Lionel Levine (Cornell University)
Title: Will this avalanche go on forever?
Abstract: In the abelian sandpile model on the d-dimensional lattice Z^d, each site that has at least 2d grains of sand gives one grain of sand to each of its 2d nearest neighbors. An "avalanche" is what happens when you iterate this move. In https://arxiv.org/abs/1508.00161 Hannah Cairns proved that for d=3 the question in the title is algorithmically undecidable: it is as hard as the halting problem! This infinite unclimbable peak is surrounded by appealing finite peaks: What about d=2? What if the initial configuration of sand is random? I’ll tell you about the “mod 1 harmonic functions” Bob Hough and Daniel Jerison and I used to prove in https://arxiv.org/abs/1703.00827 that certain avalanches go on forever.
Friday, March 2 at 3:30pm to 4:30pm
Levan Center, 201
2322 N Kenmore Ave