At IIT Bombay, I started working on algebraic properties of polynomials arising in Enumerative Combinatorics. We studied gamma-positivity, log-concavity and real rootedness of polynomials that came up in permutation enumeration. I was able to prove the polynomials that enumerated descents and excedances over the even permutations had ultra-log-concave coefficients. It is conjectured that these polynomials have only real roots. I was also able to give a criterion that certifies log-concavity of combinatorial sequences that satisfy triangular recurrences. This criterion gives a unified approach to log-concavity of many sequences that appear in combinatorics such as the Eulerian numbers, Stirling numbers and Lah numbers. 

Later on in my study at IIT Bombay, I took to studying the pattern avoidance in permutations. We were able to reformulate some recent results of Burstein, Kitaev, Han and Zhang in the language of sums of labelled posets which allowed us to ask more questions from a poset perspective. We were able to completely classify the shape-Wilf equivalence of poset patterns of length upto 5 whose connected components were chains. We also gave a new insertion encoding and bijection that we used to completely classify shape-Wilf equivalence of sets of short patterns.