Subject Area: Valuation Theory; Applications of valuations to algebraic number fields; Irreducibility of polynomials over valued fields
I am mainly interested in valuations, specially in their applications to algebraic number theory and other basic problems of algebra like discovering criteria for irreducibility of polynomials. I along with my collaborators have used prolongations of valuations to simple transcendental extensions to generalize the classical Eisenstein-Dumas Irreducibility Criterion, Sch�nemann Irreducibility Criterion, Hensels Lemma, Ehrenfeuchts Irreducibility Criterion and Akira Criterion. I jointly with my research student worked on the irreducibility of truncated binomial expansions over rationals using Newton polygons with respect to p-adic valuations.I also worked on the invariants associated with irreducible polynomials with coefficients in henselian valued fields using saturated distinguished chains. Currently I am exploring the possibility of applying these invariants to some other problems in algebra.