2024/07/22 更新

写真a

ゲスト マーティン
ゲスト マーティン
所属
理工学術院
職名
名誉教授
学位
D.Phil ( Oxford )
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経歴

  • 2012年
    -
     

    早稲田大学 理工学術院 基幹理工学部   教授

  • 1999年
    -
    2012年

    - Professor,Tokyo Metropolitan University

  • 1999年
    -
     

    Tokyo Metropolitan University Professor

  • 1997年
    -
    1999年

    Tokyo Metropolitan University Associate Professor

  • 1997年
    -
    1999年

    Associate Professor, Tokyo Metropolitan University

学歴

  •  
     
     

    Oxford University   数学研究科  

  •  
     
     

    Oxford University  

所属学協会

  •  
     
     

    Mathematical Society of London

  •  
     
     

    Mathematical Society of Japan

  •  
     
     

    Mathematical Society of London

  •  
     
     

    Mathematical Society of Japan

研究分野

  • 幾何学

研究キーワード

  • 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

▼全件表示

 

論文

  • 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年09月  [査読有り]

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

    Martin Guest, Nan-Kuo Ho

    Selecta Math.    2019年08月  [査読有り]

  • A Lie-theoretic Description of the Solution Space of the tt*-Toda Equations

    Martin A. Guest, Nan-Kuo Ho

    Mathematical Physics Analysis and Geometry   20 ( 4 )  2017年12月  [査読有り]

     概要を見る

    We give a Lie-theoretic explanation for the convex polytope which parametrizes the globally smooth solutions of the topological-antitopological fusion equations of Toda type (tt ∗-Toda equations) which were introduced by Cecotti and Vafa. It is known from Guest and Lin (J. Reine Angew. Math. 689, 1–32 2014) Guest et al. (It. Math. Res. Notices 2015, 11745–11784 2015) and Mochizuki (2013, 2014) that these solutions can be parametrized by monodromy data of a certain flat SLn+ 1ℝ-connection. Using Boalch’s Lie-theoretic description of Stokes data, and Steinberg’s description of regular conjugacy classes of a linear algebraic group, we express this monodromy data as a convex subset of a Weyl alcove of SUn+ 1.

    DOI

    Scopus

    4
    被引用数
    (Scopus)
  • 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年05月  [査読有り]

     概要を見る

    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

    14
    被引用数
    (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年  [査読有り]

     概要を見る

    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

    14
    被引用数
    (Scopus)
  • Nonlinear PDE aspects of the tt* equations of cecotti and vafa

    Martin A. Guest, Chang-Shou Lin

    Journal fur die Reine und Angewandte Mathematik   ( 689 ) 1 - 32  2014年  [査読有り]

     概要を見る

    Using nonlinear pde techniques, we construct a new family of globally smooth tt* structures. This includes tt* structures associated to the (orbifold) quantum cohomology of a finite number of complex projective spaces and weighted projective spaces. The existence of such "magical solutions" of the tt* equations, namely smooth solutions characterised by asymptotic boundary conditions, was predicted by Cecotti and Vafa. In our situation, the tt* equations belong to a class of equations which we call the tt-Toda lattice. Solutions of the tt-Toda lattice are harmonic maps which have dual interpretations as Frobenius structures or variations of (semi-infinite) Hodge structures. © De Gruyter 2014.

    DOI

    Scopus

    13
    被引用数
    (Scopus)
  • Orbifold quantum D-modules associated to weighted projective spaces

    Martin A. Guest, Hironori Sakai

    COMMENTARII MATHEMATICI HELVETICI   89 ( 2 ) 273 - 297  2014年  [査読有り]

     概要を見る

    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
    被引用数
    (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年  [査読有り]

     概要を見る

    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.

