Will this avalanche go on forever?

Meeting Details

For more information about this meeting, contact Wen-Ching W. Li, Yuxi Zheng.

Speaker: Lionel Levine, Cornell University

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 http://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 http://arxiv.org/abs/1703.00827 that certain avalanches go on forever.

---

Room Reservation Information

Room Number: 114 McAllister

Date: 09/27/2018

Time: 3:30pm - 4:40pm