The Euclidean shortest path problem in a polygonal region is one of the oldest and best-known in Computational Geometry due to its various applications.

Given a simplicial complex with weights on its simplices, and a nontrivial cycle on it, we are interested in finding the cycle with minimal weight which is homologous to the given one.

If networks of chemical reactions are the circuits of biology then catalysts are the transistors, or perhaps switches. But which species should be called catalysts? Come to the talk and find out.

Algorithms working on large data(say of size n) should be both space and time efficient. Any algorithm has to see atleast the whole data once, so time required has to be atleast n(see sublinear time algorithms for exceptions).