Author Archive: raphy

A group G has the Liouville property with respect to some generating set S if the only bounded harmonic functions on the Cayley graph of (G,S) are the constant functions. On such Cayley graphs it is interesting to ask how slowly can…
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A complete system of functions in $L_2({\mathbb R})$, can it be “localized” around a sparse set?

I will give an overview of recent results regarding the behavior of the Poisson bracket under perturbations of the functions relative to different topologies. It turns out that it exhibits both rigidity and flexibility. For instance, if the Poisson bracket…
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Given a map of discrete groups f:G –> H when is this map induced from a normal subgroup inclusion of topological groups X \subseteq Y by taking path components of X and Y?For example, the trivial map on the integers…
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Given two matrices of different sizes, A of size m x m and B of size n x n (with m<n), we say that B is a dilation of A, if A is the upper left m x m corner…
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Fourier coefficients of classical modular forms are related to classical problems in number theory such as Fermat’s sum of two squares theorem. In turn, in modern language, they are special examples of period integrals of automorphic forms. I intend to…
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