"Dessin d'enfant"의 두 판 사이의 차이

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-==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
-==related items==
-* [[Grothendieck-Teichmuller theory]]
-==computational resource==
-* https://github.com/vbeffara/Simulations
-==encyclopedia==
-* 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==
-* 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, [http://www.emis.de/journals/SLC/wpapers/s35jones.pdf Dessins d'enfants: bipartite maps and Galois groups]
-* Eriksson, [http://www.math.chalmers.se/~dener/Galois-theory-of-Covers.pdf Galois theory of Covers]
-* 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
-==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.

"Dessin d'enfant"의 두 판 사이의 차이

2020년 11월 13일 (금) 16:46 판

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