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ESCOLAR Gaw Emerson
Graduate School of Human Development and Environment / Department of Human Environmental Science
Associate Professor

Researcher basic information

■ Research Keyword
  • 応用数学
  • Algorithms
  • Representation Theory
  • Topological Data Analysis
■ Research Areas
  • Natural sciences / Applied mathematics and statistics
  • Natural sciences / Basic mathematics
  • Natural sciences / Algebra
  • Informatics / Computational science
■ Committee History
  • Jan. 2023 - Present, Applied Algebraic Topology Research Network (AATRN), Speaker Selection Committee
  • Apr. 2021 - Present, 日本応用数理学会 位相的データ解析研究部会, 幹事, https://sites.google.com/view/jsiam-tda
  • Apr. 2021 - Present, 日本応用数理学会, JSIAM Letters Associate Editor
  • Apr. 2024 - Mar. 2025, 日本応用数理学会, 代表会員
  • 2024 - Mar. 2025, 日本応用数理学会 第21回 研究部会連合発表会 実行委員会, 実行委員
  • 2022 - 2023, 10th International Congress on Industrial and Applied Mathematics (ICIAM 2023 Tokyo), Local Scientific Program Committee
  • 2022 - 2023, Nonlinear Theory and Its Applications, IEICE, "Special Section on Topological Data Analysis". (April issue 2023) Associate editor

Research activity information

■ Award
  • Oct. 2023 神戸大学大学教育推進機構, 全学共通教育ベストティーチャー賞
    エスカラ エマソン ガウ

■ Paper
  • Emerson G. Escolar, Yuta Shimada, Masahiro Yuasa
    Dec. 2024, International Journal of Gastronomy and Food Science
    Scientific journal
    Link to Kobe Univ. Repository (Kernel)

  • Toshitaka Aoki, Emerson G. Escolar, Shunsuke Tada
    In persistent homology analysis, interval modules play a central role in describing the birth and death of topological features across a filtration. In this work, we extend this setting, and propose the use of bipath persistent homology, which can be used to study the persistence of topological features across a pair of filtrations connected at their ends, to compare the two filtrations. In this setting, interval-decomposability is guaranteed, and we provide an algorithm for computing persistence diagrams for bipath persistent homology and discuss the interpretation of bipath persistence diagrams.
    2024, Japan Journal of Industrial and Applied Mathematics
    Scientific journal
    Link to Kobe Univ. Repository (Kernel)

  • Emerson G. Escolar, Yasuaki Hiraoka, Mitsuru Igami, Yasin Ozcan
    Where do firms innovate? Mapping their locations and directions in technological space is challenging due to its high dimensionality. We propose a new method to characterize firms' inventive activities via topological data analysis (TDA) that represents high-dimensional data in a shape graph. Applying this method to 333 major firms' patents in 1976-2005 reveals hitherto undocumented industry dynamics: some firms remain undifferentiated; others develop unique portfolios. Firms with unique trajectories, which we define and measure graph-theoretically as "flares"in the Mapper graph, tend to perform better. This association is statistically and economically significant, and continues to hold after we control for portfolio size, firm survivorship, and industry classification.
    ELSEVIER, Oct. 2023, RESEARCH POLICY, 52(8) (8), English
    [Refereed]
    Scientific journal

  • Hideto Asashiba, Emerson G. Escolar, Ken Nakashima, Michio Yoshiwaki
    In topological data analysis, two-parameter persistence can be studied using the representation theory of the 2d commutative grid, the tensor product of two Dynkin quivers of type A. In a previous work, we defined interval approximations using restrictions to essential vertices of intervals together with Mobius inversion. In this work, we consider homological approximations using interval resolutions, and show that the interval resolution global dimension is finite for finite posets, and that it is equal to the maximum of the interval dimensions of the Auslander-Reiten translates of the interval representations. Furthermore, in the commutative ladder case, by a suitable modification of our interval approximation, we provide a formula linking the two conceptions of approximation.
    Corresponding, ELSEVIER, Oct. 2023, JOURNAL OF PURE AND APPLIED ALGEBRA, 227(10) (10), English
    [Refereed]
    Scientific journal
    Link to Kobe Univ. Repository (Kernel)

  • Hideto Asashiba, Emerson G. Escolar, Ken Nakashima, Michio Yoshiwaki
    Corresponding, Sep. 2023, Journal of Computational Algebra, English
    [Refereed]
    Scientific journal
    Link to Kobe Univ. Repository (Kernel)

