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.

For more information about my research please visit my homepage (VPN is needed):

https://sites.google.com/site/manolisctsakiris/