"Dessin d'enfant"의 두 판 사이의 차이
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imported>Pythagoras0 |
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| (사용자 2명의 중간 판 12개는 보이지 않습니다) | |||
| 1번째 줄: | 1번째 줄: | ||
==introduction== | ==introduction== | ||
* Grothendieck's theory of dessins provides a bridge between algebraic numbers and combinatorics | * 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. | ||
| 11번째 줄: | 19번째 줄: | ||
* [[Grothendieck-Teichmuller theory]] | * [[Grothendieck-Teichmuller theory]] | ||
| + | |||
| + | ==computational resource== | ||
| + | * https://github.com/vbeffara/Simulations | ||
==encyclopedia== | ==encyclopedia== | ||
| 22번째 줄: | 33번째 줄: | ||
==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. | * 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. | ||
| 30번째 줄: | 42번째 줄: | ||
==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. | * 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 | + | * 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. | * 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. | * Beffara, Vincent. ‘Dessins D’enfants for Analysts’. arXiv:1504.00244 [math], 1 April 2015. http://arxiv.org/abs/1504.00244. | ||
| 37번째 줄: | 53번째 줄: | ||
* 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=== | ||
| + | * ID : [https://www.wikidata.org/wiki/Q3024615 Q3024615] | ||
| + | ===Spacy 패턴 목록=== | ||
| + | * [{'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
- http://www.neverendingbooks.org/index.php/kleins-dessins-denfant-and-the-buckyball.html
- http://www.neverendingbooks.org/index.php/permutation-representations-of-monodromy-groups.html
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
- 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.
- Jones, Dessins d'enfants: bipartite maps and Galois groups
- Eriksson, Galois theory of Covers
- Robalo, Galois Theory towards Dessins d'Enfants, masters thesis
- Introduction to Dessins d'Enfants, undergraduate research program
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
- ID : Q3024615
Spacy 패턴 목록
- [{'LOWER': 'dessin'}, {'LEMMA': "d'enfant"}]