Research activity information

• Sep. 2004 素粒子論グループ, 2004年度素粒子メダル奨励賞（学会講演賞部門）

• A Hamiltonian formalism for topological recursion

  Hiroyuki Fuji, Masahide Manabe, Yoshiyuki Watabiki

  A bstract We propose a string field Hamiltonian formalism that associates a class of spectral curves and provides their quantization through the Chekhov-Eynard-Orantin topological recursion. As illustrative examples, we present Hamiltonians for the (2, 2 m – 1) minimal discrete and continuum dynamical triangulation (DT) models, the supersymmetric analogue of minimal continuum DT models, the Penner model, and 4D $$ \mathcal{N} $$ = 2 SU (2) gauge theories in the self-dual Ω-background.

  Lead, Springer Science and Business Media LLC, Aug. 2026, Journal of High Energy Physics, 2026(8) (8), English

  [Refereed]

  Scientific journal


• Dynamical triangulations for 2D pure gravity and topological recursion

  Hiroyuki Fuji, Masahide Manabe, Yoshiyuki Watabiki

  A bstract We show that, in two-dimensional Euclidean quantum gravity without matter fields, the Schwinger-Dyson equations derived within the Hamiltonian framework of non-critical string field theory can be reformulated in terms of the Chekhov-Eynard-Orantin topological recursion, and we explicitly compute the associated low-order amplitudes. In particular, we establish this reformulation for two discrete models — the basic type and the strip type — as well as for the continuum limit of dynamical triangulations.

  Springer Science and Business Media LLC, May 2026, Journal of High Energy Physics, 2026(5) (5), English

  [Refereed]

  Scientific journal

  Link to Kobe Univ. Repository (Kernel)


• Some Generalizations of Mirzakhani's Recursion and Masur-Veech Volumes via Topological Recursions

  Hiroyuki Fuji, Masahide Manabe

  SIGMA (Symmetry, Integrability and Geometry: Methods and Application), May 2024, Symmetry, Integrability and Geometry: Methods and Applications, 20, English

  [Refereed]

  Scientific journal


• Witten–Reshetikhin–Turaev Function for a Knot in Seifert Manifolds

  Hiroyuki Fuji, Kohei Iwaki, Hitoshi Murakami, Yuji Terashima

  Springer Science and Business Media LLC, Mar. 2021, Communications in Mathematical Physics, 386(1) (1), 225 - 251, English

  [Refereed]

  Scientific journal


• Reconstructing GKZ via Topological Recursion

  Hiroyuki Fuji, Kohei Iwaki, Masahide Manabe, Ikuo Satake

  Springer Science and Business Media LLC, Oct. 2019, Communications in Mathematical Physics, 371(3) (3), 839 - 920, English

  [Refereed]

  Scientific journal


• Janossy densities for chiral random matrix ensembles and their applications to two-color QCD

  Hiroyuki Fuji, Issaku Kanamori, Shinsuke M. Nishigaki

  Springer Science and Business Media LLC, Aug. 2019, Journal of High Energy Physics, 2019(8) (8), English

  [Refereed]

  Scientific journal


• The boundary length and point spectrum enumeration of partial chord diagrams using cut and join recursion

  Jørgen Ellegaard Andersen, Hiroyuki Fuji, Robert C. Penner, Christian M. Reidys

  We introduce the boundary length and point spectrum, as a joint generalization of the boundary length spectrum and boundary point spectrum in arXiv:1307.0967. We establish by cut-and-join methods that the number of partial chord diagrams filtered by the boundary length and point spectrum satisfies a recursion relation, which combined with an initial condition determines these numbers uniquely. This recursion relation is equivalent to a second order, non-linear, algebraic partial differential equation for the generating function of the numbers of partial chord diagrams filtered by the boundary length and point spectrum.

  Dec. 2016, Travaux Mathematiques, 25, 213 - 232

  [Refereed]


• Partial chord diagrams and matrix models

  Jørgen Ellegaard Andersen, Hiroyuki Fuji, Masahide Manabe, Robert C. Penner, Piotr Sułkowski

  In this article, the enumeration of partial chord diagrams is discussed via matrix model techniques. In addition to the basic data such as the number of backbones and chords, we also consider the Euler characteristic, the backbone spectrum, the boundary point spectrum, and the boundary length spectrum. Furthermore, we consider the boundary length and point spectrum that unifies the last two types of spectra. We introduce matrix models that encode generating functions of partial chord diagrams filtered by each of these spectra. Using these matrix models, we derive partial differential equations - obtained independently by cut-and-join arguments in an earlier work - for the corresponding generating functions.

  Dec. 2016, Travaux Mathematiques, 233 - 283

  [Refereed]


• Enumeration of chord diagrams via topological recursion and quantum curve techniques

  Jørgen Ellegaard Andersen, Hiroyuki Fuji, Masahide Manabe, Robert C. Penner, Piotr Sułkowski

  In this paper we consider the enumeration of orientable and non-orientable chord diagrams. We show that this enumeration is encoded in appropriate expectation values of the $\beta$-deformed Gaussian and RNA matrix models. We evaluate these expectation values by means of the $\beta$-deformed topological recursion, and - independently - using properties of quantum curves. We show that both these methods provide efficient and systematic algorithms for counting of chord diagrams with a given genus, number of backbones and number of chords.

