Organization
School of Science Associate Professor
Title
Associate Professor
External link
Fujikawa Ege
Degree
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博士（理学） ( 東京工業大学 )
Research Interests
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リーマン面
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Teichmuller space
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擬等角写像
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モジュライ空間
Research Areas
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Natural Science / Basic analysis / 複素解析学
Education
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Tokyo Institute of Technology Graduate School of Science and Engineering Department of Mathematics
2000.4 - 2003.3
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Tokyo Institute of Technology Graduate School of Science and Engineering Department of Mathematics
1998.4 - 2000.3
Research History
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Tokyo Institute of Technology School of Science Associate Professor
2018.9
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Chiba University Associate Professor
2017.4 - 2018.8
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Chiba University Graduate School of Science Associate Professor
2008.4 - 2017.3
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Chiba University Graduate School of Science Assistant Professor
2007.10 - 2008.3
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Sophia University Faculty of Science and Technology Assistant Professor
2007.4 - 2007.9
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Sophia University Faculty of Science and Technology
2006.4 - 2007.3
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日本学術振興会特別研究員 (PD)
2004.4 - 2006.3
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Kyoto University Research Institute for Mathematical Sciences
2003.10 - 2004.3
Professional Memberships
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THE MATHEMATICAL SOCIETY OF JAPAN
Committee Memberships
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日本数学会 地方区代議員
2024.3 - 2025.2
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Japan Science & Engineering Challenge judge
2024
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日本学術会議 数理科学委員会数学分科会委員
2020.10 - 2026.9
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日本学術会議 連携会員
2020.10 - 2026.9
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日本数学会 地方区代議員
2019.3 - 2020.2
Committee type：Academic society
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文部科学省 科学技術・学術審議会 研究環境基盤部会 専門委員
2014.7 - 2017.3
Committee type：Academic society
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財団法人 数学オリンピック財団 理事
2012.6 - 2014.5
Committee type：Academic society
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日本数学会 雑誌「数学」常任編集委員
2010.7 - 2012.6
Committee type：Academic society
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財団法人 数学オリンピック財団 評議員
2010.6 - 2012.5
Committee type：Academic society
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財団法人 数学オリンピック財団 JCIMO委員
2010.4 - 2015.3
Committee type：Academic society
Papers
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The teichmüller space of a countable set of points on a riemann surface Reviewed
Ege Fujikawa, Masahiko Taniguchi
Conformal Geometry and Dynamics 21 ( 2 ) 64 - 77 2017
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Topological characterization of the asymptotically trivial mapping class group Invited Reviewed
Ege Fujikawa
Handbook of Group Actions Vol 1 ( ALM 31 ) 309 - 332 2015
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Coherence of Limit Points in the Fibers over the Asymptotic Teichmuller Space Reviewed
Ege Fujikawa
Computational Methods and Function Theory 14 ( 2-3 ) 357 - 370 2014.10
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Periodicity of asymptotic Teichmuller modular transformation Reviewed
Ege Fujikawa
Contemporary Mathematics 590 39 - 50 2013
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The nielsen realization problem for asymptotic teichm̈uller modular groups Reviewed
Ege Fujikawa, Katsuhiko Matsuzaki
Transactions of the American Mathematical Society 365 ( 6 ) 3309 - 3327 2013
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Non-divergent infinitely discrete Teichmüller modular transformation Reviewed
Ege Fujikawa, Katsuhiko Matsuzaki
