I am interested in commutative algebra and its interaction with geometry. Specifically, I study homological properties of modules over local rings such as the vanishing pattern of Ext and Tor functors and their geometric consequences.

My main area of research is algebraic geometry. More specifically, I am interested in toric and birational geometry and resolution of singularities. I am also interested in several topics in commutative algebra such as local cohomology, valuation theory and the application of homological methods.

I work in commutative algebra. I am particularly interested in the properties of ideals in polynomial rings or power series rings. Some topics I work on include the theory of tight closure (which has to do with the technique of reduction to positive characteristic), local cohomology, integral closures of ideals, Gröbner bases and homological algebra. In recent years I have become very interested in maximal Cohen-Macaulay modules. I love to play almost all games, but in particular I enjoy tennis, ping-pong, chess, and bridge. I read a lot, especially science-fiction, mysteries, and history.

I specialize in algebraic geometry. I study birational transforms, and the minimal model problem.I study the structures of uniruled algebraic varieties. I aim at obtaining a characterization of rational varieties.

Among my current interests are the homological conjectures in mixed characteristic, in particular, the question of whether or not cycles are integral over boundaries in certain classes of complexes consisting of finitely generated free modules. I'm also interested in Rees algebras and integral closures of ideals and modules. Other interests include multiplicity theory, local cohomology, and asymptotic properties of ideals.

My research interests are in commutative algebra and algebraic geometry. Much of my research has focused on the study of the geometry of Zariski Surfaces and certain questions concerning them posed by Oscar Zariski. I have also been intrigued by the classical Jacobian Problem.

I specialize on complete intersections and projective modules. My latest work involves some K-theory and Chern classes.

My research interests lie in algebraic geometry. I am especially interested in: (1) Problems relating algebra and geometry of algebraic varieties. In particular, vector bundle techniques, syzygies and cohomology vanishings on algebraic varieties, and (2) Problems concerning degeneration of algebraic surfaces and its application to some topics in geometry like the study of Hilbert schemes, multiplication maps, curves in projective spaces, etc.

My research interests lie in the area of Commutative Algebra and its interplay with Algebraic Geometry, motivated by the problem of giving a multiplicity based criterion for integral dependece of modules.

I am a 2nd yr grad student highly interested in teaching. I'm not local, I commute. As can be seen from my "photo", I enjoy sleeping and sketching. My hobbies also include juggling, listening to music, photography and doing some commutative algebra.