  Dec. 2016, Travaux Mathematiques, 25, 285 - 323, English

  [Refereed]

  Scientific journal


• String-Math 2012

  American Mathematical Society, Sep. 2015, Proceedings of Symposia in Pure Mathematics, English

  [Refereed]


• Super-A-polynomial for knots and BPS states

  Hiroyuki Fuji, Sergei Gukov, Piotr Sułkowski

  Feb. 2013, Nuclear Physics B, 867(2) (2), 506 - 546, English

  [Refereed]

  Scientific journal


• 3d analogs of Argyres-Douglas theories and knot homologies

  Hiroyuki Fuji, Sergei Gukov, Marko Stosic, Piotr Sułkowski

  Sep. 2012, Journal of High Energy Physics, 2013(1) (1), English

  [Refereed]

  Scientific journal


• Localization with a surface operator, irregular conformal blocks and open topological string

  Hidetoshi Awata, Hiroyuki Fuji, Hiroaki Kanno, Masahide Manabe, Yasuhiko Yamada

  Jun. 2012, Advances in Theoretical and Mathematical Physics, 16(3) (3), 725 - 804, English

  [Refereed]

  Scientific journal


• Volume Conjecture: Refined and Categorified

  Hiroyuki Fuji, Sergei Gukov, Piotr Sułkowski

  Mar. 2012, Advances in Theoretical and Mathematical Physics, 16(6) (6), 1669 - 1777, English

  [Refereed]

  Scientific journal


• Causal Dynamical Triangulation with Extended Interactions in 1+1 Dimensions

  Hiroyuki Fuji, Yuki Sato, Yoshiyuki Watabiki

  Aug. 2011, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 704(5) (5), 582 - 589, English

  [Refereed]

  Scientific journal


• Summing Up All Genus Free Energy of ABJM Matrix Model

  Hiroyuki Fuji, Shinji Hirano, Sanefumi Moriyama

  Jun. 2011, Journal of High Energy Physics, 2011(8) (8), English

  [Refereed]

  Scientific journal


• A Note on Computations of D-brane Superpotential

  Hiroyuki Fuji, Shinsaku Nakayama, Masahide Shimizu, Hisao Suzuki

  Nov. 2010, Journal of Physics A: Mathematical and Theoretical, 44(46) (46), English

  [Refereed]

  Scientific journal


• The Volume Conjecture, Perturbative Knot Invariants, and Recursion Relations for Topological Strings

  Robbert Dijkgraaf, Hiroyuki Fuji, Masahide Manabe

  Oct. 2010, Nuclear Physics B, 849(1) (1), 166 - 211, English

  [Refereed]

  Scientific journal


• The Volume Conjecture and Topological Strings

  Robbert Dijkgraaf, Hiroyuki Fuji

  Mar. 2009, Fortschritte der Physik, 57(9) (9), 825 - 856, English

  [Refereed]

  Scientific journal


• A New N=4 Membrane Action via Orbifold

  Hiroyuki Fuji, Seiji Terashima, Masahito Yamazaki

  May 2008, Nuclear Physics B, 810(1-2) (1-2), 354 - 368, English

  [Refereed]

  Scientific journal


• Open String Amplitudes in Various Gauges

  Hiroyuki Fuji, Shinsaku Nakayama, Hisao Suzuki

  Sep. 2006, Journal of High Energy Physics, 2007(1) (1), English

  [Refereed]

  Scientific journal


• Quantum fluctuations of rotating strings in AdS_5 x S^5

  Hiroyuki Fuji, Yuji Satoh

  Apr. 2005, International Journal of Modern Physics A, 21(18) (18), 3673 - 3698, English

  [Refereed]

  Scientific journal


• Gravitational Corrections for Supersymmetric Gauge Theories with Flavors via Matrix Models

  Hiroyuki Fuji, Shun'ya Mizoguchi

  May 2004, Nuclear Physics B, 698(1-2) (1-2), 53 - 91, English

  [Refereed]

  Scientific journal


• Remarks on Phase Transitions in Matrix Models and N=1 Supersymmetric Gauge Theory

  Hiroyuki Fuji, Shun'ya Mizoguchi

  Sep. 2003, Physics Letters, Section B: Nuclear, Elementary Particle and High-Energy Physics, 578(3-4) (3-4), 432 - 442, English

  [Refereed]

  Scientific journal


• Comments on Effective Superpotentials via Matrix Models

  Hiroyuki Fuji, Yutaka Ookouchi

  Oct. 2002, Journal of High Energy Physics, 6(12) (12), 1483 - 1497, English

  [Refereed]

  Scientific journal


• Penrose Limit and String Theories on Various Brane Backgrounds

  Hiroyuki Fuji, Katsushi Ito, Yasuhiro Sekino

  Aug. 2002, Journal of High Energy Physics, 6(11) (11), 95 - 131, English

  [Refereed]

  Scientific journal


• Confining Phase Superpotentials for SO/Sp Gauge Theories via Geometric Transition

  Hiroyuki Fuji, Yutaka Ookouchi

  May 2002, Journal of High Energy Physics, 7(2) (2), 587 - 608, English

  [Refereed]

  Scientific journal


• OPEN STRING ON SYMMETRIC PRODUCT

  HIROYUKI FUJI, YUTAKA MATSUO

  We discuss some basic properties of the open string on the symmetric product which is supposed to describe the open string field theory in discrete light-cone quantization (DLCQ). We first derive the consistent twisted boundary conditions for Annulus/Möbius/Klein Bottle diagrams and give the explicit form of the corresponding amplitude. They have the interpretation as the long open (or closed) string amplitude but the world sheet topology viewed from the short string and from the long string is in general different. Boundary (cross-cap) states of the short string are classified into three categories, the boundary (cross-cap) states of the long string and the "joint" state which connects two strings. The partition function has the typical structure of the string field theory in DLCQ. Tadpole condition is also analyzed and gives a reasonable gauge group SO(2¹³).

  World Scientific Pub Co Pte Lt, Feb. 2001, International Journal of Modern Physics A, 16(04) (04), 557 - 607

  Scientific journal

• On analogues of Mirzakhani's recursions and its generalizations

  藤 博之

  Mar. 2025, OCAMI-Reports, 2024(9) (9), 1 - 43, Japanese

  [Invited]

  Meeting report


• Topology of protein metastructure and $β$-sheet topology

  Jørgen Ellegaard Andersen, Hiroyuki Fuji, Yuki Koyanagi

  We introduce a new, simplified model of proteins, which we call protein metastructure. The metastructure of a protein carries information about its secondary structure and $\beta$-strand conformations. Furthermore, protein metastructure allows us to associate an object called a fatgraph to a protein, and a fatgraph in turn gives rise to a topological surface. It becomes thus possible to study the topological invariants associated to a protein. We discuss the correspondence between protein metastructures and fatgraphs, and how one can compute topological invariants, such as genus and the number of boundary components, from fatgraphs. We then describe an algorithm for generating likely candidate metastructures using the information obtained from topology of protein fatgraphs. This algorithm is further developed to predict $\beta$-sheet topology of proteins, with a possibility to combine it with an existing algorithm. We demonstrate the algorithm on the data from PDB, and improve the performance of and existing algorithm by combining with it.