  • Introduction to homological geometry Ⅰ,Ⅱ

    Guest Martin

    AMS/IP Stud. Adv. Math   36   83-121 - 123-150  2006年  [査読有り]

  • 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年08月  [査読有り]

    DOI

    Scopus

    7
    被引用数
    (Scopus)
  • Quantum cohomology via D-modules

    MA Guest

    TOPOLOGY   44 ( 2 ) 263 - 281  2005年03月  [査読有り]

     概要を見る

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

    American Mathematical Society     85 - 113  2002年  [査読有り]

  • Morse Theory in the 1990's

    Guest Martin

    Oxford University Press     146 - 207  2002年  [査読有り]  [招待有り]

  • Quantum cohomology and the periodic Toda lattice

    Martin A. Guest, Takashi Otofuji

    Communications in Mathematical Physics   217 ( 3 ) 475 - 487  2001年  [査読有り]

     概要を見る

    We describe a relation between the periodic one-dimensional Toda lattice and the quantum cohomology of the periodic flag manifold (an infinite-dimensional Kähler manifold). This generalizes a result of Givental and Kim relating the open Toda lattice and the quantum cohomology of the finite-dimensional flag manifold. We derive a simple and explicit "differential operator formula" for the necessary quantum products, which applies both to the finite-dimensional and to the infinite-dimensional situations.

    DOI

    Scopus

    4
    被引用数
    (Scopus)
  • Harmonic two-spheres in compact symmetric spaces, revisited

    FE Burstall, MA Guest

    MATHEMATISCHE ANNALEN   309 ( 4 ) 541 - 572  1997年12月  [査読有り]

  • Homological stability of oriented configuration spaces

    MA Guest, A Kozlowsky, K Yamaguchi

    JOURNAL OF MATHEMATICS OF KYOTO UNIVERSITY   36 ( 4 ) 809 - 814  1996年12月  [査読有り]

  • THE TOPOLOGY OF THE SPACE OF RATIONAL CURVES ON A TORIC VARIETY

    MA GUEST

    ACTA MATHEMATICA   174 ( 1 ) 119 - 145  1995年  [査読有り]

  • CONFIGURATION-SPACES AND THE SPACE OF RATIONAL CURVES ON A TORIC VARIETY

    MA GUEST

    BULLETIN OF THE AMERICAN MATHEMATICAL SOCIETY   31 ( 2 ) 191 - 196  1994年10月  [査読有り]

     概要を見る

    The space of holomorphic maps from S-2 to a complex algebraic variety X, i.e. the space of parametrized rational curves on X, arises in several areas of geometry. It is a well known problem to determine an integer n(D) such that the inclusion of this space in the corresponding space of continuous maps induces isomorphisms of homotopy groups up to dimension n(D), where D denotes the homotopy class of the maps. The solution to this problem is known for an important but special class of varieties, the generalized flag manifolds: such an integer may be computed, and n(D) --> infinity as D --> infinity. We consider the problem for another class of varieties, namely, toric varieties. For smooth toric varieties and certain singular ones, n(D) may be computed, and n(D) --> infinity as D --> infinity. For other singular toric varieties, however, it turns out that n(D) cannot always be made arbitrarily large by a suitable choice of D.

  • ON THE SPACE OF HOLOMORPHIC MAPS FROM THE RIEMANN SPHERE TO THE QUADRIC CONE

    MA GUEST

    QUARTERLY JOURNAL OF MATHEMATICS   45 ( 177 ) 57 - 75  1994年03月  [査読有り]

  • Group actions and deformations for Harmonie maps

    Martin A. Guest, Yoshihiro Ohnita

    Journal of the Mathematical Society of Japan   45 ( 4 ) 671 - 704  1993年  [査読有り]

    DOI

    Scopus

    40
    被引用数
    (Scopus)
  • ACTIONS OF LOOP-GROUPS ON HARMONIC MAPS

    MJ BERGVELT, MA GUEST

    TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY   326 ( 2 ) 861 - 886  1991年08月  [査読有り]

     概要を見る

    We describe a general framework in which subgroups of the loop group LAMBDA-Gl(n)C act on the space of harmonic maps from S2 to Gl(n)C. This represents a simplification of the action considered by Zakharov-Mikhailov-Shabat [ZM, ZS] in that we take the contour for the Riemann-Hilbert problem to be a union of circles; however, it reduces the basic ingredient to the well-known Birkhoff decomposition of LAMBDA-Gl(n)C, and this facilitates a rigorous treatment. We give various concrete examples of the action, and use these to investigate a suggestion of Uhlenbeck [Uh] that a limiting version of such an action ("completion") gives rise to her fundamental process of "adding a uniton". It turns out that this does not occur, because completion preserves the energy of harmonic maps. However, in the special case of harmonic maps from S2 to complex projective space, we describe a modification of this completion procedure which does indeed reproduce "adding a uniton".

