Author Archive: raphy

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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As is well known, a complex $m \times m$ matrix $A$ is a commutator (i.e., there are matrices $B$ and $C$ of the same dimensions as $A$ such that $A=[B,C]=BC-CB$) if and only if $A$ has zero trace. If $\|\cdot\|$…
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We introduce a new model for random knots and links, based on the petal projection developed by C. Adams et al. We study the distribution of various invariants of knots and links in this model. We view a knot invariant…
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On many occasions a local object (e.g. the germ of a map at a point) is essentially determined (up to a group action) by its finite jet, i.e. its restriction onto some N’th-infinitesimal neighborhood of the point. This “minimalistic stability”…
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