My research interests lie in stable homotopy theory and topological combinatorics. Computing good lower bounds for chromatic number of graphs is an important problem in combinatorics. Kozlov, Bab-son, Dochtermann and several others have proved results in this context which hinge on understanding the connectivity of certain simplicial complexes called Hom complexes. Several motions from homotopy theory of topological spaces like homotopy equivalances, etc.  have analogues in the category of graphs. In joint work with Shuchita Goyel, we are working toward understanding appropriate model structures on the graphs which give a better understanding of Hom complexes and allow us to apply other tools from homotopy theory in graphs.