  • Yusuke Imoto, Tomonori Nakamura, Emerson G Escolar, Michio Yoshiwaki, Yoji Kojima, Yukihiro Yabuta, Yoshitaka Katou, Takuya Yamamoto, Yasuaki Hiraoka, Mitinori Saitou
    Single-cell RNA sequencing (scRNA-seq) can determine gene expression in numerous individual cells simultaneously, promoting progress in the biomedical sciences. However, scRNA-seq data are high-dimensional with substantial technical noise, including dropouts. During analysis of scRNA-seq data, such noise engenders a statistical problem known as the curse of dimensionality (COD). Based on high-dimensional statistics, we herein formulate a noise reduction method, RECODE (resolution of the curse of dimensionality), for high-dimensional data with random sampling noise. We show that RECODE consistently resolves COD in relevant scRNA-seq data with unique molecular identifiers. RECODE does not involve dimension reduction and recovers expression values for all genes, including lowly expressed genes, realizing precise delineation of cell fate transitions and identification of rare cells with all gene information. Compared with representative imputation methods, RECODE employs different principles and exhibits superior overall performance in cell-clustering, expression value recovery, and single-cell–level analysis. The RECODE algorithm is parameter-free, data-driven, deterministic, and high-speed, and its applicability can be predicted based on the variance normalization performance. We propose RECODE as a powerful strategy for preprocessing noisy high-dimensional data.
    Life Science Alliance, LLC, Dec. 2022, Life Science Alliance, 5(12) (12), e202201591 - e202201591
    [Refereed]
    Scientific journal

  • Mickael Buchet, Emerson G. Escolar
    While persistent homology has taken strides towards becoming a widespread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is the serious drawback of no longer having a concise and complete descriptor analo-gous to the persistence diagrams of the former. We propose a simple algebraic construction to illustrate the existence of infinite families of indecomposable persistence modules over reg-ular commutative grids of sufficient size. On top of providing a constructive proof that those commutative grids are representation-infinite, we also provide realizations of the modules by topological spaces and Vietoris-Rips filtrations, showing that they can actually appear in real data and are not the product of degeneracies.
    CARLETON UNIV, DEPT MATHEMATICS & STATISTICS, Sep. 2022, Journal of Computational Geometry, 13(1) (1), 298 - 326, English, International magazine
    [Refereed]
    Scientific journal
    Link to Kobe Univ. Repository (Kernel)

  • Hideto Asashiba, Mickaël Buchet, Emerson G. Escolar, Ken Nakashima, Michio Yoshiwaki
    Elsevier {BV}, Apr. 2022, Computational Geometry, 105-106, 101879 - 101879
    [Refereed]
    Scientific journal

  • Emerson G. Escolar, Killian Meehan, Michio Yoshiwaki
    In order to better understand and to compare interleavings between persistence modules, we elaborate on the algebraic structure of interleavings in general settings. In particular, we provide a representation-theoretic framework for interleavings, showing that the category of interleavings under a fixed translation is isomorphic to the representation category of what we call a shoelace. Using our framework, we show that any two interleavings of the same pair of persistence modules are themselves interleaved. Furthermore, in the special case of persistence modules over R, we show that matchings between barcodes correspond to the interval-decomposable interleavings.
    Springer Science and Business Media LLC, Oct. 2021, Applicable Algebra in Engineering, Communication and Computing
    [Refereed]
    Scientific journal

  • Mickaël Buchet, Emerson G. Escolar
    A recent work by Lesnick and Wright proposed a visualisation of $2$D
    persistence modules by using their restrictions onto lines, giving a family of
    $1$D persistence modules. We give a constructive proof that any $1$D
    persistence module with finite support can be found as a restriction of some
    indecomposable $2$D persistence module with finite support. As consequences of
    our construction, we are able to exhibit indecomposable $2$D persistence
    modules whose support has holes as well as an indecomposable $2$D persistence
    module containing all $1$D persistence modules with finite support as line
    restrictions. Finally, we also show that any finite-rectangle-decomposable $n$D
    persistence module can be found as a restriction of some indecomposable
    $(n+1)$D persistence module.
    2020, J. Appl. Comput. Topol., 4(3) (3), 387 - 424
    [Refereed]
    Scientific journal

  • Asashiba Hideto, Escolar Emerson G, Hiraoka Yasuaki, Takeuchi Hiroshi
    Springer Science and Business Media {LLC}, Jan. 2019, JAPAN JOURNAL OF INDUSTRIAL AND APPLIED MATHEMATICS, 36(1) (1), 97 - 130
    [Refereed]
    Scientific journal

