Seminar on classification of homogeneous structures - NMAI075

• Title: Seminář z klasifikace homogenních struktur
• Guaranteed by: Department of Applied Mathematics (32-KAM)
• Faculty: Faculty of Mathematics and Physics
• Actual: from 2019
• Semester: winter
• E-Credits: 3
• Hours per week, examination: winter s.:0/2, C [HT]
• Capacity: unlimited
• Min. number of students: unlimited
• 4EU+: no
• Virtual mobility / capacity: no
• State of the course: not taught
• Language: Czech, English
• Teaching methods: full-time
• Guarantor: doc. Mgr. Jan Hubička, Ph.D.
• Class: DS, diskrétní modely a algoritmy; Informatika Mgr. - volitelný; M Mgr. MSTR
• Classification: Informatics > Discrete Mathematics, Theoretical Computer Science; Mathematics > Discrete Mathematics

Annotation

English

A structure is homogeneous if every partial isomorphism extends to an automorphism. For example, every homogeneous graph is thus also edge and vertex transitive. It is intuitively clear that such extremely symmetric structures are rare. The classification programme of homogeneous structures is a project of giving complete catalogs of homogeneous structures of given type (graphs, digraphs, metric spaces etc.)

Last update: Kynčl Jan, doc. Mgr., Ph.D. (10.05.2018)

Czech

Struktura je homogenní, pokud každý izomorfismus dvou konečných podstruktur jde rozšířit na automorfismus. Každý homogenní graf je tedy vrcholově, hranově i nehranově tranzitivní. Takto symetrických struktur je málo, mají ale zajímavé aplikace. Program klasifikace homogenních struktur se zabývá hledáním katalogů homogenních struktur daného typu (grafů, digrafů, metrických prostorů atd.) Na semináři budeme diskutovat aktuální i klasické výsledky z oblasti.

Last update: Kynčl Jan, doc. Mgr., Ph.D. (10.05.2018)

Literature

English

Cherlin, Gregory: Homogeneous Ordered Graphs and Metrically Homogeneous Graphs; Draft of the monograph: http://sites.math.rutgers.edu/~cherlin/Paper/inprep.html

Lachlan, Alistair H., and Robert E. Woodrow. "Countable ultrahomogeneous undirected graphs." Transactions of the American Mathematical Society (1980): 51-94.

Cherlin, Gregory, and Alistair H. Lachlan. "Stable finitely homogeneous structures." Transactions of the American Mathematical Society 296.2 (1986): 815-850.

Cherlin, Gregory L. "Homogeneous directed graphs." Finite and Infinite Combinatorics in Sets and Logic. Springer, Dordrecht, 1993. 81-95.

Last update: Kynčl Jan, doc. Mgr., Ph.D. (10.05.2018)

Czech

Cherlin, Gregory: Homogeneous Ordered Graphs and Metrically Homogeneous Graphs; Draft monografie: http://sites.math.rutgers.edu/~cherlin/Paper/inprep.html

Lachlan, Alistair H., and Robert E. Woodrow. "Countable ultrahomogeneous undirected graphs." Transactions of the American Mathematical Society (1980): 51-94.

Cherlin, Gregory, and Alistair H. Lachlan. "Stable finitely homogeneous structures." Transactions of the American Mathematical Society 296.2 (1986): 815-850.

Cherlin, Gregory L. "Homogeneous directed graphs." Finite and Infinite Combinatorics in Sets and Logic. Springer, Dordrecht, 1993. 81-95.

Last update: Kynčl Jan, doc. Mgr., Ph.D. (10.05.2018)

Syllabus

English

In 2018/2019 we will focus on a new monograph by Cherlin, in particular on the chapter on classification of metrically homogeneous graphs.

Last update: Kynčl Jan, doc. Mgr., Ph.D. (10.05.2018)

Czech

V roce 2018/2019 se budeme věnovat nové monografii Cherlina, specificky kapitole o klasifikaci metricky homogenních grafů.

Last update: Kynčl Jan, doc. Mgr., Ph.D. (10.05.2018)