Mathematical Research Seminar - Archive
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18.04.2011. ob 10:00 Seminarska soba v Galebu
Predavatelj: dr. Alexander Mednykh (Sobolev Institute of Mathematics, Novosibirsk, Russia)
Title: Counting coverings and maps
Abstract: In this lecture we give a new method to count finite sheeted coverings of
manifolds with a finitely generated fundamental group. We apply it to count
branched and unbranched coverings over compact surfaces (bordered or with
empty border).
As a consequence, we suggest a new approach to count maps on surfaces up to
orientation preserving homeomorphism. The further development of the method
gives us a possibility to count chiral maps (or twins) by number of edges on a
closed orientable surface.
manifolds with a finitely generated fundamental group. We apply it to count
branched and unbranched coverings over compact surfaces (bordered or with
empty border).
As a consequence, we suggest a new approach to count maps on surfaces up to
orientation preserving homeomorphism. The further development of the method
gives us a possibility to count chiral maps (or twins) by number of edges on a
closed orientable surface.
You can download the slides from the talk here: DOWNLOAD!
04.04.2011. ob 10:00 Seminarska soba v Galebu
Predavatelj: Q.Sergio Hiroki Koike
Title: On isomorphism of cyclic Haar graphs.
Abstract: Given a cyclic group and a subset of this group, we define a cyclic Haar graphs as a bipartite graph with two copies of the cyclic group and a edge {i,i+j} with i in one partition and i+j in the other.
Given a fix cyclic Haar graph H(n,A). We say that A is an HI-set if for any subset B of the cyclic group such that the cyclic Haar graphs H(n,A) and H(n,B) are isomorphic then there is an element f in the affine group of the cyclic group which maps B into A. The graph isomorphism problem in the class of cyclic Haar graphs is, esentially, to describe the pairs A and B for which the graphs H(n,A) and H(n,B) are isomorphic but there is not such function which maps B into A.
In this talk we will discuss some tools to find which graphs are isomorphic and there is an element f in the affine group of the cyclic group which maps B into A.
Abstract: Given a cyclic group and a subset of this group, we define a cyclic Haar graphs as a bipartite graph with two copies of the cyclic group and a edge {i,i+j} with i in one partition and i+j in the other.
Given a fix cyclic Haar graph H(n,A). We say that A is an HI-set if for any subset B of the cyclic group such that the cyclic Haar graphs H(n,A) and H(n,B) are isomorphic then there is an element f in the affine group of the cyclic group which maps B into A. The graph isomorphism problem in the class of cyclic Haar graphs is, esentially, to describe the pairs A and B for which the graphs H(n,A) and H(n,B) are isomorphic but there is not such function which maps B into A.
In this talk we will discuss some tools to find which graphs are isomorphic and there is an element f in the affine group of the cyclic group which maps B into A.