  • THE ENERGY FUNCTION AND HOMOGENEOUS HARMONIC MAPS

    MA GUEST

    PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY   62   77 - 98  1991年01月  [査読有り]

     概要を見る

    For equivariant maps from a compact homogeneous space into an adjoint orbit of a compact Lie group, it is shown that the energy function is the restriction of a quadratic function on the Lie algebra, providing the orbit has the metric induced from the Lie algebra. This is related to similar functions studied by R. Bott [2] and by F. C. Kirwan [7]. One obtains a simple version of the harmonic map equation, and an identity relating the energy and the square of the norm of the moment map. Several applications are given, including an example which illustrates how a change of metric in a flag manifold affects the harmonicity of equivariant maps from the two-sphere to the flag manifold.

  • HOLOMORPHIC-CURVES IN LOOP-GROUPS

    MA GUEST, AN PRESSLEY

    COMMUNICATIONS IN MATHEMATICAL PHYSICS   118 ( 3 ) 511 - 527  1988年  [査読有り]

  • GEOMETRY OF MAPS BETWEEN GENERALIZED FLAG MANIFOLDS

    MA GUEST

    JOURNAL OF DIFFERENTIAL GEOMETRY   25 ( 2 ) 223 - 247  1987年03月  [査読有り]

  • TOPOLOGY OF THE SPACE OF ABSOLUTE MINIMA OF THE ENERGY FUNCTIONAL

    MA GUEST

    AMERICAN JOURNAL OF MATHEMATICS   106 ( 1 ) 21 - 42  1984年  [査読有り]

▼全件表示

書籍等出版物

  • From quantum cohomology to integrable systems

    Guest Martin

    Oxford University Press  2008年

  • Harmonic Maps, Loop Groups, and Integrable Systems

    ゲスト マーティン( 担当: 単著)

    Cambridge University Press  1997年

共同研究・競争的資金等の研究課題

  • 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)

    研究期間:

    2010年
    -
    2011年
     

    MartinGuest

     概要を見る

    ある種の微分方程式は幾何学と可積分系の理論の観点から研究が行われている.そのような微分方程式の解は隣り合った質点の間に非線形の相互作用が働く格子モデルの運動としてシミュレートし,可視化することができる.量子場理論からの重要な例として, CecottiとVafaによって研究が始められたtt*戸田格子がある. Guestは0C.-S. Linとの共同研究で解の存在に関する理論的な結果を得た.この結果はコンピュータによるシミュレーションとも合致する.蔵本格子などその他の例について現在研究中である.シンクロナイゼーションの数学的な解釈などへの更なる応用が期待される.

  • 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))

    研究期間:

    2009年
    -
    2011年
     

    MartinGuest

     概要を見る

    報告者は興味深い非自明な現象を示す,いくつかの重要な例についての進展を得ることが出来た.論文 "Nonlinear PDE aspects of the tt* equations of Cecotti and Vafa" (M. Guest and C.-S. Lin, J. reine angew. Math., 印刷中)では,tt*-戸田方程式の,滑らかな解の族の存在を示した.これは技術的観点に於けるブレイクスルーである,すなわち,既存のループ群論的アプローチが適用できない非コンパクトの場合にも,偏微分方程式論が有用であることを示したことは大きな進展である."Isomonodromy aspects of the tt* equations of Cecotti and Vafa I. Stokes data" (M. Guest, A. Its, and C.-S. Lin, arXiv:1209.2045) に於いてはtt*-戸田方程式の解の大域的な滑らかさを,付随する線形方程式のモノドロミーデータ(ストークスデータ)に関連付けることにより,また別の技術的側面に関するブレイクスルーがあった.より詳しくには,tt*-戸田方程式の全ての滑らかな大域解に対して,そのストークスデータを明示的に計算することが出来た.これらの技術はまた,微分幾何学に於けるその他の問題にも適用可能であると推測される。

  • 可積分系による量子コホモロジー・フロベニウス多様体・調和写像の研究

    文部科学省  科学研究費補助金(基盤研究(A))

    研究期間:

    2006年
    -
    2008年
     

    マーティンゲスト, 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, セルゲイケトフ, 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

