Author Archive: raphy

We shall discuss certain symplectic invariants known as symplectic capacities. In particular, we will show how these invariants in the classical phase space can be used to obtain information on the length of the shortest periodic billiard trajectory in a…
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In this talk, we show some interesting relations between the problem of attacking multiple encryption schemes and attacking knapsack systems. The underlying relation, of problems of a bi-composite nature, allows introducing a series of algorithms for the dissection of these…
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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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