In this talk we describe a physical problem, based on electromagnetic fields, whose topological constraints are higher dimensional versions of Kirchhoff's laws, involving 2-simplicial complexes embedded in R^3 rather than graphs. However, we show that, for the skeleton of this complex, involving only triangles and edges, we can build a matroid dual which is a graph. On this graph we build an 'ordinary' electrical circuit, solving which we obtain the solution to our original problem. Construction of this graph is through a 'sliding' algorithm which simulates sliding on the surfaces of the triangles, moving from one triangle to another which shares an edge with it but which also is adjacent with respect to the embedding of the complex in R^3. For this purpose, the only information needed is the order in which we encounter the triangles incident at an edge, when we rotate say clockwise with respect to the orientation of the edge. The dual graph construction is linear time on the size of the 2-complex. (Joint work with Prof Hariharan Narayanan, TIFR Bombay)
H. Narayanan joined the EE department, IIT Bombay in June 1974 as a faculty member. Except for the period 1983-1985 when he was a visiting faculty at University of California, Berkeley, he has continued with the EE Department at IIT Bombay. He retired in 2013, and was re-employed in different positions with the EE Department. He will finally bid a farewell on 11 Jan 2018. His interest since 1968 has been in network topology and its links with combinatorial optimization. He hopes to continue working in this area.