  29 Nov. 2021


• Witten とトポロジカル場の理論の登場

  藤 博之

  Oct. 2014, 数理科学, 617, 54 - 55, Japanese

  [Invited]

  Introduction commerce magazine


• Superstring Theories and Unification of Knot Homologies

  Fuji Hiroyuki

  The quantum field theory has been playing important roles in the research of the knot invariants since a connection between the Chern-Simons gauge theory and the Jones polynomial was uncovered. In developments for the past decade, the novel class of knot invariants has been found via the concept of "categorification" in mathematics. On the other hand in the string theory, the concept of "D-brane" has been introduced, and we get new physical interpretation for such knot invariants. In recent years, the unification of various categorified knot invariants has been discussed by combining new approaches in physics and mathematics. In this article, we will survey on recent developments in this researc area.

  The Physical Society of Japan, 05 Dec. 2013, Butsuri, 68(12) (12), 801 - 809, Japanese

  [Refereed]


• Colored HOMFLY homology and Super-A-polynomial

  Hiroyuki Fuji

  Jun. 2013, Intelligence of Low Dimensional Topolgy 2013 Proceedings, English

  Introduction international proceedings


• 結び目不変量と量子場の理論

  藤 博之

  Sep. 2012, サマースクール数理物理２０１２講義録, Japanese

  [Invited]

  Lecture materials


• 体積予想とChern-Simons理論

  藤 博之

  Aug. 2012, 素粒子論研究（電子版）, 13(2) (2)


• 体積予想と量子場の理論—特集 数学から物理へ,物理から数学へ

  藤 博之

  東京 : サイエンス社, Jan. 2012, 数理科学, 50(1) (1), 30 - 35, Japanese


• Gravitational Corrections to Supersymmetric Gauge Theory with Matter in Fundamental Respresentation via Matrix Model

  Hiroyuki Fuji, Shun'ya Mizoguchi

  Jun. 2004, Proceedings, 12th International Conference, SUSY 2004, 887 - 890, English

  Introduction international proceedings


• Comments on Effective Superpotentials via Matrix Models(Developments of Superstring Theory,YITP Workshop)

  Fuji Hiroyuki, Ookouchi Yutaka

  Soryushiron Kenkyu Editorial Office, 2003, Soryushiron Kenkyu Electronics, 107(6) (6), F61 - F68, English

  Introduction international proceedings


• 14pRD-6 confining phase superpotentials via Geometric trasstion

  藤 博之

  The Physical Society of Japan, 2002, Meeting Abstracts of the Physical Society of Japan, 57.2.1, 8, Japanese


• Open Superstring on Symmetric Product

  Hiroyuki Fuji

  The string theory on symmetric product describes the second-quantized string theory. The development for the bosonic open string was discussed in the previous work. In this paper, we consider the open superstring theory on the symmetric product and examine the nature of the second quantization. The fermionic partition functions are obtained from the consistent fermionic extension of the twisted boundary conditions for the non-abelian orbifold, and they can be interpreted in terms of the long string language naturally. In the closed string sector, the boundary/cross-cap states are also constructed. These boundary states are classified into three types in terms of the long string language, and explain the change of the topology of the world-sheet. To obtain the anomaly-free theory, the dilaton tadpole must be cancelled. This condition gives SO(32) Chan-Paton group as ordinary superstring theory.

  13 Dec. 2001


• Open String on Symmetric Product

  藤 博之

  以上の結果をまとめると、対称積空間S^NR^<24>上のopen string理論のspectrumを知る為に分配関数の生成関数を計算した結果、指数の肩に一体系の分配関数が乗った形となった。これは場の理論において真空のFeynman diagramを足し上げると指数の肩に一粒子既約なdiagramが乗った形で表されることに対応する。よって対称積空間上のopen string理論のspectrumはunoriented open/closed stringの多体系と等価であると結論づけられる。すなわち、"Open string on S^NR^<24>←→SO(2^<13>)open/closed string field theory"という対応が明らかになった。今後の研究の主な課題は以下のとおりである。まず相互作用の問題がある。この定式化における相互作用はopen stringの端点を入れ替えるoperatorのみで記述されるが、これがconsistentに理論に導入できるか否かは明らかではない。次に、ここではNeumann型境界条件を持つopen stringのみを考えたが、Dirichlet型境界条件に対応する理論がD-braneの多体系を如何に記述できるかを考える必要がある。さらに、"Open Matrix String Theory"を構築するには、この定式化の超弦理論版を考え、(1+1)次元の超対称ゲージ理論との対応を調べる必要がある。

  Soryushiron Kenkyu Editorial Office, 2000, Soryushiron Kenkyu Electronics, 102(3) (3), C138 - C139, Japanese

• 物理学ミニマ

  野尻, 伸一, 伊藤, 好孝, 藤, 博之, 門田, 健司, 杉山, 直

  名古屋大学出版会, Jun. 2014, Japanese, ISBN: 9784815807740

• 位相的漸化式入門とその応用(1)(2)

  藤 博之

  第60回函数論サマーセミナー, Aug. 2026, Japanese

  [Invited]


• ファットグラフに基づく位相的漸化式入門

  藤 博之

  NITEP大阪城セミナー, May 2026, Japanese

  Public discourse


• 弦の場の理論と位相的漸化式

  藤 博之

  パンルヴェ方程式と可積分系, Mar. 2026, Japanese

  [Invited]

