"Dessin d'enfant"의 두 판 사이의 차이

수학노트
둘러보기로 가기 검색하러 가기
imported>Pythagoras0
 
(사용자 2명의 중간 판 18개는 보이지 않습니다)
1번째 줄: 1번째 줄:
 +
==introduction==
 +
* Grothendieck's theory of dessins provides a bridge between algebraic numbers and combinatorics
 +
* a dessin is essentially a bipartite graph embedded on a compact, oriented surface (without boundary), and that the absolute Galois group <math>\operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})</math> acts on (isomorphism classes of) dessins.
 +
* Grothendieck-Teichmüller group of a finite group <math>G</math>, denoted <math>\mathcal{GT}(G)</math>
 +
* there is an action of <math>\mathcal{GT}(G)</math> on those dessins whose monodromy group is <math>G</math>, and the Galois action on the same objects factors via a map <math>\operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q}) \longrightarrow \mathcal{GT}(G)</math>
 +
* Motivation for the study of all groups <math>\mathcal{GT}(G)</math>, for all groups <math>G</math>, is increased by the fact that the combined map
 +
:<math>
 +
\operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q}) \longrightarrow \mathcal{GT} := \lim_G \, \mathcal{GT}(G)
 +
</math>
 +
is injective.
 +
 +
 
==memo==
 
==memo==
 
* http://www.neverendingbooks.org/index.php/kleins-dessins-denfant-and-the-buckyball.html
 
* http://www.neverendingbooks.org/index.php/kleins-dessins-denfant-and-the-buckyball.html
7번째 줄: 19번째 줄:
 
* [[Grothendieck-Teichmuller theory]]
 
* [[Grothendieck-Teichmuller theory]]
  
 +
 +
==computational resource==
 +
* https://github.com/vbeffara/Simulations
  
 
==encyclopedia==
 
==encyclopedia==
 
* http://en.wikipedia.org/wiki/Dessin_d'enfant
 
* http://en.wikipedia.org/wiki/Dessin_d'enfant
 +
 +
 +
==books==
 +
* Guralnick, Robert M., and John Shareshian. 2007. Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I: Generic Covers and Covers with Many Branch Points. American Mathematical Soc.
 +
* Schneps, Leila, ed. 1994. The Grothendieck Theory of Dessins D’enfants. Vol. 200. London Mathematical Society Lecture Note Series. Cambridge: Cambridge University Press. http://www.ams.org/mathscinet-getitem?mr=1305390.
  
  
 
==expositions==
 
==expositions==
 +
* Norbert A'Campo, Lizhen Ji, Athanase Papadopoulos, On Grothendieck's tame topology, http://arxiv.org/abs/1603.03016v1
 +
* Cueto, Moises Herradon. “The Field of Moduli and Fields of Definition of Dessins D’enfants.” arXiv:1409.7736 [math], September 26, 2014. http://arxiv.org/abs/1409.7736.
 
* Planat, Michel. “Drawing Quantum Contextuality with ‘Dessins D’enfants’.” arXiv:1404.6986 [math-Ph, Physics:quant-Ph], April 28, 2014. http://arxiv.org/abs/1404.6986.
 
* Planat, Michel. “Drawing Quantum Contextuality with ‘Dessins D’enfants’.” arXiv:1404.6986 [math-Ph, Physics:quant-Ph], April 28, 2014. http://arxiv.org/abs/1404.6986.
 
* Jones, [http://www.emis.de/journals/SLC/wpapers/s35jones.pdf Dessins d'enfants: bipartite maps and Galois groups]
 
* Jones, [http://www.emis.de/journals/SLC/wpapers/s35jones.pdf Dessins d'enfants: bipartite maps and Galois groups]
18번째 줄: 40번째 줄:
 
* Robalo, [https://dspace.ist.utl.pt/bitstream/2295/575330/1/dissertacao.pdf Galois Theory towards Dessins d'Enfants], masters thesis
 
* Robalo, [https://dspace.ist.utl.pt/bitstream/2295/575330/1/dissertacao.pdf Galois Theory towards Dessins d'Enfants], masters thesis
 
* [http://www.math.purdue.edu/~egoins/notes/reuf4.pdf Introduction to Dessins d'Enfants], undergraduate research program
 