Proceedings of the 19th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications 97 - 102 2013
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Discontinuity of asymptotic Teichmuller modular group Reviewed
Ege Fujikawa
Contemporary Mathematics 575 77 - 88 2012
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STABLE QUASICONFORMAL MAPPING CLASS GROUPS AND ASYMPTOTIC TEICHMULLER SPACES Reviewed
Ege Fujikawa, Katsuhiko Matsuzaki
AMERICAN JOURNAL OF MATHEMATICS 133 ( 3 ) 637 - 675 2011.6
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Structure theorem for holomorphic self-covers and its applications Reviewed
Ege Fujikawa, Katsuhiko Matsuzaki, Masahiko Taniguchi
RIMS Kôkyûroku Bessatsu B17 21 - 36 2010
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Elliptic modular transformations on Teichmüller and asymptotic Teichmüller spaces Reviewed
Ege Fujikawa
RIMS Kôkyûroku Bessatsu B17 1 - 20 2010
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Limit set of quasiconformal mapping class group on asymptotic Teichmüller space Reviewed
Ege Fujikawa
Lecture note series in the Ramanujan Mathematical Society ( 10 ) 167 - 178 2010
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The projection of limit sets of modular groups on asymptotic Teichmüller spaces Reviewed
Ege Fujikawa, Katsuhiko Matsuzaki
Proceedings of the 16th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications 86 - 92 2009
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Pure mapping class group acting on teichmüller space Reviewed
Ege Fujikawa
Conformal Geometry and Dynamics 12 ( 15 ) 227 - 239 2008.12
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Dynamics on teichmüller spaces and self-covering of riemann surfaces Reviewed
Ege Fujikawa, Katsuhiko Matsuzaki, Masahiko Taniguchi
Mathematische Zeitschrift 260 ( 4 ) 865 - 888 2008.12
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Elliptic quasiconformal mapping classes acting on asymptotic Teichmüller spaces Reviewed
Ege Fujikawa, Katsuhiko Matsuzaki
Proceedings of the 15th International Conference on Finite or Infinite Dimensional Complex Analysis and Applications, Osaka Municipal Universities Press 169 - 173 2008
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Non-stationary and discontinuous quasiconformal mapping class groups Reviewed
Ege Fujikawa, Katsuhiko Matsuzaki
Osaka Journal of Mathematics 44 ( 1 ) 173 - 185 2007.3
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Smale's mean value conjecture and the coefficients of univalent functions Reviewed
Anthony Conte, Ege Fujikawa and Nikola Lakic
Proceedings of the American Mathematical Society 135 ( 10 ) 3295 - 3300 2007
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Another approach to the automorphism theorem for Teichmuller spaces Reviewed
Ege Fujikawa
In the Tradition of Ahlfors-Bers, IV 432 39 - 44 2007
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Geometric function theory and Smale's mean value conjecture Reviewed
Ege Fujikawa and Toshiyuki Sugawa
Proceedings of the Japan Academy, Ser. A 82 ( 7 ) 97 - 100 2006.9
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The action of geometric automorphisms of asymptotic Teichmuller spaces Reviewed
Ege Fujikawa
Michigan Mathematical Journal 54 ( 2 ) 269 - 282 2006
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Recurrent and periodic points for isometries of L-infinity spaces Reviewed
Ege Fujikawa, Katsuhiko Matsuzaki
Indiana University Mathematics Journal 55 ( 3 ) 975 - 997 2006
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A Lower Bound of Maximal Dilatations of Quasiconformal Automorphisms Acting on Fuchsian Groups Reviewed
Ege Fujikawa
Kodai Mathematical Journal 28 ( 2 ) 220 - 229 2005
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The order of periodic elements of teichmüller modular groups Reviewed
Ege Fujikawa
Tohoku Mathematical Journal 57 ( 1 ) 45 - 51 2005
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On the action of the mapping class group for Riemann surfaces of infinite type Reviewed
Ege Fujikawa, Hiroshige Shiga, Masahiko Taniguchi
Journal of the Mathematical Society of Japan 56 ( 4 ) 1069 - 1086 2004
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Modular groups acting on infinite dimensional Teichmuller spaces Reviewed
E Fujikawa
IN THE TRADITION OF AHLFORS AND BERS, III 355 ( 355 ) 239 - 253 2004
