Fall Emphasis Semester 2019

Mathematical Sandpiles and Homological Mirror Symmetry

September 9, 2019– December 20, 2019

Organizers: Ludmil Katzarkov (Miami) and Ernesto Lupercio (Cinvestav)

Overview: In the late 80’s, motivated by the study of char we call now complex systems, physicists stumbled upon a deceptively simple cellular automaton as a toy model for self-organized criticality and stated theorems that from the mathematical perspective are remarkable conjectures. In the last few years a spurt of activity surrounding these conjectures has happened, in particular new connections to the XX! Century field of Tropical Geometry were found. These connections suggest two new avenues of research, in one direction with the advent of quantum toric geometry and quantum tropical geometry, the theory of sandpiles is insensitive to the quantization and provides a guide as to this geometric realm which suggest an amplification to the homological mirror symmetry program, in the opposite direction homological mirror symmetry may provide inspiration to deal with some of the ocnjectures regarding self/organized criticality in sandpiles. 

Main Workshops 

Introductory Workshop on HMS, Logic and Sandpiles (09/09/19-09/13/19)

Quantum Toric Geometry and Chimeras (10/21/2019-10/25/2019) 

Tropical Geometry and Sandpiles (11/17/2019- 11/22/2019) 

Short Courses and Seminars 

Introductory Workshop on HMS, Logic and Sandpiles (09/09/19-09/14/19)