  • Mickaël Buchet, Emerson G. Escolar
    While persistent homology has taken strides towards becoming a widespread tool for data analysis, multidimensional persistence has proven more difficult to apply. One reason is the serious drawback of no longer having a concise and complete descriptor analogous to the persistence diagrams of the former. We propose a simple algebraic construction to illustrate the existence of infinite families of indecomposable persistence modules over regular grids of sufficient size. On top of providing a constructive proof of representation infinite type, we also provide realizations by topological spaces and Vietoris-Rips filtrations, showing that they can actually appear in real data and are not the product of degeneracies.
    Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2018, 34th International Symposium on Computational Geometry, SoCG 2018, June 11-14, 2018, Budapest, Hungary, 15:1-15:13, English
    [Refereed]
    International conference proceedings

  • Yasuaki Hiraoka, Takenobu Nakamura, Akihiko Hirata, Emerson G. Escolar, Kaname Matsue, Yasumasa Nishiura
    This article proposes a topological method that extracts hierarchical structures of various amorphous solids. The method is based on the persistence diagram (PD), a mathematical tool for capturing shapes of multiscale data. The input to the PDs is given by an atomic configuration and the output is expressed as 2D histograms. Then, specific distributions such as curves and islands in the PDs identify meaningful shape characteristics of the atomic configuration. Although the method can be applied to a wide variety of disordered systems, it is applied here to silica glass, the Lennard-Jones system, and Cu-Zr metallic glass as standard examples of continuous random network and random packing structures. In silica glass, the method classified the atomic rings as short-range and medium-range orders and unveiled hierarchical ring structures among them. These detailed geometric characterizations clarified a real space origin of the first sharp diffraction peak and also indicated that PDs contain information on elastic response. Even in the Lennard-Jones system and Cu-Zr metallic glass, the hierarchical structures in the atomic configurations were derived in a similar way using PDs, although the glass structures and properties substantially differ from silica glass. These results suggest that the PDs provide a unified method that extracts greater depth of geometric information in amorphous solids than conventional methods.
    NATL ACAD SCIENCES, Jun. 2016, PROCEEDINGS OF THE NATIONAL ACADEMY OF SCIENCES OF THE UNITED STATES OF AMERICA, 113(26) (26), 7035 - 7040, English
    [Refereed]
    Scientific journal

  • Emerson G. Escolar, Yasuaki Hiraoka
    In this work, we discuss the problem of finding optimal cycles for homology groups of simplicial complexes and for persistent homology of filtrations. We review the linear programming formulation of the optimal homologous cycle problem and its extension to allow for multiple cycles. By inserting these linear programming problems into the persistent homology algorithm, we are able to compute an optimal cycle, that has been optimized at birth, for every persistent interval in the persistent diagram.
    SPRINGER-VERLAG TOKYO, 2016, OPTIMIZATION IN THE REAL WORLD: TOWARD SOLVING REAL-WORLD OPTIMIZATION PROBLEMS, 13, 79 - 96, English
    [Refereed]
    International conference proceedings

  • Emerson G. Escolar, Yasuaki Hiraoka
    This is a summary paper of Escolar and Hiraoka (Persistence modules on commutative ladders of finite type. Discrete Comput Geom 55, 100-157 (2016)) which presents an extension of persistence modules as representations on quivers with nontrivial relations. In particular, the mathematical and algorithmic results in that paper enable us to detect robust and common topological structures of two geometric objects. In this paper, we only deal with a special type of persistence modules defined on the so-called commutative triple ladder for the sake of simplicity. We aim to explain the essence of Auslander-Reiten theory in connection with persistence modules.
    SPRINGER JAPAN, 2016, MATHEMATICAL CHALLENGES IN A NEW PHASE OF MATERIALS SCIENCE, 166, 69 - 82, English
    [Refereed]
    International conference proceedings

  • Emerson G. Escolar, Yasuaki Hiraoka
    We study persistence modules defined on commutative ladders. This class of persistence modules frequently appears in topological data analysis, and the theory and algorithm proposed in this paper can be applied to these practical problems. A new algebraic framework deals with persistence modules as representations on associative algebras and the Auslander-Reiten theory is applied to develop the theoretical and algorithmic foundations. In particular, we prove that the commutative ladders of length less than 5 are representation-finite and explicitly show their Auslander-Reiten quivers. Furthermore, a generalization of persistence diagrams is introduced by using Auslander-Reiten quivers. We provide an algorithm for computing persistence diagrams for the commutative ladders of length 3 by using the structure of Auslander-Reiten quivers.
    SPRINGER, Jan. 2016, DISCRETE & COMPUTATIONAL GEOMETRY, 55(1) (1), 100 - 157, English
    [Refereed]
    Scientific journal

