Stochastic Topology and its applications

Our research group aims to explore and understand the topology of random combinatorial and geometric structures. These include percolation and first passage percolation models on lattices, configuration spaces, as well as a variety of random simplicial and cubical complexes [1,2]. We also aim to find structures exhibiting extremal topology and study their properties [3].
In many of our projects, we perform computational experiments to gain intuition about the topological behavior of a model and use them to suggest conjectures for future mathematical research (for an example, see our 3D Eden Model simulation below [2,4]). Towards that end, we develop and apply tools and techniques from applied and computational geometry and topology, such as TGDA*. We also use MCMCM-H** algorithms and other algorithms used for performing computational experiments in statistical mechanics.

Selected publications

Software