Invited Talk by Dr. Saswata Shannigrahi on Problems and Results on Uniform Hypergraphs
Title: Problems and Results on Uniform Hypergraphs
Speaker:Dr. Saswata Shannigrahi
Host Faculty: Dr. Saurabh Joshi
Room No:212, Academic Block-A
In this talk, we will discuss recent results on uniform hypergraphs. In particular, we will talk about a new problem, namely, the rectilinear crossing number of uniform hypergraphs, described below. Graph drawing in the plane is a well-studied area of research for many years. One particularly interesting drawing of a graph is rectilinear drawing, defined as an embedding of the graph on a plane with vertices placed in general position and edges connecting corresponding vertices as straight line segments. In our works (published in Discrete Applied Mathematics, followed by another accepted article in Computational Geometry: Theory and Applications), we define the d-dimensional rectilinear drawing of a d-uniform hypergraph with n vertices as an embedding of the hypergraph with vertices as points in R^d with and hyperedges drawn as (d−1)-simplices spanned by the d vertices in the corresponding hyperedges. The d-dimensional rectilinear crossing number of a d-uniform hypergraph is defined as the minimum number of crossing pairs of hyperedges among all d-dimensional rectilinear drawings of the hypergraph. In this talk, we will present several results on the d-dimensional rectilinear crossing number of uniform hypergraphs.
Dr. Saswata Shannigrahi obtained B.E. Degree in Computer Science and Engineering (2005) from Jadavpur University, M.S. and Ph.D. degrees (2011) in Computer Science from Tata Institute of Fundamental Research, Mumbai. After spending a short period as a post-doctoral researcher at Kansas University, he returned to India as Assistant Professor and Ramanujan Fellow (hosted at IIT Guwahati and IIIT Delhi) in 2011. His research interest lies in the area of graph and hypergraph theory and its applications in data structures, algorithms and social network analysis. His notable honors and awards include the IBM Ph.D. Fellowship 2009-10, Microsoft Research India Rising Star Award 2011 and Ramanujan Fellowship 2011-16.