  • Takenobu Nakamura, Yasuaki Hiraoka, Akihiko Hirata, Emerson G. Escolar, Yasumasa Nishiura
    The characterization of the medium-range (MRO) order in amorphous materials and its relation to the short-range order is discussed. A new topological approach to extract a hierarchical structure of amorphous materials is presented, which is robust against small perturbations and allows us to distinguish it from periodic or random configurations. This method is called the persistence diagram (PD) and introduces scales to many-body atomic structures to facilitate size and shape characterization. We first illustrate the representation of perfect crystalline and random structures in PDs. Then, the MRO in amorphous silica is characterized using the appropriate PD. The PD approach compresses the size of the data set significantly, to much smaller geometrical summaries, and has considerable potential for application to a wide range of materials, including complex molecular liquids, granular materials, and metallic glasses.
    IOP PUBLISHING LTD, Jul. 2015, NANOTECHNOLOGY, 26(30) (30), 304001, English
    [Refereed]
    Scientific journal

  • Emerson G. Escolar, Yasuaki Hiraoka
    2014, A Mathematical Approach to Research Problems of Science and Technology - Theoretical Basis and Developments in Mathematical Modeling, 101 - 118

  • Emerson Escolar, Yasuaki Hiraoka
    Indonesian Mathematical Society, 2014, Journal of the Indonesian Mathematical Society, 20(1) (1), 47 - 75, English
    [Refereed]
    Scientific journal

  • Emerson G. Escolar, Yasuaki Hiraoka
    Persistence modules on commutative ladders naturally arise in topological data analysis. It is known that all isomorphism classes of indecomposable modules, which are the counterparts to persistence intervals in the standard setting of persistent homology, can be derived for persistence modules on commutative ladders of finite type. Furthermore, the concept of persistence diagrams can be naturally generalized as functions defined on the Auslander-Reiten quivers of commutative ladders. A previous paper [4] presents an algorithm to compute persistence diagrams by inductively applying echelon form reductions to a given persistence module. In this work, we show that discrete Morse reduction can be generalized to this setting. Given a quiver complex double-struck X, we show that its persistence module H q(double-struck X) is isomorphic to the persistence module H q(double-struck A) of its Morse quiver complex double-struck A. With this preprocessing step, we reduce the computation time by computing H q(double-struck A) instead, since double-struck A is generally smaller in size. We also provide an algorithm to obtain such Morse quiver complexes. © 2014 Springer-Verlag.
    Springer Verlag, 2014, Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 8592, 144 - 151, English
    International conference proceedings

■ MISC
  • E.G. エスカラ
    Lead, Jun. 2023, 数理科学 2023年6月号 Ｎｏ.720, 71 - 94, Japanese
    [Invited]
    Introduction scientific journal

  • The Whole in the Parts: Putting $n$D Persistence Modules Inside Indecomposable $(n + 1)$D Ones
    Mickaël Buchet, Emerson G. Escolar
    Multidimensional persistence has been proposed to study the persistence of topological features in data indexed by multiple parameters. In this work, we further explore its algebraic complications from the point of view of higher dimensional indecomposable persistence modules containing lower dimensional ones as hyperplane restrictions. Our previous work constructively showed that any finite rectangle-decomposable $n$D persistence module is the hyperplane restriction of some indecomposable $(n+1)$D persistence module, as a corollary of the result for $n=1$. Here, we extend this by dropping the requirement of rectangle-decomposability. Furthermore, in the case that the underlying field is countable, we construct an indecomposable $(n+1)$D persistence module containing all $n$D persistence modules, up to isomorphism, as hyperplane restrictions. Finally, in the case $n=1$, we present a minimal construction that improves our previous construction.
    04 Dec. 2020

  • Nakamura T., Hiraoka Y., Hirata A., Escolar E., Matsue K., Nishiura Y.
    The Physical Society of Japan (JPS), 2015, Meeting Abstracts of the Physical Society of Japan, 70, 2947 - 2947, Japanese

  • 8aAp-9 A characterization of the amorphous silica structure by persistent homology II
    Nakamura Takenobu, Hiraoka Yasuaki, Hirata Akihiko, Escolar Emerson, Matsue Kaname, Nishiura Yasumasa
    The Physical Society of Japan (JPS), 22 Aug. 2014, Meeting abstracts of the Physical Society of Japan, 69(2) (2), 128 - 128, Japanese

