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RESEARCH INTERESTS: My research is broad and at the interface between the fields of Commutative Algebra, Algebraic Geometry, and Combinatorics. I have worked on problems involving free resolutions, toric varieties, Hilbert schemes, complete intersections, subspace arrangements, monomial resolutions, Gröbner basis, Koszul algebras, shellings, and Castelnuovo-Mumford regularity. Some of my research interests are focused on the structure of free resolutions and their applications. I study resolutions over polynomial rings and their quotients. In essence constructing a resolution over a ring R consists of repeatedly solving systems of R-linear equations. From another point of view, resolutions provide a homological method for describing the structure of modules (the idea to associate a resolution to a module was introduced in Hilbert's famous 1890,1893-papers).
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