* [http://www.math.purdue.edu/~egoins/notes/reuf4.pdf Introduction to Dessins d'Enfants], undergraduate research program
−
 
  
 
==articles==
 
==articles==
 +
* Pierre Guillot, The Grothendieck-Teichmüller group of <math>PSL(2, q)</math>, arXiv:1604.04415 [math.GR], April 15 2016, http://arxiv.org/abs/1604.04415
 +
* Khashayar Filom, Ali Kamalinejad, Dessins on Modular Curves, http://arxiv.org/abs/1603.01693v1
 +
* Planat, Michel, and Hishamuddin Zainuddin. “Zoology of Atlas-Groups: Dessins D’enfants, Finite Geometries and Quantum Commutation.” arXiv:1601.04865 [math-Ph, Physics:quant-Ph], January 19, 2016. http://arxiv.org/abs/1601.04865.
 +
* Hilany, Boulos El. “Counting Positive Intersection Points of a Trinomial and a <math>\mathbf{T}</math>-Nomial Curves via Groethendieck’s Dessin D’enfant.” arXiv:1512.05688 [math], December 17, 2015. http://arxiv.org/abs/1512.05688.
 +
* Wang, Na-Er, Roman Nedela, and Kan Hu. “Totally Symmetric Dessins with Nilpotent Automorphism Groups of Class Three.” arXiv:1511.06863 [math], November 21, 2015. http://arxiv.org/abs/1511.06863.
 +
* Cueto, Moisés Herradón. “An Explicit Quasiplatonic Curve with Field of Moduli <math>\mathbb Q(\sqrt[3]{2})</math>.” arXiv:1509.05819 [math], September 18, 2015. http://arxiv.org/abs/1509.05819.
 +
* Fine, Jonathan 2015Bias and Dessins. arXiv:1506.06389 [math]. http://arxiv.org/abs/1506.06389, accessed July 11, 2015.
 +
* Beffara, Vincent. ‘Dessins D’enfants for Analysts’. arXiv:1504.00244 [math], 1 April 2015. http://arxiv.org/abs/1504.00244.
 +
* Bose, Sownak, James Gundry, and Yang-Hui He. “Gauge Theories and Dessins d’Enfants: Beyond the Torus.” arXiv:1410.2227 [hep-Th], October 8, 2014. http://arxiv.org/abs/1410.2227.
 
* Guillot, Pierre. 2014. “Some Computations with the Grothendieck-Teichm"uller Group and Equivariant Dessins D’enfants.” arXiv:1407.3112 [math], July. http://arxiv.org/abs/1407.3112.
 
* Guillot, Pierre. 2014. “Some Computations with the Grothendieck-Teichm"uller Group and Equivariant Dessins D’enfants.” arXiv:1407.3112 [math], July. http://arxiv.org/abs/1407.3112.
 
* Kazarian, Maxim, and Peter Zograf. 2014. “Virasoro Constraints and Topological Recursion for Grothendieck’s Dessin Counting.” arXiv:1406.5976 [math], June. http://arxiv.org/abs/1406.5976.
 
* Kazarian, Maxim, and Peter Zograf. 2014. “Virasoro Constraints and Topological Recursion for Grothendieck’s Dessin Counting.” arXiv:1406.5976 [math], June. http://arxiv.org/abs/1406.5976.
 +
[[분류:migrate]]
  
−
 
+
==메타데이터==
−
 
+
===위키데이터===
−
==books==
+
* ID : [https://www.wikidata.org/wiki/Q3024615 Q3024615]
−
* Guralnick, Robert M., and John Shareshian. 2007. Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I: Generic Covers and Covers with Many Branch Points. American Mathematical Soc.
+
===Spacy 패턴 목록===
−
* Schneps, Leila, ed. 1994. The Grothendieck Theory of Dessins D’enfants. Vol. 200. London Mathematical Society Lecture Note Series. Cambridge: Cambridge University Press. http://www.ams.org/mathscinet-getitem?mr=1305390.
+
* [{'LOWER': 'dessin'}, {'LEMMA': "d'enfant"}]