  Invited oral presentation


• Topological Recursions from a Hamiltonian Formalism

  Hiroyuki Fuji

  The 21st “Kagoshima Algebra-Analysis-Geometry Seminar”, Feb. 2026, English

  [Invited]

  Invited oral presentation


• 2次元曲面の力学的単体分割と位相的漸化式

  藤 博之

  東北大学数学教室談話会, Oct. 2025, Japanese

  [Invited]

  Public discourse


• On analogues of Mirzakhani's recursion formula via minimal string theories

  Hiroyuki Fuji

  結び目理論，幾何学的リー群論，及びその応用2024, Mar. 2025, English, 東京理科大学神楽坂キャンパス, Japan

  [Invited]

  Invited oral presentation


• 位相的漸化式入門

  藤 博之

  神楽坂 数理物理，幾何セミナー, Nov. 2024, Japanese, オンライン（東京理科大学・神戸大学）

  [Invited]

  Public discourse


• Some generalizations of Mirzakhani's recursion and Masur-Veech volumes via topological recursions

  藤 博之

  スケイン代数とその周辺, Oct. 2024, Japanese, I-site なんば, Japan

  [Invited]

  Invited oral presentation


• Causal dynamical triangulations and topological recursions

  藤 博之

  離散的手法による場と時空のダイナミクス2024, Sep. 2024, 東京工業大学, Japan


• Dynamical triangulations of Riemann surfaces and topological recursions

  Hiroyuki Fuji

  New Aspects in Topological Recursion, Resurgence and Related Topics, Jul. 2024, English, RIMS, Kyoto University, Japan, International conference

  [Invited]

  Invited oral presentation


• Dynamical triangulations of Riemann surfaces and topological recursions

  藤 博之

  Geometry on singular points and its application & 幾何学セミナー, Jul. 2024, Japanese, 神戸大学理学部数学科, Japan

  [Invited]

  Invited oral presentation


• Some generalizations of Mirzakhani's recursion and Masur-Veech volumes via topological recursions

  藤 博之

  神戸大学理学研究科数学専攻談話会, Jun. 2024, Japanese, 神戸大学理学部数学科, Japan

  [Invited]


• Some generalizations of Mirzakhani's recursion and Masur-Veech volumes via topological recursions

  藤 博之

  Topics on mathematical structures in string theory, Feb. 2024, Japanese, 東京大学駒場キャンパス, Japan

  [Invited]

  Invited oral presentation


• 復元解析に基づくAJ予想の拡張

  藤 博之

  M-theory, Strings, and all That, Sep. 2020, Japanese, オンライン, Japan

  Oral presentation


• Fatgraph models for RNA molecules

  藤 博之

  総研大-理研iTHEMS 連携ワークショップ「遺伝と数理」, Jul. 2019, Japanese, レクトーレ葉山, Japan

  [Invited]

  Invited oral presentation


• RNAを表現するファットグラフモデルと行列模型

  藤 博之

  多元数理科学研究科談話会, Jun. 2019, Japanese, 名古屋大学大学院多元数理科学研究科, Japan

  [Invited]

  Public discourse


• Reconstructing GKZ equation via topological recursion

  Hiroyuki Fuji

  KIAS Physics Seminar, Sep. 2018, English, KIAS, Korea, Republic of

  [Invited]

  Public discourse


• A review on topological recursion

  Sep. 2018, English, KIAS

  [Invited]

  Public discourse


• Fatgraph models for RNA molecules

  藤 博之

  iTHEMS seminar, Mar. 2017, Japanese, 理化学研究所, Japan

  [Invited]

  Public discourse


• Partial chord diagrams and matrix models

  Hiroyuki Fuji

  Colloquium“The Algebra and Geometry of Modern Physics”at Department of Physics, Mar. 2017, English, University of Warsaw, Poland

  [Invited]

  Invited oral presentation


• Enumerating chord diagrams via matrix models

  Hiroyuki Fuji

  RMT2015: Random matrix theory from fundamental mathematics to biological applications, Nov. 2015, English, OIST, Japan, International conference

  [Invited]

  Invited oral presentation


• On the enumeration of chord diagrams and the BPZ equation via the matrix model

  Hiroyuki Fuji

  Quantization of Spectral Curves, Nov. 2015, English, Osaka City University, Japan, International conference

  [Invited]

  Invited oral presentation


• Enumerating chord diagrams via matrix models

  Hiroyuki Fuji

  96e rencontre entre mathématiciens et physiciens théoriciens : Géométrie et biophysique, University of Strasbourg, Sep. 2015, English, University of Strasbourg, France, International conference

  [Invited]

  Invited oral presentation


• Matrix model approach to RNA

  藤 博之

  離散的手法による場と時空のダイナミクス2015, Sep. 2015, Japanese, 岡山衛生会館5階第1、第2会議室, Japan

  Oral presentation


• Knot homology and Super-A-polynomial

  Hiroyuki Fuji

  Geometry, Quantum Topology and Asymptotics, Jul. 2014, English, Confucius Institute of the University Geneva, Switzerland, International conference

  [Invited]

  Invited oral presentation


• Super-A-polynomial

  Hiroyuki Fuji

  Quantum Curves and quantum knot invariants, Jun. 2014, English, BIRS, Baff, Canada

  [Invited]

  Invited oral presentation


• Categorification of the knot invarinats via strings

  Hiroyuki Fuji

  Low Dimensional Topology and Number Theory VI, Mar. 2014, English, Soft Research Park Center, Fukuoka, Japan, International conference

  [Invited]

  Invited oral presentation


• The knot homology and Calabi-Yau Geometry via String Theory

  Hiroyuki Fuji

  Conference on Calabi-Yau Geometry, Jan. 2014, English, Taiwan National University, Taiwan, Province of China, International conference

  [Invited]

  Invited oral presentation


• The Volume Conjecture and Super-A-polynomial

  Hiroyuki Fuji

  Physics and Mathematics of Link Homology, Jun. 2013, English, Université de Montréal, Canada, International conference

