On resolutions of ideals associated to subspace arrangements and the algebraic matroid of the determinantal variety

THIS THESIS DESCRIBES THE GRADED MINIMAL FREE RESOLUTION OF A PRODUCT OF IDEALS, EACH GENERATED BY LINEAR FORMS. IT ALSO STUDIES A PHENOMENON OF LINEARIZATION OF THE RESOLUTION OF AN ARBITRARY IDEAL, UPON MULTIPLICATION BY SUFFICIENTLY MANY IDEALS OF GENERIC POINTS IN PROJECTIVE SPACE. FURTHER, IT PROVIDES A CLASS OF BASE SETS OF THE ALGEBRAIC MATROID OF THE DETERMINANTAL VARIETY AND CONJECTURES THAT THESE COMPLETELY CHARACTERIZE THE MATROID. FINALLY, IT PROVIDES DETERMINANTAL CONDITIONS FOR HOMOMORPHIC SENSING, A PROBLEM THAT STUDIES THE UNIQUENESS OF IMAGES OF POINTS IN A VECTOR SUBSPACE UNDER A FINITE SET OF LINEAR TRANSFORMATIONS.