2021년 2월 17일 (수) 01:22 기준 최신판

introduction

  • Grothendieck's theory of dessins provides a bridge between algebraic numbers and combinatorics
  • a dessin is essentially a bipartite graph embedded on a compact, oriented surface (without boundary), and that the absolute Galois group \(\operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q})\) acts on (isomorphism classes of) dessins.
  • Grothendieck-Teichmüller group of a finite group \(G\), denoted \(\mathcal{GT}(G)\)
  • there is an action of \(\mathcal{GT}(G)\) on those dessins whose monodromy group is \(G\), and the Galois action on the same objects factors via a map \(\operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q}) \longrightarrow \mathcal{GT}(G)\)
  • Motivation for the study of all groups \(\mathcal{GT}(G)\), for all groups \(G\), is increased by the fact that the combined map

\[ \operatorname{Gal}(\overline{\mathbb{Q}}/\mathbb{Q}) \longrightarrow \mathcal{GT} := \lim_G \, \mathcal{GT}(G) \] is injective.


memo


related items


computational resource

encyclopedia


books

  • Guralnick, Robert M., and John Shareshian. 2007. Symmetric and Alternating Groups as Monodromy Groups of Riemann Surfaces I: Generic Covers and Covers with Many Branch Points. American Mathematical Soc.
  • Schneps, Leila, ed. 1994. The Grothendieck Theory of Dessins D’enfants. Vol. 200. London Mathematical Society Lecture Note Series. Cambridge: Cambridge University Press. http://www.ams.org/mathscinet-getitem?mr=1305390.


expositions

articles

  • Pierre Guillot, The Grothendieck-Teichmüller group of \(PSL(2, q)\), arXiv:1604.04415 [math.GR], April 15 2016, http://arxiv.org/abs/1604.04415
  • Khashayar Filom, Ali Kamalinejad, Dessins on Modular Curves, http://arxiv.org/abs/1603.01693v1
  • Planat, Michel, and Hishamuddin Zainuddin. “Zoology of Atlas-Groups: Dessins D’enfants, Finite Geometries and Quantum Commutation.” arXiv:1601.04865 [math-Ph, Physics:quant-Ph], January 19, 2016. http://arxiv.org/abs/1601.04865.
  • Hilany, Boulos El. “Counting Positive Intersection Points of a Trinomial and a \(\mathbf{T}\)-Nomial Curves via Groethendieck’s Dessin D’enfant.” arXiv:1512.05688 [math], December 17, 2015. http://arxiv.org/abs/1512.05688.
  • Wang, Na-Er, Roman Nedela, and Kan Hu. “Totally Symmetric Dessins with Nilpotent Automorphism Groups of Class Three.” arXiv:1511.06863 [math], November 21, 2015. http://arxiv.org/abs/1511.06863.
  • Cueto, Moisés Herradón. “An Explicit Quasiplatonic Curve with Field of Moduli \(\mathbb Q(\sqrt[3]{2})\).” arXiv:1509.05819 [math], September 18, 2015. http://arxiv.org/abs/1509.05819.
  • Fine, Jonathan 2015Bias and Dessins. arXiv:1506.06389 [math]. http://arxiv.org/abs/1506.06389, accessed July 11, 2015.
  • Beffara, Vincent. ‘Dessins D’enfants for Analysts’. arXiv:1504.00244 [math], 1 April 2015. http://arxiv.org/abs/1504.00244.
  • Bose, Sownak, James Gundry, and Yang-Hui He. “Gauge Theories and Dessins d’Enfants: Beyond the Torus.” arXiv:1410.2227 [hep-Th], October 8, 2014. http://arxiv.org/abs/1410.2227.
  • Guillot, Pierre. 2014. “Some Computations with the Grothendieck-Teichm"uller Group and Equivariant Dessins D’enfants.” arXiv:1407.3112 [math], July. http://arxiv.org/abs/1407.3112.
  • Kazarian, Maxim, and Peter Zograf. 2014. “Virasoro Constraints and Topological Recursion for Grothendieck’s Dessin Counting.” arXiv:1406.5976 [math], June. http://arxiv.org/abs/1406.5976.

메타데이터

위키데이터

Spacy 패턴 목록

  • [{'LOWER': 'dessin'}, {'LEMMA': "d'enfant"}]
원본 주소 "https://wiki.mathnt.net/index.php?title=Dessin_d%27enfant&oldid=51732"