Talk 3

Title: A Study of Electrical Circuits via AlgebraicTopology

Speaker:  Leonardo Abath

Affiliation: Professor,  Universidade Federal de Pernambuco de Pernambuco 

Abstract: In this talk, we present an alternative formulation of circuit theory, taking into account its physical distribution in space. For example, we will consider an electrical circuit as a graph or a one-dimensional simplicial complex, where the branches and the nodes of the electrical circuit will generate two different vector spaces. Furthermore, Kirchhoff's current law and Kirchhoff's voltage law are reformulated as concise equations; the method of currents in the meshes, and the method of potentials in the nodes are also reformulated. With this alternative approach, demonstrating the existence and uniqueness of solutions to the equations of an electrical circuit becomes easier and more direct. And, at the end, we comment on the important contributions made by Gustav Kirchhoff, Hermann Weyl and Steve Smale applying these connections between circuit theory, algebraic topology and graph theory.