Joint Seminar in Combinatorial Geometry and Optimization
Event details
| Date | 12.02.2013 |
| Hour | 14:15 › 15:15 |
| Speaker | Dragan Masulovic |
| Location |
MA B1 524
|
| Category | Conferences - Seminars |
Title: Classifying homomorphism-homogeneous structures
Abstract:
A structure is homogeneous if every isomorphism between finite
substructures of the structure extends to an automorphism of the structure.
The theory of (countable) homogeneous structures gained its momentum in 1953 with the
famous theorem of Frai sse which states that
countable homogeneous structures can be recognized by the fact that their
collections of finitely induced substructures have the amalgamation property.
Nowdays it is a well-established theory with deep consequences in many areas of mathematics.
In their 2006 paper, P. Cameron and J. Nev setvril discuss
a variant of homogeneity with respect to various types of morphisms of structures,
and in particular introduce the notion of homomorphism-homogeneous structures:
a structure is called homomorphism-homogeneous if every homomorphism between
finite substructures of the structure extends to an endomorphism of the structure.
In this talk we shall present an overview of classification results for some classes of finite
structures including posets, graphs and point-line geometries. We shall also present an overview
of a few known results on homomorphism-homogeneous algebras, and reflect on the problem of
computational complexity of deciding if a finite structure is homomorphism-homogeneous.
Abstract:
A structure is homogeneous if every isomorphism between finite
substructures of the structure extends to an automorphism of the structure.
The theory of (countable) homogeneous structures gained its momentum in 1953 with the
famous theorem of Frai sse which states that
countable homogeneous structures can be recognized by the fact that their
collections of finitely induced substructures have the amalgamation property.
Nowdays it is a well-established theory with deep consequences in many areas of mathematics.
In their 2006 paper, P. Cameron and J. Nev setvril discuss
a variant of homogeneity with respect to various types of morphisms of structures,
and in particular introduce the notion of homomorphism-homogeneous structures:
a structure is called homomorphism-homogeneous if every homomorphism between
finite substructures of the structure extends to an endomorphism of the structure.
In this talk we shall present an overview of classification results for some classes of finite
structures including posets, graphs and point-line geometries. We shall also present an overview
of a few known results on homomorphism-homogeneous algebras, and reflect on the problem of
computational complexity of deciding if a finite structure is homomorphism-homogeneous.
Practical information
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