Mathematical Sciences Department, Discrete Math Seminar - Ralihe Raul Villagran, WPI "Determinantal ideals and sandpile groups of graphs" UH405

Monday, September 25, 2023
3:00 pm to 3:50 pm
Floor/Room #

Mathematical Sciences Department

Discrete Math Seminar

Speaker: Ralihe Raul Villagran, WPI

Monday, September 25, 2023 

3:00 pm – 3:50 pm 

Unity Hall 405 

Title: Determinantal ideals and sandpile groups of graphs 

Abstract: Given a graph G=(V,E) with Laplacian matrix L(G) = Deg(G) - A(G). Then the algebraic structure of the sandpile group of G. denoted as S(G), can be described by (the Smith normal form of) its Laplacian matrix.  In this talk we introduce the generalized Laplacian matrix (of G), L(G,X) = Diag(X)-A(G) and its determinantal ideals (the ideals generated by the determinants of submatrices of certain size). Moreover, we will see some examples on how these ideals can be helpful in the study of sandpile groups. 



Mathematical Sciences