  [Invited]

  Keynote oral presentation


• 弦理論から生命科学へのアプローチ

  藤 博之

  数理解析からの転写過程の理解への展望, May 2013, 東京大学数理科学研究科, Japan


• Colored HOMFLY Homology and Super-A-polynomial

  Hiroyuki Fuji

  Intelligence of Low Dimensional Topology, 2013, English, RIMS, Kyoto University, Japan, International conference

  [Invited]

  Invited oral presentation


• Volume Conjecture and Colored Superpolynomials

  Hiroyuki Fuji

  Synthesis of integrabilities in the context of duality between the string theory and gauge theories, Sep. 2012, English, Stekrov Mathematical Institite, Higher School of Economics, Russian Federation, International conference

  [Invited]

  Invited oral presentation


• 結び目不変量と量子場の理論

  藤 博之

  Summer School 数理物理 2012, Sep. 2012, Japanese, 東京大学数理科学研究科, Japan

  [Invited]

  Public discourse


• Superpolynomial and Physics

  藤 博之

  離散的手法による場と時空のダイナミクス2012, Aug. 2012, Japanese, 理化学研究所, Japan

  Oral presentation


• 体積予想とChern-Simons理論

  藤 博之

  場の理論と弦理論2012, Jul. 2012, Japanese, 京都大学基礎物理学研究所, Japan

  [Invited]

  Keynote oral presentation


• On asymptotic limit of superpolynomials

  Hiroyuki Fuji

  String-Math 2012, English, Universität Bonn, Bonn, Germany, International conference

  [Invited]

  Keynote oral presentation


• Volume Conjecture, QFT, Strings

  藤 博之

  静岡集中セミナー, Jun. 2012, Japanese, 静岡大学, Japan

  [Invited]

  Invited oral presentation


• The Volume Conjecture and Topological Strings

  Hiroyuki Fuji

  New Recursion Formula and Integrability for Calabi-Yau Spaces, Oct. 2011, English, BIRS, Banff, Canada, International conference

  [Invited]

  Invited oral presentation


• Topological String and Related topics

  藤 博之

  量子可積分系の新展開２, Sep. 2011, Japanese, 富士研修所, Japan

  [Invited]

  Keynote oral presentation


• Surface Operator and Topological String

  Hiroyuki Fuji

  Low dimensional topology and number theory III, Mar. 2011, English, Nishijin plaza, Kyushu University, Japan, International conference

  [Invited]

  Invited oral presentation


• Volume Conjecture and Topological String

  Hiroyuki Fuji

  The 3rd Taiwan String Winter School, Dec. 2010, English, 東海大学, 台中市, Taiwan, Province of China, International conference

  [Invited]

  Invited oral presentation


• 位相的弦理論について

  藤 博之

  東工大・茨城大学合同合宿, Oct. 2010, Japanese, 草津セミナーハウス

  [Invited]

  Public discourse


• 三次元重力理論と体積予想

  藤 博之

  離散的手法による場と時空のダイナミクス2010, Sep. 2010, Japanese, 京都大学基礎物理学研究所, Japan

  Oral presentation


• Volume Conjecture and Topological Recursion

  Hiroyuki Fuji

  Low dimensional topology and number theory II, Mar. 2010, English, The University of Tokyo, Komaba Campus, Japan, International conference

  [Invited]

  Invited oral presentation


• Volume Conjecture and Topological Recursion

  藤 博之

  KEK理論研究会２０１０, Mar. 2010, Japanese, 高エネルギー加速器研究機構, Japan

  [Invited]

  Invited oral presentation


• Volume Conjecture and Topological Recursion

  Hiroyuki Fuji

  Recent Advances in Gauge Theories and CFTs, Mar. 2010, English, Yukawa Institute, Japan, International conference

  [Invited]

  Invited oral presentation


• On Computation of Disk Instantons-B-model Approach-

  藤 博之

  YITP Seminar Series, Mar. 2009, Japanese, 京都大学基礎物理学研究所, Japan

  [Invited]

  Invited oral presentation


• Volume Conjecture and Topological Strings

  Hiroyuki Fuji

  Geometry and Physics, Mar. 2008, English, The University of Melbourne, Australia, International conference

  Oral presentation


• Volume Conjecture and Topological String

  藤 博之

  Mini Workshop on Mirror Symmetry 2008, Jan. 2008, Japanese, 北海道大学, Japan

  [Invited]

  Invited oral presentation


• Gravitational Corrections to SQCD via Matrix Models

  Hiroyuki Fuji

  Mathematical Aspects of String Theory, Jul. 2004, English, RIMS, Kyoto University, Japan, International conference

  [Invited]

  Invited oral presentation


• Gravitational Corrections to SQCD via Martix Models

  藤 博之

  理研集中セミナー「行列模型と超対称ゲージ理論」, Jul. 2004, Japanese, 理化学研究所, Japan

  [Invited]

  Invited oral presentation


• Gravitational Corrections to SQCD via Matrix Models

  Hiroyuki Fuji

  Susy 2004 : the 12th international conference on supersymmetry and unification of fundamental interactions, Jun. 2004, English, Tsukuba, Japan, International conference

  Oral presentation


• Gravitational Corrections to SQCD via Matrix Models

  藤 博之

  日本物理学会第59回年次大会, Mar. 2004, Japanese, 九州大学箱崎地区, Japan

  Oral presentation


• Nonperturbative Aspects of Gauge Theories via Matrix Models

  Hiroyuki Fuji

  An International Meeting on Noncommutative Geometry and Physics 2004, Feb. 2004, English, Keio University, Japan, International conference

  [Invited]

  Invited oral presentation


• Higher Genus Corrections via Matrix Models

  藤 博之

  KEK理論研究会２００３, Mar. 2003, Japanese, 高エネルギー加速器研究機構, Japan

  [Invited]

