My main research areas are Algebraic Topology, especially Toric Topology and Algebraic Combinatorics. 

Toric topology studies spaces with toric actions. The central objects of study are moment-angle complexes, subspaces of the polydisc assigned to simplicial complexes. The origins of the field lie in the notion of toric varieties that originally appeared in Algebraic Geometry. Smooth toric varieties or toric manifolds correspond to regular, complete fans. The normal fan of a simple, Delzant polytope produces the projective toric manifold. Their generalization are quasytoric manifolds given by locally standard toric actions with the orbit space being topologically a simple polytope. The seminal paper that launched the entire field and that still inspires new research, as well as the most important monograph in the field, are:

M. Davis, T. Januszkiewicz, Convex polytopes, Coxeter orbifolds and torus actions, Duke Math. J. 62(2) (1991), 417–451.

V. M. Buchstaber, T. E. Panov, Toric topology, Math. Surv. Monogr. 204, (2015) AMS .

One of the most important object of study in Algebraic combinatorics is the Stanley chromatic symmetric function of graphs, which is a generalization of the chromatic polynomial of graphs. Combinatorially, this function is an enumerator of proper graph colorings, geometrically it can be described as the enumerator of integer points inside the maximal cones of the normal fan of a graphical zonotope, while algebraically it is obtained as a universal morphism from the combinatorial Hopf algebra of graphs to the Hopf algebra of symmetric functions. Such enumerators can be associated with a broader class of polytopes known as generalized permutohedra, in which way combinatorial, or algebraic, invariants of various combinatorial objects, such as building sets or matroids, are obtained. The foundational paper of the field where the chromatic symmetric function of graphs is defined

R. Stanley, A symmetric function generalization of the chromatic  polynomial of a graph, Advances in Math. 111(1), (1995), 166–194.