THE ALGEBRA OF AVALANCHES
From Sandpiles to the Hidden Symmetries of the Universe
On November 10, 2025, at 10:00 a.m. in Room 403 of IMI–BAS, Professor Ernesto Lupercio will deliver a public lecture. Professor Lupercio, chair of the research group “Topological, Computational, and Algebraic Aspects of Complex Systems” at ICMS–Sofia, is an internationally recognized mathematician and recipient of the ICTP Ramanujan Prize and the Marcos Moshinsky Research Award.
Why do avalanches, neural networks, and financial systems all seem to live on the edge of chaos?
This public lecture introduces the mathematics of the Teotitlán group — a new algebraic structure that captures how complex systems organize themselves. Born from the humble sandpile, the Teotitlán group reveals that every collapse leaves behind a hidden order, an “arithmetic memory” encoded in the geometry of the system.
From grains of sand to networks, from topology to machine learning, we discover how balance, symmetry, and information emerge spontaneously.
No formulas required — just curiosity, pattern, and imagination.
Ernesto Lupercio completed his PhD in mathematics under the guidance of Ralph Cohen at Stanford University. He has held academic positions at the Max Planck Institute, the University of Michigan, the University of Wisconsin–Madison and the Center for Research and Advanced Studies of the National Polytechnic Institute (CINVESTAV). Lupercio has received international recognition, including the ICTP Ramanujan Prize (2010) and the Marcos Moshinsky Research Award (2013). In 2007, he was named a Young Global Leader in Science by the World Economic Forum.
In 2007, Ernesto was recognized as a Young Global Leader in Science by the World Economic Forum. In 2010, he was honored with the Ramanujan Prize by the International Center for Theoretical Physics (ICTP), the Norwegian Academy of Letters and Sciences, and the International Mathematical Union (IMU). This award recognized his exceptional contributions to algebraic topology, geometry, and mathematical physics, as well as his significant impact on mathematics in Mexico through his mentorship and collaborations. In 2013, he received the prestigious Marcos Moshinsky Research Award, the highest recognition from the Marcos Moshinsky Foundation for young scientists of exceptional quality and promise.