  Invited oral presentation


• Comments on Effective Superpotentials via Matrix Models

  Hiroyuki Fuji

  Developments of Superstring Theory, Nov. 2002, English, Yukawa Institute, Kyoto University, Japan

  [Invited]

  Invited oral presentation


• Confining Phase Superpotentials via Geometric Transition

  藤 博之

  日本物理学会 第57回物理学会秋季大会, Sep. 2002, Japanese, 立教大学, Japan

  Oral presentation


• Open String Theory on Symmetric Product

  藤 博之

  研究集会「場の理論２０００」, Jul. 2002, Japanese

  Oral presentation


• Comments on Effective Superpotentials via Matrix Models

  藤 博之

  日本物理学会第58回年次大会, 東北学院大学

• THE PHYSICAL SOCIETY OF JAPAN


• THE MATHEMATICAL SOCIETY OF JAPAN

• Quantum Modular Forms and their Applications

  樋上 和弘, 村上 斉, 藤 博之, 寺嶋 郁二

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Kyushu University, 01 Apr. 2022 - 31 Mar. 2027

  (1) 量子モジュラー形式はこれまでに無かった概念であり、結び目や3次元多様体の量子不変量が量子モジュラー性をもつとされる。よく知られている例がトーラス結び目の色つきJones多項式やSeifert多様体のWitten-Reshetikhin-Turaev(WRT)不変量などであるが、実際に量子モジュラー性を示すのは困難が多く、漸近極限を調べることが大変有用となる。当該年度はトーラス結び目のDehn手術から得られる多様体のWRT不変量を漸近極限を詳細に解析し、Chern-Simons不変量やReidemeister捩れとの関係を明らかにした。 (2) 双曲結び目の不変量の量子モジュラー性の解析には状態積分が有用である。これまでに研究されていないものも含めた幾つかの結び目について解析を進めている。特に、位相的漸化式や厳密WKB法などさまざまな手法の有用性を試みている。 (3) トーラス結び目の色つきJones多項式は偽テータ関数と非常に相性が良い。擬テータ関数は頂点作用素代数にも現れるため、量子モジュラー性の解明には頂点作用素代数の手法も有用であるものと期待される。当該年度において、(s,t)対数型頂点作用素代数の指標が(2s,2t)トーラス絡み目の色つきJones多項式とが一致することを、学振特別研究員との共同研究で見いだした。また、色つきJones多項式の「しっぽ」と呼ばれる部分と指標との関連性も指摘した。 (4) 当該年度には二重アフィンヘッケ代数を用いた量子不変量の再構成についての研究をひきつづき行った。


• 幾何的漸化式に基づく量子トポロジーと弦の場の量子構造の数理の究明

  藤 博之, 樋上 和弘, 村上 斉, 真鍋 征秀

  日本学術振興会, 科学研究費助成事業, 基盤研究(C), 大阪工業大学, 01 Apr. 2020 - 31 Mar. 2025

  幾何学的漸化式は，位相的漸化式の量子トポロジーによる解釈の中から提唱された，リーマン面のモジュライ空間の構造を調べる手法であり，交差数やWeil-Petersson体積をはじめとした様々な不変量が普遍的に満たす構造が見出された．本研究課題は，２次元量子重力理論や非臨界弦の場の理論を基に幾何学的漸化式の物理的側面に関する理解を深めることを目的としている． ２次元重力理論に関する研究では，リーマン面上の有理微分形式のモジュライ空間に適切な測度を導入して定められるMasur-Veech（MV）体積が満たす幾何学的漸化式の物理的解釈を与える問題に取り組んだ．Mirzakhaniによる双曲構造を導入したリーマン面を基にした再定式化によると，MV体積は境界付き双曲リーマン面内部に巻き付いた閉測地線の数え上げ問題として再解釈される．この再定式化を２次元重力理論において解釈すると，Jackiew-Teitelboim（JT）重力理論の重力場に結合した無質量スカラー粒子の世界線の数え上げ問題となることが予想される．この点を示すため，MV体積（の多項式拡張）が満たす幾何学的漸化式と，JT重力理論の重力場に結合した無質量スカラー粒子の分配関数を比較したところ，両者の一致が確認され，我々の物理的解釈に関する予想が示された．さらに，本年度の研究ではスカラー粒子による解釈を基に，全ての長さが一定に保った測地線の数え上げ問題への拡張などが定められることも提唱した． 非臨界弦の場の理論に関する研究では，格子重力理論である動的単体分割(DT)を基にした非臨界弦の場の理論のSchwinger-Dyson方程式の解析を行った．特に，(2,2m-1)極小模型で表される物質場が結合した重力理論に対するDT模型のSchwinger-Dyson方程式が，位相的漸化式に書き換えられることを証明した．（現在論文執筆中．）


• Asymptotic behaviors of quantum invariants of knots and three-manifolds

  Murakami Hitoshi

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Tohoku University, 01 Apr. 2020 - 31 Mar. 2024

  The quantum invariants are invariants for knots/links and for three-dimensional manifolds, associated with a Lie algebra and its representation. In this research, we consider the colored Jones polynomial and the Witten-Reshetikhin-Turaev invariant, which are basic quantum invariants, calculated those invariants for iterated torus knots and for closed three-manifolds obtained by Dehn surgery along torus knots, and studied their asymptotic behaviors . In both cases, there it was shown that there appear the Chern-Simons invariant and the Reidemeister torsion associated with a representation of the fundamental group to SL(2;C). These results support the volume conjecture and its generalizations, and the three-manifold version of the volume conjecture.


• Primitive forms and topological recursion

  Satake Ikuo

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), 01 Apr. 2018 - 31 Mar. 2024

  Principal investigator Satake approached the case where the LG model is defined by a one-variable potential with a concrete example. However the case of one-variable was solved by Milanov's discussion of primitive forms and topological recursion for Hurwitz coverings, which gave a high-species oscillatory integral representation. In order to use the coverings obtained from periodic maps as spectral curves of the LG model defined by multivariate potentials, the theory of Good invariants was developed. This also gave a new perspective on finite mirror group invariants. Fuji, a co-researcher of this project, studied topological recursion and clarified the physical meaning of geometric quantities such as the Masur-Veech volume, which has been studied in hyperbolic geometry.