■ Books And Other Publications
  • 位相的データ解析から構造発見へ : パーシステントホモロジーを中心に
    池, 祐一, Emerson Gaw Escolar, 大林, 一平, 鍛冶, 静雄
    Joint work, サイエンス社, Sep. 2023, Japanese, ISBN: 9784781915807

■ Lectures, oral presentations, etc.
  • レシピ空間の位相的な解析とその発展
    島田優多, エスカラ エマソン ガウ, 湯浅正洋
    日本応用数理学会 若手の会 第10回学生研究発表会, Mar. 2025, Japanese
    Poster presentation

  • Barcoding Invariants and Their Equivalent Discriminating Power
    Emerson Gaw Escolar, Woojin Kim
    日本応用数理学会第21回研究部会連合発表会 [研究部会 OS] 位相的データ解析, Mar. 2025, Japanese, Co-authored internationally
    Oral presentation

  • 位相的データ解析とその応用例
    Emerson G. Escolar
    パーシステントホモロジーセミナー, Nov. 2024, Japanese
    [Invited]
    Public discourse

  • Introduction to Topological Data Analysis and Recent Progress in Multiparameter Persistence
    Emerson G. Escolar
    NTT基礎数学セミナー, Sep. 2024, Japanese, NTT武蔵野研究開発センタ, Domestic conference
    [Invited]
    Public discourse

  • 位相的データ解析とその応用例
    エスカラ エマソン ガウ
    AI・データ利活用研究会 第74回, Jul. 2024, Japanese
    [Invited]
    Public discourse

  • ネットワークサイエンスから見た料理のレシピ
    Kobe Studio Seminar for Studies ワークショップ: 料理のレシピと映像制作，その数理的な展開, May 2024, Japanese
    Public discourse

  • Computing bipath persistent homology
    青木 利隆, ESCOLAR Emerson Gaw, 多田 駿介
    日本数学会2024年度年会, Mar. 2024, Japanese, 大阪公立大学
    Oral presentation

  • Computing bipath persistent homology
    青木 利隆, ESCOLAR Emerson Gaw, 多田 駿介
    日本応用数理学会 第20回 研究部会連合発表会, Mar. 2024, Japanese, 長岡技術科学大学
    Oral presentation

  • データの「穴」に着目：パーシステントホモロジーについて
    エスカラ エマソン ガウ
    Kobe Studio Seminar for Studies ワークショップ: 数学，計算機，そしてデータサイエンス, Feb. 2024, Japanese
    Others

  • 料理空間の位相的データ解析 ~ 新しい料理の提案への応用 ~
    Emerson Gaw ESCOLAR, 湯浅 正洋
    日本数学会応用数学分科 2023年度応用数学合同研究集会, Dec. 2023
    Oral presentation

  • On interval covers and resolutions of persistence modules
    Emerson Gaw ESCOLAR
    Magnitude 2023, Dec. 2023, English, International conference
    [Invited]
    Invited oral presentation

  • 位相的データ解析で生成した料理レシピの調理と有用性
    湯浅正洋, Emerson Gaw ESCOLAR
    日本調理科学会近畿支部第49回研究発表会, Dec. 2023
    Oral presentation

  • リスク認知地図の新たな表現に関する試み
    村山留美子, Emerson G. ESCOLAR
    日本リスク学会 2023年度年次大会, Nov. 2023
    Poster presentation

  • A topological analysis of the space of recipes
    Emerson Gaw ESCOLAR, 湯浅 正洋
    日本数学会 2023 年度秋季総合分科会 応用数学分科会, Sep. 2023, Japanese
    Oral presentation

  • On Interval Global Dimension of Posets: a Characterization of Case 0
    青木 利隆, ESCOLAR, Emerson Gaw, 多田 駿介
    日本数学会 2023 年度秋季総合分科会 代数学分科会, Sep. 2023
    Oral presentation

  • On interval global dimension of posets: a characterization of case 0
    多田 駿介, 青木 利隆, Emerson Gaw Escolar
    第 55 回環論および表現論シンポジウム, Sep. 2023
    Oral presentation

  • Approximation by interval-decomposables and interval resolutions of 2D persistence modules
    Hideto Asashiba, Emerson G. Escolar, Ken Nakashima, Michio Yoshiwaki
    TDA Week 2023, Aug. 2023, English, International conference
    [Invited]
    Invited oral presentation

