1 citations · 1 across the 3 of their papers we have counts for
5 papers
Deconstructing Functions on Quadratic Surfaces into Multipoles
Gabriel Katz
Any homogeneous polynomial of degree , being restricted to a unit sphere , admits essentially a unique representation of the form $λ_0 + \sum_{k = 1}^d λ_k [\p…
Curves in cages: an algebro-geometric zoo
Gabriel Katz
The paper is concerned with families of plane algebraic curves that contain a given and quite special finite set X of points in the projective plane. We focus on the case in which…
How tangents solve algebraic equations, or a remarkable geometry of discriminant varieties
Gabriel Katz
Let denote the discriminant variety of degree polynomials in one variable with at least one of its roots being of multiplicity . We prove that the ta…
Harmonic maps M^3 --> S^1 and 2-cycles, realizing the Thurston norm
Gabriel Katz
Let be an oriented 3-manifold. We investigate when one of the fibers or a combination of fiber components, , of a \emph{harmonic} map with Morse-ty…
Morse theory of harmonic forms
Michael Farber, Gabriel Katz, Jerome Levine
We consider the problem of whether it is possible to improve the Novikov inequalities for closed 1-forms, or any other inequalities of a similar nature, if we assume, additionally,…