Thesiss

Simplicial complexes are a generalization of networks that can encode many-body interactions between more than two nodes. Whereas networks represent the interactions between the parts of a complex system using nodes and links, the simplices in a simplicial complex represent inte…

In this work, connectivity graphs have been studied as models of local interactions in multi-agent robotic systems. A systematic study of the space of connectivity graphs has been done from a geometric and topological point of view. Some results on the realization of connectivit…

The first story begins with a question of Steenrod. He asked if the product in the cohomology of a triangulated space, which is associative and graded commutative, can be induced from a cochain level product satisfying the same two properties. He answered it in the negative afte…