  • On Interval Resolutions of Persistence Modules
    Emerson G. Escolar
    SIAM Conference on Applied Algebraic Geometry (AG23) Minisymposium Recent Developments in Multi-Parameter Persistence, Jul. 2023, English, Eindhoven University of Technology, Netherlands, International conference
    [Invited]
    Invited oral presentation

  • Introduction to Topological Data Analysis
    Emerson G. Escolar
    Kobe Studio Seminar for Studies from Trials, May 2023, Japanese
    [Invited]
    Public discourse

  • Persistent Homology and Representation Theory
    Emerson G. Escolar
    Meets Series Topology Meets Data, Jan. 2023, Japanese, ⼀橋講堂, Domestic conference
    [Invited]
    Public discourse

  • Multiparameter persistent homology and interval approximations
    Emerson G. Escolar
    General Topology Symposium 2022, Dec. 2022, International conference
    [Invited]
    Nominated symposium

  • Mapping Firms' Locations in Technological Space: A Topological Analysis of Patent Statistics
    Emerson G. Escolar
    ICMMA 2022 International Conference on Topology and its Applications to Engineering and Life Science, Nov. 2022, English, Meiji Institute for Advanced Study of Mathematical Sciences Center for Mathematical Modeling and Applications, online, International conference
    [Invited]
    Invited oral presentation

  • Introduction to Topological Data Analysis and Research on Interval Resolutions of Multiparameter Persistence
    Emerson G. Escolar
    九州⼤学 IMI 共同利⽤・短期共同研究、機械学習への組合せ論的アプローチ（非公開部), Sep. 2022
    [Invited]
    Others

  • Approximation by interval-decomposables and interval resolutions of 2D persistence modules
    中島 健, 浅芝 秀人, Emerson G. Escolar, 吉脇 理雄
    日本数学会2022年度秋季総合分科会, Sep. 2022, Japanese, 北海道大学
    Oral presentation

  • 可換梯子型パーシステンス加群の表現論的区間分解の計算法
    中島 健, 浅芝 秀人, Emerson G. Escolar, 吉脇 理雄
    日本応用数理学会2022年度年会, Sep. 2022, Japanese, 北海道大学
    Oral presentation

  • Approximation by interval-decomposables and interval resolutions of persistence modules
    Emerson G. Escolar, Hideto Asashiba, Ken Nakashima, Michio Yoshiwaki
    The 54th Symposium on Ring Theory and Representation Theory, Sep. 2022
    Oral presentation

  • Interleavings and Matchings as Representations
    Emerson G. Escolar, Killian Meehan, Michio Yoshiwaki
    日本応用数理学会 第18回 研究部会連合発表会, Mar. 2022, Japanese
    Oral presentation

  • Interval Decomposability/Approximation of Persistence Modules, and their Computation
    Emerson G. Escolar
    TDA Week, Feb. 2022, English
    [Invited]
    Invited oral presentation

  • Interval Decomposability/Approximation of Persistence Modules, and their Computation
    Emerson G. Escolar
    Asia Pacific Seminar on Applied Topology and Geometry, Jan. 2022, English
    [Invited]
    Invited oral presentation

  • Introduction to Topological Data Analysis
    Emerson G. Escolar
    Ateneo de Manila University, School of Science & Engineering, Department of Mathematics, Mathematics Research Seminar Series, Oct. 2021, English
    [Invited]
    Public discourse

  • Interval Decomposability/Approximation of Persistence Modules, and their Computation
    Emerson G. Escolar
    Topics on Topological Data Analysis, Aug. 2021, Japanese
    [Invited]
    Invited oral presentation

  • Mapping Firms' Locations in Technological Space: A Topological Analysis of Patent Statistics
    Emerson G. Escolar
    ILJU POSTECH MINDS Workshop on Topological Data Analysis and Machine Learning, Jul. 2021, English
    [Invited]
    Invited oral presentation

  • 区間表現による2Dパーシステント表現の近似
    中島 健, 浅芝 秀人, Emerson G. Escolar, 吉脇 理雄
    日本応用数理学会 2021年 研究部会連合発表会, Mar. 2021
    Oral presentation

  • The Whole in the Parts: Putting nD Persistence Modules Inside Indecomposable (n+1)D Ones
    M. Buchet, E.G. Escolar
    日本応用数理学会 2021年 研究部会連合発表会, Mar. 2021, Japanese, online
    Oral presentation

  • Introduction to Topological Data Analysis: Ideas and Applications
    Emerson G. Escolar
    departmental colloquium talk (2021 in-house training program), Jan. 2021, Department of Mathematics and Computer Science, College of Science, University of the Philippines Baguio (online)
    Public discourse

