Colloquium Mathematics, Anne Fey (TUD)

 

Join us for coffee and tea at 15.45 p.m.

 

 

Date: Tuesday, June 14^th 2011

Speaker: Anne Fey (TUD)

Room: 5161.0267 (Bernoulliborg),

Time: 16.15

 

 

Title: Limiting shapes for nonabelian sandpile growth models,

 

Abstract:

Joint work with Haiyan Liu.

On a grid, start with a pile of height n > 1 at the origin, and a pile of height h < 1 on every other grid vertex. Split every pile that has height at least 1, that is, distribute its total height equally among the neighbors. We are interested in the set S of sites where we split a pile at least once.

Depending on h, n and possibly even on the order in which we split piles, either S reaches a final size or S keeps increasing. We show that the first case occurs for h small enough and arbitrary splitting order, and we give bounds for the size of S, using similar methods as for the abelian sandpile growth model.

In the second case, our model behaves strikingly different from the abelian sandpile growth model. With the parallel splitting order, S can have a multitude of different limiting shapes. We demonstrate several of them, leaving plenty of opportunity for further research. 

  

 

 

 

 

Colloquium coordinators are Prof.dr. A.C.D. van Enter (e-mail : A.C.D.van.Enter@rug.nl) and

Dr. M.E. Dür (e-mail: M.E.Dur@rug.nl)