     概要を見る

    この研究は可積分系(大きな群対称性を持つ微分方程式系)に関連した現代幾何学の諸問題に関わる研究である。これらの問題は(曲面論を含む)古典的な微分幾何学および量子論と弦理論の幾何学に端を発する。ループ群や無限次元グラスマン多様体の理論をはじめ、無限次元の手法が用いられる。主要な結果の1つとして、D加群による量子コホモロジーの理論への新しいアプローチが挙げられる。このプロジェクトの大きな特徴は、この研究領域を発展させるために、この分野をリードする国内外の研究者達と共同で研究活動を行うことである。

  • 幾何学とトポロジーにおける可積分系の研究と計算機支援による実験と視覚化

    文部科学省  科学研究費補助金(基盤研究(A))

    研究期間:

    2002年
    -
    2005年
     

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

     概要を見る

    本研究課題では可積分系に関連した幾何学とトポロジーの研究を行った。本研究には平均曲率一定曲面、等径部分多様体、Lagrange部分多様体、調和写像、量子コホモロジーの分類に関する研究が含まれていた。研究代表者は量子コホモロジーのD加群構造について研究成果を上げ、量子コホモロジーと可積分系の関係について系統的な研究を始めた。コンピューター実験は本研究プロジェクトにおいて重要な役割を果たした。微分作用素と微分方程式の計算にMapleが使われ、格子モデルの実験に3D-XplorMathが使われ、平均曲率一定曲面の研究にCMCLabが使われた。本研究課題の支援により「幾何学と可視化」に関する国内・国際研究集会を数回開催した。これらの研究集会においてドイツ・アメリカからの研究者によってコンピューター実験と可視化における新しい技術が紹介された。これらのコンピューター技術の推進と普及が本研究課題の主目的であった。リサーチ・アシスタントと数人の研究者が日本語のドキュメントを作成し、研究集会においてソフトウェアの紹介を行った。二つのWebサーバーを立ち上げたことは本研究プロジェクトにおいて重要である。"GEOM"は日本数学会幾何学分科会の活動に利用され、"TMGUS"では首都大学東京における幾何学研究に関する情報を公開している。研究プロジェクトの後半に3回コンピューター・チュートリアルを開催し...

  • 幾何学とトポロジーにおける可積分系の応用

    文部科学省  科学研究費補助金(基盤研究(C))

    研究期間:

    2000年
    -
    2001年
     

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

     概要を見る

    調和写像および調和写像のなす空間の幾何学およびトポロジーに関する結果が得られた。特に、Riemann面からコンパクトLie群もしくは対称空間への調和写像に関する研究において成果を得た。Guestは極小曲面のWeierstrass表現公式の一般化を用いて、2次元球面からユニタリ群への調和写像、さらに一般的に任意のRiemann面からの有限ユニトン数の調和写像について研究を行った。Uhlenbeck, Segal, Dorfmeister-Pedit-Wu, Burstall-Guestによる以前の研究結果により、上述のような調和写像を記述するために有効な手段が発展した。特に、明示的な標準形で表示することにより、上述のような調和写像全体のなす空間を研究するために利用されている。主な応用としては、2次元球面からユニタリ群への調和写像の空間の連結成分の記述が挙げられる。大仁田は、それとは異なり、ゲージ理論に関するHitchinの仕事に基づいた手法によって、調和写像の空間の幾何(特にプレシンプレクティック幾何)を研究するための枠組みを得た。調和写像方程式は可積分系と見なすことができ、上記の研究結果から他の可積分系を解明することができる。次に述べる可積分系の2つの例はこの視点から研究され、前置きとなる結果が得られた。まず第1の例はGuestによって研究された量子微分方程式の理論である。調...

  • Geometry

  • Topology

  • Integrable System

  • Geometry

  • Topology

  • Integrable System

▼全件表示

Misc

  • Integrable systems,Topology,and Physics

    Martin Guest, Reiko Miyaoka, Yoshihiro Ohnita

    Contemp. Math 309, Amer.Math Soc    2002年

    DOI

 

特別研究期間制度(学内資金)

  • Research on differential geometry

    2018年04月
    -
    2019年03月

    Germany   Mannheim U.

    Germany   T. U. Munich

特定課題制度(学内資金)

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

    2013年  

     概要を見る

    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".

  • 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年  

     概要を見る

    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.