  • Mapping Firms' Locations in Technological Space: A Topological Analysis of Patent Statistics
    Emerson G. Escolar, 平岡裕章, 伊神満, Yasin Ozcan
    [2nd AIP Open Seminar] Talks by Topological Data Analysis Team, Nov. 2020, Online
    Public discourse

  • Mapperを用いた企業の技術戦略の位相的データ解析
    Emerson G. Escolar, 平岡裕章, 伊神満, Yasin Ozcan
    日本応用数学会2020年度年会, 正会員主催OS：位相的データ解析, Sep. 2020, online, zoom
    Oral presentation

  • Mapperを用いた企業の技術戦略の位相的データ解析
    Emerson G. Escolar, 平岡裕章, 伊神満, Yasin Ozcan
    TDA for Applications - Tutorial & Workshop, Jun. 2020, online
    Public discourse

  • Mapping firms’ locations in technological space: a topological analysis of patent statistics
    Emerson G. Escolar, 平岡裕章, 伊神満, Yasin Ozcan
    Kyoto University Applied Mathematics Seminar, May 2020, Kyoto University, Kyoto
    Public discourse

  • Mapping firms’ locations in technological space: A topological analysis of patent statistics
    Emerson G. Escolar, 平岡裕章, 伊神満, Yasin Ozcan
    日本数学会 2020年度年会, Mar. 2020, （会は中止だが、発表は成立）
    Oral presentation

  • 企業の技術戦略の位相的データ解析
    Emerson G. Escolar, 平岡裕章, 伊神満, Yasin Ozcan
    2019年度応用数学合同研究集会, Dec. 2019, 龍谷大学
    Oral presentation

  • Every 1D Persistence Module is a Restriction of Some Indecomposable 2D Persistence Module
    M. Buchet, E.G. Escolar
    ICIAM 2019 Thematic Minisymposium: "Geometry and Topology in Data Analysis", Jul. 2019, Valencia, Spain, Spain
    Oral presentation

  • Every 1D Persistence Module is a Restriction of Some Indecomposable 2D Persistence Module
    M. Buchet, E.G. Escolar
    Workshop "Computational Applications of Quiver Representations: TDA and QPA", May 2019, Bielefeld University, Bielefeld, Germany, Germany, International conference
    Oral presentation

  • Every 1D Persistence Module is a Restriction of Some Indecomposable 2D Persistence Module
    M. Buchet, E.G. Escolar
    MSJ Spring Meeting 2019, Mar. 2019, Japanese, Tokyo Institute of Technology
    Oral presentation

  • Every 1D Persistence Module is a Restriction of Some Indecomposable 2D Persistence Module
    M. Buchet, E.G. Escolar
    Workshop on Applied Topology 2019, Jan. 2019, Kyoto
    Oral presentation

  • Realization of Indecomposable Persistence Modules of Large Dimension
    M. Buchet, E.G. Escolar
    Applied Geometry & Topology 2018, Jul. 2018, Kyoto University, Kyoto
    Oral presentation

  • Computing Indecomposable Decompositions of Persistence Modules
    guest lecture at Institute of Geometry, Jun. 2018, TU Graz, Graz, Austria
    Oral presentation

  • Realizations of Indecomposable Persistence Modules of Arbitrarily Large Dimension
    M. Buchet, E.G. Escolar
    34th International Symposium on Computational Geometry (SoCG 2018), Jun. 2018, Budapest, Hungary, Hungary, International conference
    Oral presentation

  • Vietoris-Rips Realization of Indecomposable Persistence Modules of Arbitrarily Large Dimension
    M. Buchet, E.G. Escolar
    MSJ Spring Meeting 2018, Mar. 2018, The University of Tokyo
    Oral presentation

  • Representation Theory and Persistent Homology in TDA
    RIKEN-AIP Math Group Joint Seminar, Izuyama Kensyuu Center
    Oral presentation

  • Vietoris-Rips Realization of Indecomposable Persistence Modules of Arbitrarily Large Dimension
    M. Buchet, E.G. Escolar
    2017年度応用数学合同研究集会, Dec. 2017, 龍谷大学瀬田キャンパス
    Oral presentation

  • Vietoris-Rips Realization of Indecomposable Persistence Modules of Large Dimension
    M. Buchet, E.G. Escolar
    Applied Algebraic Topology 2017, Hokkaido University, Sapporo, Japan, International conference
    Oral presentation

