2064 Engr Bldg IILocate on Campus Map
Campus Box 7911
NC State University
Raleigh, NC 27695-7911
I am a post doctoral researcher in ECE department at North Carolina State University, under the advisement of Dr. Hamid Krim.
My research so far focused mostly on fidelity of deployment and operation in sensor networks. The motivation for the research stems from the observation that problems in this field, such as tracking caverage and correlated failures, can be posed purely in topological terms. Sensor networks also pose unique techinical challenges due to limited resources available, and due to the need for distributed algorithms. My work was to discover/develop appropriate mathematical and computational tools, to perform the required tasks efficiently, distributively, and with minimal information.
More specifically, my research areas may be divided into the following categories:
Homology theory and computational homology
Homology theory is a part of algebraic topology, which deals with assiginging topological invariants called homology groups to topological spaces. Homology groups are one of the basic topological invariants one can compute and give significant information. I have worked on application of homology theory to the problems of detection and localization of coverage holes and worm holes in sensor networks.
The theory of persistent and zig-zag persistent homology develped recently has already found several interesting and effective applications. I believe there are many more applications to come for analyzing networks. I am currently working on application of zig-zag persistent homology to mobile networks.
Computational homology, as the name suggests, deals with developing algorithms to compute homology. I have worked on developing distributed algorithms for computing homology with field coefficients. This work employs the use of combinatorial Lapalcians and harmonics .
In addition straight forward applications such as sensor networks, I believe that the future of fast computing is in distributed algorithms and using computer clusters instead of a single high speed processor. In many ways it is already the present. Much is known about distributed algorithms on different kinds of networks, such as relationship between convergence of gossip algorithms to the spectrum of the graph Laplacian. Most of my work involves developing distributed algorithms.
Unlike classical geometry, discrete geoemtry deals with point clouds and metrics on them. The major topics include triangulations, digital representation, discrete differential calculus and discrete Morse theory. I have worked on distributed computation of Alpha shapes and relationship between Alpha complexes and Delaunay-Čech comlexes.
Some of the problems of my interst in the near future include distributed computation of persistent and zig-zag persistent homology, exploring applications of algebraic topology and distributed algorithms in smart grids and in machine learning . I also want to explore the mathematics on some fundamental questions about distributed algorithms.
My long term research goals include introducing new mathematical tools and their applications to the Engineering community, and to foster inter-disciplinary projects.
- 2006 - B.Tech in Electronics and Communications Engineering, Indian Institute of Technology, Roorkee, UT, India.
2008 - MS in Electrical Engineering, N C State University, Raleigh, NC
2013 - PhD in Electrical Engineering, N C State University, Raleigh, NC