• Asymptotic behaviors of quantum invariants of knots and three-manifolds

  Murakami Hitoshi

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Tohoku University, 01 Apr. 2017 - 31 Mar. 2021

  We study a topological interpretation of the asymptotic behavior of the colored Jones polynomial of a knot. Especially, we show that for an iterated torus knot, one can obtain the Chern-Simons invariant and the twisted Reidemeister torsion of the knot complement from the asymptotic expansion of the colored Jones polynomial. Moreover, we obtain a relationship of the complex number in the parameter of the colored Jones polynomial to the parameter used to define the Chern-Simons invariant and the Reidemeister torsion. Indeed, we prove that this parameter determines a representation of the knot group to the Lie group SL(2;C).


• Studies on Mock Modular Forms and Quantum Invariants

  Hikami Kazuhiro

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (B), Kyushu University, 01 Apr. 2016 - 31 Mar. 2021

  A mock modular form is defined as a holomorphic part of the harmonic Maass forms. A typical example is the Ramanujan mock theta function, which has a weight 1/2 mock modular form. It is originally related to the integer partition. Recently it is recognized that mock modular form plays an important role in quantum topology. In the present research, we studied quantum modular form by use of the cluster algebra and the double affine Hecke algebra, and clarified new aspects of quantum invariants.


• On applications of fatgraph techniques to the molecular biology via matrix models

  Fuji Hiroyuki

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Challenging Research (Exploratory), Kagawa University, 30 Jun. 2017 - 31 Mar. 2020

  In this research project, various fatgraph techniques are applied to the study of the molecular biology. The basic concept of the fatgraph was introduced originally in the perturbative study of the quantum field theory, and such idea is found to be useful to represent the geometry and topology of moduli spaces in mathematics. In recent years, the fatgraph is applied to characterize the biomolecules such as RNAs and proteins, and it is found to be useful to improve the predictions of their secondary structures. In our work, we focused mainly on the following two aspects of the fatgraph techniques: (1) propose a new model to predict the secondary structure of proteins, (2) develop the basic aspects of fatgraph techniques via matrix models. On the aspect (1), we found a novel mathematical model to predict the reduced secondary structure referred to "meta-structure" of proteins. On the aspect (2), we have proposed novel fatgraph techniques in the mirror symmetry and two-color QCD.


• Mathematical aspects of the quantum field theory and its applications

  Fuji Hiroyuki, Andersen Jørgen Ellegaard, Penner Robert C., Sułkowski Piotr, Reidys Christian M., Manabe Masahide

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Research Activity Start-up, Kagawa University, 28 Aug. 2015 - 31 Mar. 2017

  Mathematical aspects of the quantum field theory and its applications to the molecular biology has been studied in this research project. We applied fatgraphs and random matrix model techniques to the geometric study of Ribonucleic Acid (RNA). The fatgraph is the one dimensional oriented graph utilized widely in geometry, topology, representation theory and quantum field theory. The fatgraph is also useful to describe geometric and topological characterizations of the biohighpolymers such as proteins and RNAs. In this research, we introduced a novel kind of combinatorial parameters referred to "boundary length and point spectrum" which enables us to characterize the secondary structure of RNAs including pseudoknot structures. We constructed a matrix model for RNAs. Using this model, one can enumerate the number of fatgraphs with the fixed type of the boundary length and point spectrum, and this enumerative model would be useful to understand statistical behaviors in RNA databases.


• Quantum invariants of knots and representations of knot groups

  Murakami Hitoshi

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Scientific Research (C), Tohoku University, 01 Apr. 2014 - 31 Mar. 2017

  In this research I studied mainly on the volume conjecture and its generalization about the colored Jones polynomial of a knot. As a result, I proved a generalization of the volume conjecture, that is, I proved that the asymptotic behavior of the colored Jones polynomial gives the Chern-Simons invariant and the Reidemeister torsion of the knot complement.


• 弦理論に基づく結び目不変量の解析

  藤 博之

  日本学術振興会, 科学研究費助成事業, 若手研究(B), 東京大学, 01 Apr. 2013 - 31 Mar. 2017

  本研究課題は，弦理論を用いて結び目不変量をはじめとした，様々な幾何学的不変量を解析することを目指している．本研究の中核をなす課題の一つとして，結び目の量子不変量に対する圏化を，物理的手法，特に超弦理論を用いてアプローチし，数学的に得られた研究成果の物理的解釈を与えると同時に，新たな不変量の構築や他の幾何学的不変量との関係を探ることが目標である．弦理論の研究では，D-ブレーンや様々な双対性の発見により，その物理量と幾何学的不変量との関係がより親密となっている．その中でも，3次元多様体とその中に配置された絡み目に対する量子不変量は，弦理論の分配関数に対応するという予想が確立し，この対応を基に近年は弦理論を用いて，量子不変量の背後に内在する構造の研究が進められている．こうした構造の中でも，近年の研究で急速に明らかになってきたのは「圏化」と呼ばれる概念である．圏化の結び目不変量への応用は，10年程前にM.Khovanov氏によって提唱され，Jones多項式をはじめとした結び目の量子不変量の背後にある高次の圏構造が明らかとなった．その後，圏化の研究はトポロジーや代数の分野では研究が進められ，数多くの進展がもたらされてきた．一方，この圏化を弦理論からどのような形で理解し，実現できるのかという問題は，様々な弦理論の進展と共に徐々に明らかとなり，この2年間でその正体が「BPS状態」によって記述できる事が判明し，顕著な進展を遂げている．これまでの研究では，弦理論によって「色付きHOMFLYホモロジー」と呼ばれる，数々の量子不変量の圏化を統一的に取り扱うホモロジーが提唱され，このホモロジーの研究を推進してきた．本研究課題では，この研究をさらに推進し，弦理論の双対性を通じて，結び目不変量の圏化の新たな場の理論の枠組みによる実現を探ると同時に，「圏化」の概念を物理へ応用する問題にも取り組んだ．


• Mathematical Aspects of Open String Theory and its Applications

  FUJI Hiroyuki

  Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research, Grant-in-Aid for Young Scientists (B), Nagoya University, 2009 - 2012

  In this research, I have focused on the mathematical aspects of the open string theory, and studied on the non-perturbative aspects of the quantum field theory and mathematical aspects of the string theory in particular for the relation with the geometry. In the physics side, I have mainly studied on the non-perturbative aspects of the quantum gravity on basis of the lattice model and AdS/CFT. In the mathematics side, I have found a novel quantum integrable structure of the knot invariants based on the topological string theory, and proposed a new topological invariant which arises from the categorification from the view point of the theoretical physics.

