My research interest lies in the intersection of Commutative and Computational Algebra, Combinatorics and Algebraic Statistics. Algebraic Statistics is relatively new subject where we benefit from algebraic tools to explore various areas in Statistics. Recently, my research has been around the topics concerning investigation of questions related to binomial ideals, toric rings, Koszul Algebras and their filtrations, lattice ideals, combinatorics of partially ordered sets, application of Gröbner bases, and algebraic and homological properties of powers of ideals. A strong motivation of my interest in ideals generated by binomials, specifically, ideals generated by minors of a matrix come from Algebraic Statistics where such ideals naturally arise.

__Previous Positions:__

- Postdoctoral Fellow, The Abdus Salam International Centre of Theoretical Physics, Trieste, Italy (March 2016- August 2016)
- Postdoctoral Fellow,
**JSPS fellowship**, Osaka University, Japan. (December 2014 – February 2016) - Postdoctoral Fellow, The Abdus Salam International Centre of Theoretical Physics, Trieste, Italy, 2014.
- Long-Term Visiting Scientist, The Abdus Salam International Centre of Theoretical Physics, Trieste, Italy, 2013.
- Postdoctoral Fellow, Abdus Salam School of Mathematical Sciences, GCU, Lahore, Pakistan, March-June, 2012.
- Postdoctoral Fellow, Abdus Salam School of Mathematical Sciences, GCU, Lahore, Pakistan, September-December, 2012

__Refereed Papers:__

*On the relations of isotonian algebras**,*with Jürgen Herzog and Akihiro Shikama,**Proceedings of American Mathematical Society**, doi.org/10.1090/proc/13502.*Simple polyominoes are prime*, with Takafumi Shibata and Akihiro Shikama,**Journal of Commutative Algebra**, to appear.*Isotonian Algebras,*Mina Bigdeli, Jürgen Herzog, Takayuki Hibi and Akihiro Shikama,**Nagoya Mathematical Journal**, DOI 10.1017/nmj.2017.4.__Hankel__ideals of 2-minors associated with pairs of proper intervals graphs, with Faryal Chaudhry,**Journal of Algebra and its Applications**, Vol. 16, No. 2, pp. 1750070, 2017.*Alexander duality for monomial ideals associated with isotone maps between posets,*with Jürgen Herzog and Akihiro Shikama,**Journal of Algebra and its Applications**, Vol. 14, No. 5, pp. 1650089, 2016.*Gröbner bases of balanced polyominoes*, with J. Herzog and A. Shikama,**Mathematische Nachrichten**, Vol. 288, pp. 775-783, 2015.*Polarization of Koszul cycles with applications to powers of edge ideals of Whisker graphs*with Jürgen Herzog, Takayuki Hibi,**Proceedings of American Mathematical Society**, Vol. 143(7), pp. 2767-2778, 2015.*A Koszul filtration for the second squarefree Veronese subring,*with Takayuki Hibi, Akihiro Shikama,**International Journal of Algebra,**9, pp. 7-14, 2015.*Persistence and stability properties of powers of ideals*, with Jürgen Herzog,**Journal of Pure and Applied Algebra**, 219, pp. 530-542, 2015.*Indispensable Hibi relations and Gröbner basis*,**Algebra Colloquium,**22, No. 4, pp. 567-580, 2015.*Nonsimple polyominoes and prime ideals,*with Takayuki Hibi,**Illinois Journal of Mathematics**, Vol. 59, No. 2, pp. 391-398, 2015.*The binomial edge ideal of a pair of graphs*, with Viviana Ene, Jürgen Herzog, Takayuki Hibi,**Nagoya Mathematical Journal**, Vol. 213, pp. 105-125, 2014.*On characteristic poset and Stanley,*with Sarfraz Ahmad, Imran Anwar,**Analele Stiintifice ale Universitatii Ovidius Constanta**, Vol. 22(2), pp. 21-28, 2014.*Regularity of join-meet ideals of distributive lattices*, with Viviana Ene, Asia Rauf,**Electronic Journal of Combinatorics**, Vol. 20, No. 3, P20, 2013.*Ideals generated by diagonal 2-minors*, with V. Ene,**Communications in Algebra**, Vol. 41, No. 8, pp.3058-3066, 2013.*Ideals generated by 2-minors, collections of cells and stack polyominoes*,**Journal of Algebra**, Vol. 357, No. 3, pp. 279 – 303, July, 2012.