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The order of conformal automorphisms of riemann surfaces of infinite type Reviewed
Ege Fujikawa
Kodai Mathematical Journal 26 ( 1 ) 16 - 25 2003
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Limit sets and regions of discontinuity of Teichmuller modular groups Reviewed
E Fujikawa
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY 132 ( 1 ) 117 - 126 2003
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Discreteness of the mapping class group for Riemann surfaces of infinite analytic type Reviewed
Ege Fujikawa, Hiroshige Shiga and Masahiko Taniguchi
PROCEEDINGS OF THE SECOND ISAAC CONGRESS, VOLS 1 AND 2 7 1015 - 1021 2000
MISC
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現代数学への誘い / 複素解析学入門
藤川英華
現代数学 2025年 ( 2月号 ) 2025.2
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複素関数の微積分からリーマン面のモジュライ空間へ : タイヒミュラー空間論への道すじ Invited
藤川 英華
サイエンス社 数理科学 特集：「複素解析の視点」－ 遍在する複素関数 － 52 ( 10 ) 21 - 27 2014.10
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藤川 英華
日本評論社 数学セミナー 特集：不等式の世界 48 ( 2 ) 22 - 25 2009.2
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Limit sets on Teichmuller space and on asymptotic Teichmuller space(Complex Dynamics and its Related Topics)
Fujikawa Ege
RIMS Kokyuroku 1537 94 - 98 2007.2
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Discontinuity of the action of pure mapping class groups(Complex Analysis and Geometry of Hyperbolic Spaces)
Fujikawa Ege
RIMS Kokyuroku 1518 146 - 153 2006.10
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The dynamics on Teichmuller spaces induced by holomorphic self-coverings(Complex Dynamics and its Related Fields)
Fujikawa Ege, Matsuzaki Katsuhiko, Taniguchi Masahiko
RIMS Kokyuroku 1494 44 - 48 2006.5
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Properties of limit sets of Teichmuller modular groups (Complex Dynamics)
Fujikawa Ege
RIMS Kokyuroku 1447 66 - 71 2005.8
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Biholomorphic maps between asymptotic Teichmuller spaces (Perspectives of Hyperbolic Spaces II)
Fujikawa Ege
RIMS Kokyuroku 1387 95 - 99 2004.7
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The order of conformal automorphisms of Riemann surfaces of infinite type : supplement (Perspectives of Hyperbolic Spaces)
Fujikawa Ege
RIMS Kokyuroku 1329 62 - 68 2003.6
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Dynamics of modular groups acting on infinite dimensional Teichmuller spaces (Complex dynamics and related fields)
Fujikawa Ege
RIMS Kokyuroku 1269 137 - 142 2002.6
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Sufficient conditions for Teichmuller modular groups to be of the second kind (Hyperbolic Spaces and Discrete Groups II)
Fujikawa Ege
RIMS Kokyuroku 1270 88 - 92 2002.6
Awards
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令和元年度理学院若手教員教育賞
2020.3 Tokyo Institute of Technology
Ege Fujikawa
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千葉大学先進科学賞
2013.9 千葉大学
藤川 英華
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第11回大学女性協会守田科学研究奨励賞
2009.6 社団法人 大学女性協会
藤川 英華
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日本数学会賞建部賢弘奨励賞
2006.9 社団法人 日本数学会
藤川 英華
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手島記念研究賞博士論文賞
2004.3 財団法人 手島工業教育資金団
藤川 英華
Research Projects
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無限次元タイヒミュラー空間上の複素力学系的理論の構築
Grant number：19K03513 2019.4 - 2024.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C) Grant-in-Aid for Scientific Research (C)
Ege Fujikawa
Authorship：Principal investigator
Grant amount：\4420000 （ Direct Cost: \3400000 、 Indirect Cost：\1020000 ）
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Research on the Teichmuller spaces of fractal structures
Grant number：15K04925 2015.4 - 2018.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
Taniguchi Masahiko, Fujimura MASAYO, Matsuzaki KATSUHIKO, Fujikawa EGE
Grant amount：\4550000 （ Direct Cost: \3500000 、 Indirect Cost：\1050000 ）
We formulate the concept of the Teichmuller space of a fractal structure and establish the fundamental theory on it. This is one of the main purposes of this research project. More precisely, we introduce the Teichmuller space of a countable set of points associated with the fractal structure on a general Riemann surface. Furthermore, we show that such a space admits a natural complex analytic structure if the fractal structure possesses standard bounded geometry.
