Author Archive: raphy

I will discuss Goodwillie’s calculus of functors on topological spaces. To mimic the set-up in real analysis, topological spaces are considered small if their nontrivial homotopy groups start only in higher dimensions. They can be considered close only in relation…
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We shall discuss the Chirikov standard map, an area-preserving map of the torus to itself in which quasi-periodic and chaotic dynamics are believed to coexist. We shall describe how the problem can be related to the spectral properties of a one-dimensional discrete Schrodinger…
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At the most basic level, a linear differential algebraic group (LDAG) is a group of matrices whose entries are functions satisfying a fixed set of polynomial differential equations. These groups are important for applications to differential Galois theory. Although LDAGs…
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We study certain 2 degree-of-freedom Hamiltonian systems arising from an approximation scheme for solutions of the 2d nonlinear Schrodinger equation with cubic-quintic or saturated nonlinearities (possibly in a grade-indexed medium). The solutions of these systems can be of various different…
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In recent years much progress was achieved in the understanding of the extrema of Gaussian and non Gaussian fields that possess a hierarchical structure. Examples are branching random walks, the two dimensional Gaussian free field, cover time of the torus,…
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Over the course of the last 15 years or so, Minhyong Kim has developed a method for making effective use of the fundamental group to bound sets of solutions to hyperbolic equations; his method opens a new avenue in the…
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Let C be a smooth projective curve (of genus g>1) over an algebraically closed field K. Let J(C) be the Jacobian of C. By Torelli’s theorem J(C), as a principally polarized Abelian variety determines C up to isomorphism. In 2010,…
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