Newton polytopes and complete intersections:

Motivic Milnor fibers over complete intersection varieties and their virtual Betti numbers

Index of a real singular point and its Newton diagram 

Newton polytopes and discriminants:

Newton polyhedra of discriminants of projections

                        (Ref: Discrete Comput. Geom., 44 (2010), no. 1, 96--148)

Elimination theory and Newton polytopes 

(with A. G. Khovanskii; Ref: Funct. An. and Other Math., 2 (2008), no. 1, 45--71)

Orientability of real resultant singularities                   (Ref: RIMS Kokyuroku, 1610 (2008), 18--29)

Determinantal singularities and Newton polyhedra 

(Ref: Proc. of the Steklov inst. 259 (2007), 16--34)

Tropical and convex geometry:

Tropical varieties with polynomial weights and corner loci of piecewise polynomials (2011)

On the existence of mixed fiber bodies  

(Ref: Moscow Mathematical Journal, 8 (2008), no. 3, 433--442)

Newton polytopes and singularities of vector fields (my PhD thesis, 2004):

Summary/survey  (preprint, 2009)

Determinantal singularities and Newton polyhedra 

(Ref: Proc. of the Steklov inst. 259 (2007), 16--34)

Indices of 1-forms, intersection indices, and Newton polyhedra 

(Ref: Sb. Math. 197 (2006), no. 7-8, 1085--1108; translated by the journal)

Indices of 1-forms, resultants, and Newton polyhedra 

(Ref: Russian Math. Surveys 60 (2005), no. 2, 352--353)

Indices of 1-forms and Newton polyhedra   

(Ref: Rev. Mat. Complut. 18 (2005), no. 1, 233--242)

Quasiperiodic topology:

Densities of topological invariants of quasiperiodic subanalytic sets

(Ref: Izvestiya: Mathematics, 73 (2009), no. 3, 611–-626)

Densities of the Betti numbers of pre-level sets of quasi-periodic functions 

(Ref: Russian Math. Surveys 55 (2000), no. 2, 338--339)