• 神戸大学 数理・データサイエンス・AI教育 FDシンポジウム 2026

  Presenter, 30 Mar. 2026 - 30 Mar. 2026


• 第５回中学生高校生データサイエンスコンテスト

  神戸大学

  Commentator, 08 Nov. 2025 - 08 Nov. 2025


• 第４回中学生・高校生データサイエンスコンテスト

  神戸大学数理・データサイエンスセンター

  27 May 2024 - 26 Oct. 2024, 神戸大学


• 実験観察講習会講師

  香川県中学校教育研究会理科部会

  Lecturer, Jul. 2015, 講師, 「光の性質を探る」という題目で，小中学教諭向けの講演を行った．

• ファットグラフ&TDA勉強会2025

  ファットグラフ&TDA勉強会2025

  藤 博之，真鍋征秀

  08 Mar. 2025 - 10 Mar. 2025, 神戸大学理学部

  Academic society etc


• 離散的手法による場と時空のダイナミクス2024

  離散的手法による場と時空のダイナミクス2024

  綿引芳之

  02 Sep. 2024 - 05 Sep. 2024, 東京工業大学

  Academic society etc


• One-day Lectures on Inspirations from Mathematics

  One-day Lectures on Inspirations from Mathematics

  Hiroyuki Fuji

  25 Jul. 2024 - 25 Jul. 2024, Kobe University

  Academic society etc


• 離散的手法による場と時空のダイナミクス2023

  離散的手法による場と時空のダイナミクス2023

  11 Sep. 2023 - 14 Sep. 2023, 筑波大学 筑波キャンパス 総合研究棟D 1階 公開講義室

  Academic society etc


• 離散的手法による場と時空のダイナミクス2022

  離散的手法による場と時空のダイナミクス2022

  22 Aug. 2022 - 25 Aug. 2022, 東京理科大学神楽坂キャンパス(＋オンライン(Zoom))

  Academic society etc


• M-theory, strings, and that

  M-theory, strings, and that

  19 Sep. 2020 - 20 Sep. 2020, オンライン

  Academic society etc


• 離散的手法による場と時空のダイナミクス2019

  離散的手法による場と時空のダイナミクス2019

  09 Sep. 2019 - 12 Sep. 2019, 島根大学松江キャンパス 本部棟3階特別会議室

  Academic society etc


• 離散的手法による場と時空のダイナミクス2018

  離散的手法による場と時空のダイナミクス2018

  09 Sep. 2018 - 12 Sep. 2018, 東北大学片平キャンパス、知の館(TFC) 3階レクチャーホール

  Academic society etc


• Chern-Simonsゲージ理論の解析接続に関する話題

  Chern-Simonsゲージ理論の解析接続に関する話題

  Sep. 2018 - Sep. 2018, 香川大学

  Academic society etc


• 第40回四国セミナー

  第40回四国セミナー

  Dec. 2017 - Dec. 2017, 香川大学

  Academic society etc


• Discrete Approaches to the Dynamics of Fields and Space-Time

  Discrete Approaches to the Dynamics of Fields and Space-Time

  19 Sep. 2017 - 23 Sep. 2017, APCTP, Korea

  Academic society etc


• 離散的手法による場と時空のダイナミクス2016

  離散的手法による場と時空のダイナミクス2016

  16 Sep. 2016 - 19 Sep. 2016, 静岡労政会館 5階視聴覚室

  Academic society etc


• 離散的手法による場と時空のダイナミクス2015

  離散的手法による場と時空のダイナミクス2015

  14 Sep. 2015 - 18 Sep. 2015, 岡山衛生会館5階第1、第2会議室

  Academic society etc


• 離散的手法による場と時空のダイナミクス2012

  離散的手法による場と時空のダイナミクス2012

  30 Aug. 2012 - 01 Sep. 2012, 理化学研究所（和光本所）研究本館4階会議室435,437

  Academic society etc


• Gauge Theory, Gravity, and String Theory

  Gauge Theory, Gravity, and String Theory

  Nagoya University GCOE Spring School 2011

  21 Mar. 2011 - 24 Mar. 2011, Nagoya University

  Academic society etc


• 離散的手法による場と時空のダイナミクス2010

  離散的手法による場と時空のダイナミクス2010

  27 Sep. 2010 - 01 Oct. 2010, 京都大学基礎物理学研究所

  Academic society etc


• Sapporo Winter School 2009

  Sapporo Winter School 2009

  北海道大学大学院理学院宇宙理学専攻

  Jan. 2009 - Jan. 2009, 北海道大学


• Sapporo Winter School 2007

  Sapporo Winter School 2007

  北海道大学大学院理学院宇宙理学専攻

  Feb. 2007 - Feb. 2007

  Academic society etc


• KEK理論研究会2005

  KEK理論研究会2005

  高エネルギー加速器研究機構理論部

  14 Mar. 2005 - 17 Mar. 2005, 高エネルギー加速器研究機構

  Academic society etc


• KEK理論研究会2004

  KEK理論研究会2004

  高エネルギー研究機構理論部

  16 Mar. 2004 - 18 Mar. 2004, 高エネルギー加速器研究機構

  Academic society etc