Manolis C.Tsakiris
研究领域:Applied Algebraic Geometry, Commutative Algebra, Machine Learning

I do research both in pure and applied mathematics. Their intersection point is algebraic geometry. In pure mathematics I research the algebraic workhorse of algebraic geometry, known as commutative algebra. Subjects of interest include Hilbert Functions, Castelnuovo-Mumford regularity, local cohomology, algebraic matroids, determinantal varieties & subspace arrangements. On the side of the applications, I like using algebraic geometry to analyze problems from compressed sensing & robust principal component analysis, where the objects of the problem are of algebraic geometric nature. This is the situation in many instances, such as low-rank matrix completion, subspace clustering, phase retrieval & structure from motion in computer vision. There, popular mathematical models such as low-rank matrices, Grassmannians and unions of linear subspaces, also happen to be natural objects of algebraic geometry, called algebraic varieties. A graduate student that enters my group is free to work either on applied algebraic geometry or on pure commutative algebra, according to his or her preference.

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