Ljubljana-Leoben 2012

This year we have decided to have two keynote speakers:

• Pablo Spiga (Milano)
  "How vertex stabilizers grow?"

  Abstract. Here we are interested in highly transitive graphs. There are various natural ways to “measure” the degree of transitivity of a graph and, in this talk, we look at two possibilities. First, we consider graphs Γ having a group of automorphisms acting transitively on the paths of length s ≥ 1, starting at a given vertex. Clearly, the larger the value of s is, the more symmetric the graph will be. However, we show that large values of s impose severe restrictions on the local structure of Γ and, sometimes, on the size of the stabilizer of a vertex of Γ. This will lead us to the second perspective. We take the size of the stabilizer of a vertex of Γ as a measure of the transitivity. This measure is somehow unbiased among the graphs having the same number of vertices. Again we present some results showing, in some very specific cases, that nature is not as diverse as one might expect: graphs have either rather small vertex stabilizers or they can be classified. Finally we give some applications of these investigations: to the enumeration problem of vertex transitive graphs and to the problem of creating a database of small vertex transitive graphs. Still, we will have more problems than results.

• Wolfgang Woess (Graz)
  "On the duality between jump processes on ultrametric spaces and random walks on trees"

  Abstract. The purpose of these notes is to clarify the duality between a natural class of jump processes on compact ultrametric spaces -- studied in current work of Bendikov, Girgor'yan and Pittet -- and nearest neighbour walks on trees. Processes of this type have appeared in recent work of Bellisard and of Kigami. Every compact ultrametric space arises as the boundary of a locally finite tree. The dualty between the random processes arises via the Dirichlet forms: one on the tree associated with a random walk and the other on the boundary of the tree, which is given in terms of the Naim kernel. Here, it is explained that up to a linear time change by a unique constant, there is a one-to-one correspondence between the above processes and Dirichlet regular random walks.

Thursday, 20. September

Friday, 21. September

Saturday, 22. September

Complete programme is available in the book of abstracts pfd file.

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Conference fee

The registration fee is 50 EUR (25 EUR for students) and includes the conference dinner. For foreign participants, it is payable in cash upon arrival.

There will be a modest solidarity fund on a first-come, fist-served basis for anyone who can not cover the registration fee from his or her own funding.

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Iva Antončič, University of Primorska
Nino Bašić, University of Ljubljana
Katja Berčič, University of Primorska
Karina Chuda, Comenius University
Johannes Cuno, Graz University of Technology
Petr Gregor, Charles University
Robert Jajcay, Comenius University
György Kiss, Eötvös Loránd University
Sandi Klavžar, University of Ljubljana
Sergio Hiroki Koike Quintanar, University of Primorska
Gašper Košmrlj, University of Ljubljana
István Kovács, University of Primorska
Klavdija Kutnar, University of Primorska
Boštjan Kuzman, University of Ljubljana
Borut Lužar, IMFM
Martin Mačaj, Comenius University
Aleksander Malnič, University of Primorska
Dragan Marušič, University of Primorska
Štefko Miklavič, University of Primorska
Martin Milanič, University of Primorska
Polona Pavlič, IMFM
Tomaž Pisanski, University of Ljubljana
Primož Potočnik, University of Ljubljana
Rok Požar, University of Primorska
Jernej Rus, University of Ljubljana
Nina Schmuck, University of Klagenfurt
Norbert Seifter, University of Leoben
Pablo Spiga, University of Milano-Bicocca
Martin Škoviera, Comenius University
Riste Škrekovski, University of Ljubljana
Primož Šparl, University of Ljubljana
Gabriel Verret, University of Primorska
Vida Vukašinović, Jožef Stefan Institute, Ljubljana
Wolfgang Woess, Graz University of Technology
Sara Sabrina Zemljič, IMFM

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When you register, please indicate whether you would like to contribute a talk. All participants are welcome to contribute; however, the number of time slots for talks will be limited, as we would like to ensure enough time for free discussion and problem session

The title and abstract form will be added at a later date. We hope to collect the submissions by September 1st.

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If you plan to come to Bovec before the conference or stay after and are looking for things to do, there is a nice website about Bovec tourism with everything you might want to know.

Unfortunately, there are no more free rooms at the venue (Alp Hotel Bovec). They have kindly offered to help anyone who still needs accomodation - feel free to contact them at info@hotel-alp.si or call +386 5 388 40 00.

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