  • An Introduction to Quiver Representation Theory for Topological Data Analysis
    E.G. Escolar
    A3 foresight workshop: Modeling and Simulation of Hierarchical and Heterogeneous Flow Systems with Applications to Materials Science III, Nov. 2016, Tohoku Forum for Creativity, Tohoku University
    Oral presentation

  • Persistence of Common Topological Features via Commutative Ladder Quivers
    E.G. Escolar, Y. Hiraoka
    EASIAM 2016, Jun. 2016, University of Macau, Macau, China
    Oral presentation

  • Introduction to representation theory for topological data analysis
    Emerson Gaw ESCOLAR
    A3 foresight winter school on Mathematics on Materials Science: Topological Data Analysis and Dynamics, Feb. 2016, AIMR, Tohoku University
    Oral presentation

  • Matrix Method for Persistence Modules on Commutative Ladders of Finite Type
    Minisymposium on Topological Data Analysis and Dynamics, 8th International Congress on Industrial and Applied Mathematics, Aug. 2015, Beijing, China
    Oral presentation

  • Morse Reduction for Persistence Modules on Commutative Ladders of Finite Type
    E.G. Escolar, Y. Hiraoka
    2014年度応用数学合同研究集会, Dec. 2014, 龍谷大学
    Oral presentation

  • Computing Persistence Modules of Quiver Complexes
    E.G. Escolar, Y. Hiraoka
    Short presentation (student session), Mathematics of Fluid Dynamics and Material Science, 1st Joint Conference of A3 Foresight Program, Nov. 2014, International Convention Center Jeju, Korea, International conference
    Oral presentation

  • Optimal Cycles in Homology via Linear Programming
    E.G. Escolar, Y. Hiraoka
    IMI Workshop on Optimization in the Real World, Oct. 2014, Kyushu University
    Oral presentation

  • Computing Persistence Modules on Commutative Ladders of Finite Type
    E.G. Escolar, Y. Hiraoka
    MSJ Autumn Meeting 2014, Sep. 2014, Hiroshima University
    Oral presentation

  • Computing Persistence Modules on Commutative Ladder Quivers of Finite Type
    E.G. Escolar, Y. Hiraoka
    The 4th International Congress on Mathematical Software. Session: Software for Computational Topology, Hanyang University, Seoul, Korea, International conference
    Oral presentation

  • Computing Persistence Modules on Commutative Ladder Quivers of Finite Type
    E.G. Escolar, Y. Hiraoka
    Workshop on Topological Data Analysis, Department of Mathematics. Kyoto University, International conference
    Oral presentation

  • Optimal Cycles of Homology Groups
    Intersection of Pure Mathematics and Applied Mathematics IV, Feb. 2014, Kyushu University, Fukuoka, Japan
    Oral presentation

  • Morse Reduction for Zigzag Complexes
    E.G. Escolar, Y. Hiraoka
    AKOOS-PNU International Conference 2014, Busan National University, Busan, South Korea, International conference
    Oral presentation

  • Morse Reduction for Zigzag Complexes
    E.G. Escolar, Y. Hiraoka
    The 9th East Asia SIAM Conference, The 2nd Conference on Industrial and Applied Mathematics (EASIAM-CIAM 2013), Institut Teknologi Bandung, Bandung, West Java, Indonesia, International conference
    Oral presentation

■ Affiliated Academic Society
  • 日本応用数理学会

  • 日本数学会

■ Works
■ Research Themes
  • トポロジカルな視点による様々なプロセスの新しいデータ解析技術の開発
    Escolar EmersonGaw
    日本学術振興会, 科学研究費助成事業, 基盤研究(C), 神戸大学, 01 Apr. 2024 - 31 Mar. 2027

  • Establishing data descriptive science and its cross-disciplinary applications
    白井 朋之, 本多 正平, Escolar EmersonGaw
    Japan Society for the Promotion of Science, Grants-in-Aid for Scientific Research Grant-in-Aid for Transformative Research Areas (A), Grant-in-Aid for Transformative Research Areas (A), Kyushu University, 16 Jun. 2022 - 31 Mar. 2027

  • 高次元のリスク認知構造の新たな表現に関する検討
    村山 留美子, Escolar EmersonGaw
    日本学術振興会, 科学研究費助成事業, 挑戦的研究(萌芽), 神戸大学, 30 Jun. 2023 - 31 Mar. 2026

  • ESCOLAR Emerson Gaw, 湯浅正洋
    公益財団法人カシオ科学振興財団, 第40回研究助成, Dec. 2022 - Jan. 2024, Principal investigator

■ Social Contribution Activities
■ Academic Contribution Activities
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