The second purpose of this research project is to introduce geometric global coordinates for such a Teichmuller space. On this point, for several important cases such as the iterated function systems by Mobius transformations, Kleinian group actions, and infinitely generated Koebe group actions, we introduce natural geometric global coordinates on the Teichmuller space of the corresponding fractal structure, and obtain a global representation of it. -
New perspective on Riemann surfaces of infinite genus and their deformation spaces
Grant number：26610014 2014.4 - 2017.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Challenging Exploratory Research
SHIGA Hiroshige
Grant amount：\3510000 （ Direct Cost: \2700000 、 Indirect Cost：\810000 ）
On the deformation theory of Riemann surfaces, quasiconformal maps have played an important role. In this project, we succeeded in constructing a counterexample of Sullivan-Thurston’claim for quasiconformal motions. We also give a necessary and sufficient condition for a holomorphic motion of a subset of the Riemann sphere parametrized over a Riemann surface to be extended to a holomorphic motion of the Riemann sphere. The condition is given by the monodromy of the motion. This result is related to quasiconformal maps but it has also a topological aspect, the monodromy.
A new concept of Teichmuller space for Riemann surface with countably many points is considered. The research of those Teichmuller spaces will generalize holomorphic motions to those of subsets of Riemann surfaces. Therefore, it will give new interesting problems to related fields of mathematics. -
無限次元タイヒミュラー空間の幾何構造の構築
2013.4 - 2019.3
科学研究費補助 基盤研究(C)
藤川 英華
Authorship：Principal investigator Grant type：Competitive
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Resolution of conjugation problems on circle diffeomorphism groups
Grant number：24654035 2012.4 - 2016.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Challenging Exploratory Research
Matsuzaki Katsuhiko, TANIGUCHI MASAHIKO, FUJIKAWA EGE
Grant amount：\3770000 （ Direct Cost: \2900000 、 Indirect Cost：\870000 ）
(1) We introduced the Teichmueller space of circle diffeomorphisms with Hoelder continuous derivatives and established its foundation. (2) We proved that if a group of Moebius transformations is conjugate to a group of circle diffeomorphisms with Hoelder continuous derivatives by a symmetric homeomorphism, then the conjugating map actually has a Hoelder continuous derivative of the same order. (3) We obtained a necessary and sufficient condition for a group of circle diffeomorphisms with α-Hoelder continuous derivatives for α>1/2 to be conjugate to a group of Moebius transformations by a circle diffeomorphism with an α-Hoelder continuous derivative in terms of uniform integrability of the complex dilatations of quasiconformal extensions of the group elements. (4) Even if we do not assume α>1/2, we showed that if the integrability of quasiconformal extensions is uniformly bounded by a certain constant sufficiently small, then the above result still holds true.
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無限次元タイヒミュラー空間論の新展開：モジュライ空間の構成
2011.4 - 2013.3
科学研究費補助金 若手研究(B)
藤川 英華
Authorship：Principal investigator Grant type：Competitive
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Various aspects on the study of Geometric Function Theory
Grant number：22340025 2010.4 - 2015.3
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
SUGAWA Toshiyuki, SHIGA Hiroshige, YANAGIHARA Hiroshi, SAKAN Ken-ichi, MATSUZAKI Katsuhiko, FUJIKAWA Ege, MIZUTA Yoshihiro, TANIGUCHI Masahiko, FUJIWARA Koji, ABE Makoto
Grant amount：\17290000 （ Direct Cost: \13300000 、 Indirect Cost：\3990000 ）
Geometric Function Theory deals with problems finding relations between geometrically described (simply-connected) domains in the plane and analytic properties of conformal mappings onto them. Bieberbach conjectured that, for a conformal mapping f(z)=a_0+a_1z+a_2z^2+... normalized by a_0=0, a_1=1, the modulus |a_n| of a_n is not greater than n.This conjecture was finally proved by de Branges in his 1985 paper. In the present research project, for example, we showed that the set of conformal mappings as above with half-integral coefficients consists of exactly 21 functions. The similar set for the integral coefficients was previously known to consist of 9 functions.
