Persistent DNA, RNA and Protein Analysis 

My applied research has been focusing on developing topological and geometric approaches for visualizing and studying DNA sequences in collaboration with algebraic topologist and geometer Dr. Dong Quan Nguyen http://nd.edu/~dnguye15. 

The key ideas are to represent DNA sequences using mathematical representations based on which one can associate each DNA sequence with topological objects such as persistent barcodes or persistent diagrams.  These topological objects explore and detect the hidden features or patterns of DNA sequences using tools from algebraic topology. Under our proposed topological framework one can easily compare differences between DNA sequences from different diseases, cancer types or subtypes by comparing their topological representations. The approaches can be used for clustering diseases and studying their evolutionary relationships. Such approaches can be applied to analyzing RNA sequences and proteins. Our approaches have appealing visualization features.