Thematic Einstein Semester on

Geometric and Topological Structure of Materials

Summer Semester 2021

Speaker


Yuval Peled   (Hebrew U)


Title


Minimum weight disk triangulations and fillings


Abstract


We study the minimum total weight of a disk triangulation using any number of vertices out of   { 1, … , n }   where the boundary is fixed and the  
( n 3 )
  triangles have independent uniform (0,1) weights. We show that, with high probability, the minimum weight is equal to   (c+o(1))n-1/2 log n   for an explicit constant c. Further, we prove that, with high probability, the minimum weights of a homological filling and a homotopical filling of the cycle (123) are both attained by the minimum weight disk triangulation. We will discuss a related open problem concerning simple-connectivity of random simplicial complexes, where a similar phenomenon is conjectured to hold. Based on joint works with Itai Benjamini, Eyal Lubetzky, and Zur Luria.



Contact


tes-summer2021@math.tu-berlin.de