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無限次元タイヒミュラー空間と複素解析的モジュライ空間の構造の解明
2008.4 - 2011.3
科学研究費補助金 若手研究(B)
藤川 英華
Authorship：Principal investigator Grant type：Competitive
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Teichmuller spaces of symmetric structures and the rigidity and fixed-point problems of quasiconformal mapping class groups
Grant number：20340030 2008 - 2012
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (B)
MATSUZAKI Katsuhiko, TANIGUCHI Masahiko, SUGAWA Toshiyuki, SAKAN Kenichi, SHIGA Hiroshige, NAKANISHI Toshihiro, MIYACHI Hideki, ITO Kentaro, FUJIKAWA Ege
Grant amount：\16900000 （ Direct Cost: \13000000 、 Indirect Cost：\3900000 ）
We define various classes for self-homeomorphisms of the unit circle from a viewpoint of their quasiconformal extension, and study the parameter spaces of those families, which are regarded as Teichmuller spaces. In particular, for the Teichmuller space of symmetric homeomorphisms, we consider conditions for a group acting on this space to have a fixed point in it. As an application, we give a condition for a group of diffeomorphisms to be conjugate to the canonical group action of the circle (Mobius transformations) as well as a condition for the deformation of such a group to be trivial (that is, to have rigidity).
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リーマン面の双曲幾何学と漸近的変形空間の正則自己同型群
2007.4 - 2008.3
財団法人日本科学協会 笹川科学研究助成金
藤川 英華
Authorship：Principal investigator Grant type：Competitive
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無限次元タイヒミュラー空間とモジュラー群の作用
2007.4 - 2008.3
財団法人実吉奨学会 研究助成金
藤川 英華
Authorship：Principal investigator Grant type：Competitive
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Extension property of holomorphic maps and the structure of complex manifolds
Grant number：19540100 2007 - 2009
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
KATO Masahide, YOKOYAMA Kazuo
Grant amount：\2080000 （ Direct Cost: \1600000 、 Indirect Cost：\480000 ）
We are studying a method to get some information of the structure of a given complex manifold by measuring the extendibility of holomorphic maps of Hartogs domains to the given manifold. As an application of the method, we have obtained the following result. For a finitely generated three dimensional discrete projective transformation group Γ with some discontinuity condition, we can define canonically a non-singular quotient space X(Γ) of an open subset of a projective 3-space. We have shown that, if X(Γ) contains a compact connected component with positive algebraic dimension, then X(Γ) is connected, and that X(Γ) is biholomorphic to one of the three kinds of well-known 3-folds.
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Algebraic analytical study of non-local differential Equations and convolution equations
Grant number：19540165 2007 - 2008
Japan Society for the Promotion of Science Grants-in-Aid for Scientific Research Grant-in-Aid for Scientific Research (C)
ISHIMURA Ryuichi, OKADA Yasunori, FUJIKAWA Ege, TSUTSUI Toru, NAGISA Masaru, TATUI Hiroki, MIYAMOTO Ikuko
Grant amount：\4420000 （ Direct Cost: \3400000 、 Indirect Cost：\1020000 ）
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無限次元タイヒミュラー空間と擬等角写像類群の力学系
2006.4 - 2008.3
科学研究費補助金 若手研究（スタートアップ）
藤川 英華
Authorship：Principal investigator Grant type：Competitive
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無限次元タイヒミュラー空間上に作用するモジュラー群の力学系
2004.4 - 2006.3
科学研究費補助金 特別研究員奨励費
藤川 英華
Authorship：Principal investigator Grant type：Competitive
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無限次元タイヒミュラー空間上に作用するモジュラー群の力学系
2003.4 - 2004.3
財団法人住友財団 基礎科学研究助成金
藤川 英華
Authorship：Principal investigator Grant type：Competitive
Social Activities
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ドーナツの変形って何だろう？
Role(s)： Lecturer
東京大学 数学の魅力 ー女子中高生のためにー 2019.3
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Analysis and Geometry of Riemann Surfaces and Related Topics
Role(s)： Planner
2013.6
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「数学を楽しむ： ドーナツの形はどのくらいあるか」
Role(s)： Lecturer
サイエンスカフェ・イン・高輪 2012.3
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第43回函数論サマーセミナー
Role(s)： Planner, Organizing member
2008.8
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京都大学数理解析研究所共同研究「無限次元タイヒミュラー空間とモジュライ空間」
Role(s)： Planner
京都大学数理解析研究所 2007.11
Media Coverage
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高校生と数学者の出会い
日仏科学 フォーラム 2008.10