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Unramified graph covers of finite degree
Post-edited
Authors : Li, Winnie (Author of the conference)
CIRM (Publisher )
05C25 - Graphs and abstract algebra (groups, rings, fields, etc.)
05C50 - Graphs and linear algebra (matrices, eigenvalues, etc.)
11R32 - Galois theory
11R44 - Distribution of prime ideals
11R45 - Density theorems
CIRM (Publisher )
Abstract :
Given a finite connected undirected graph $X$, its fundamental group plays the role of the absolute Galois group of $X$. The familiar Galois theory holds in this setting. In this talk we shall discuss graph theoretical counter parts of several important theorems for number fields. Topics include
(a) Determination, up to equivalence, of unramified normal covers of $X$ of given degree,
(b) Criteria for Sunada equivalence,
(c) Chebotarev density theorem.
This is a joint work with Hau-Wen Huang.
MSC Codes : (a) Determination, up to equivalence, of unramified normal covers of $X$ of given degree,
(b) Criteria for Sunada equivalence,
(c) Chebotarev density theorem.
This is a joint work with Hau-Wen Huang.
05C25 - Graphs and abstract algebra (groups, rings, fields, etc.)
05C50 - Graphs and linear algebra (matrices, eigenvalues, etc.)
11R32 - Galois theory
11R44 - Distribution of prime ideals
11R45 - Density theorems
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Information on the Video
Film maker : Hennenfent, GuillaumeLanguage : English Available date : 13/04/16 Conference Date : 30/03/2016 Subseries : Research talks arXiv category : Number Theory ; Combinatorics Mathematical Area(s) : Combinatorics ; Number Theory Format : MP4 (.mp4) - HD Video Time : 00:47:11 Targeted Audience : Researchers Download : https://videos.cirm-math.fr/2016-03-30_Li.mp4 
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Information on the Event
Event Title : Dynamics and graphs over finite fields: algebraic, number theoretic and algorithmic aspects / Dynamique et graphes sur les corps finis : aspects algebriques, arithmétiques et algorithmiquesEvent Organizers : Chang, Mei-Chu ; von zur Gathen, Joachim ; Ostafe, Alina ; Pappalardi, Francesco Dates : 29/03/16 - 02/04/16 Event Year : 2016 Event URL : http://conferences.cirm-math.fr/1391.html
Citation Data
DOI : 10.24350/CIRM.V.18951603Cite this video as: Li, Winnie (2016). Unramified graph covers of finite degree. CIRM. Audiovisual resource. doi:10.24350/CIRM.V.18951603 URI : http://dx.doi.org/10.24350/CIRM.V.18951603 |
See Also
- [Multi angle] Generators of elliptic curves over finite fields / Author of the conference Voloch, José Felipe.
- [Multi angle] Class number statistics for imaginary quadratic fields / Author of the conference Kurlberg, Pär.
- [Multi angle] Primes, exponential sums, and L-functions / Author of the conference Banks, William.
Bibliography
- Cassels, J.W.S. (Ed.), & Fröhlich, A. (Ed.). (2010). Algebraic number theory. London: London Mathematical Society -
- Huang, H-W., & Li, W. Unramified graph covers of finite degree, preprint, 2015 -
- Somodi, M. (2015). On Sunada equivalent graph coverings. Journal of Combinatorics and Number Theory, 7(2) -
- A. Terras, Zeta Functions of Graphs: A Stroll through the Garden. Cambridge Studies in Advanced Mathematics, vol. 128 (2010) - http://bibli.cirm-math.fr/Record.htm?idlist=1&record=19271403124910996859
