と展開

    2013  

     View Summary

    Research was carried out on several sub-projects related to differential geometry and integrable systems. This involved researchers in Japan as well as researchers in foreign countries, especially Germany and Taiwan.Guest made two visits to Mannheim University (Germany) in order to work with Claus Hertling on the tt* equations. Progress was made on describing the moduli space of solutions in the simplest nontrivial case, namely the 3rd Painleve equation, and a joint article is in preparation. As part of the second visit, Guest spent 2 days at the Technical University of Berlin in order to collaborate with Alexander Its, as part of an ongoing project on the Riemann-Hilbert approach to the tt* equations.A workshop on "Isomonodromic deformations and related topics" was held at Waseda University on 22-23 November 2013. The speakers and titles were Shinobu Hosono (Tokyo University) "Differential rings over the moduli spaces of Calabi-Yau manifolds II"; Martin Guest (Waseda University) "On the Riemann-Hilbert problem for the tt*-Toda equations"; Masa-Hiko Saito (Kobe University) "Lagrangian fibrations in duality on moduli spaces of rank 2 logarithmic connections over the projective line"; Daisuke Yamakawa (Tokyo Institute of Technology) "Fourier-Laplace transform and isomonodromic deformations"; Kazunori Miyazaki (Kobe University) "On compactifications of moduli of unramified irregular singular connections and Okamoto-Painleve pairs"; Makoto Miura (Tokyo University) "Hibi toric varieties and mirror symmetry". The workshop was attended by approximately 20 people. Web page: http://www.f.waseda.jp/martin/conf/2013isomonodromy.htmlAn informal workshop was held at Waseda University on 2 August 2013, with talks by M. Guest, H. Iritani (Kyoto University), A. Strangeway (Imperial College, London). Guest attended and gave an invited talk at the 11th Pacific Rim Geometry Conference, held at Fudan University, Shanghai, on 10-13 December 2013. Cooperation with researchers in Taiwan is a significant aspect of this project, and Ting-Jung Kuo (National Taiwan University) and Shu-Cheng-Chang (National Taiwan University) visited Waseda University for the period 2-9 November 2013. They gave informal talks at Waseda, and seminar talks at Tokyo Metropolitan University on 8 November 2013 organised by Takashi Sakai (Tokyo Metropolitan University). Research and secretarial assistance in connection with this project and proposals for Kakenhi applications was also supported by this project.

  • Description of solutions of the tt*equations, from the viewpoint of symplectic geometry

    2013  

     View Summary

    The main activity supported by this grant was research collaboration with Prof. Nan-Kuo Ho (National Tsing Hua University, Taiwan) on the topic stated in the title of the project. We studied a certain space of solutions of the tt* equations, originating in previous joint research of M. Guest, A. Its, and C.-S. Lin. We understood how this space can be regarded as a subspace of a moduli space of flat bundles or Higgs bundles. This gives a link with the Hitchin-Kobayashi correspondence, which is an important and active topic of current research spanning the boundary of geometry and mathematical physics. In particular we used the framework of P. Boalch, "Stokes matrices, Poisson Lie groups and Frobenius manifolds" Invent. Math. 146 (2001) 479–506. Further work in this direction is in progress and a joint article is in preparation.Prof. Nan-Kuo Ho visited Waseda University for the period 12-16 February 2014. A workshop "Symplectic geometry of moduli spaces of connections" was held on 14 February 2014 at Waseda University. The speakers and titles were: Tosiaki Kori (Waseda University) "A canonical pre-symplectic structure on the space of connections over a four-manifold and an induced pre-symplectic structure on the space of connections over a three-manifold"; Yuji Hirota (Keio University) "On prequantization of Dirac manifolds"; Hokuto Konno (Waseda University) "The moduli space of flat SU(2)-connections on a surface with boundary: an example"; Martin Guest (Waseda University) "Linear and nonlinear convexity, and the relation with singular connections on surfaces"; Nan-Kuo Ho (National Tsing Hua University, Taiwan) "On the moduli space of singular connections: a survey".

Overseas Activities

  • Research on differential geometry

    2018.04
    -
    2019.03

    Germany   T. U. Munich

    Germany   Mannheim U.

 

Syllabus

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