Author Archive: raphy

Equivariant symplectic geometry is a meeting point for many areas of mathematics: it models symmetries of phase space in classical mechanics, extends algebraic-geometric phenomena, provides a geometric context for representations of Lie groups, and connects with geometry of convex polytopes….
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Topological dynamics studies behaviour of orbits under continuous transformations. Algebraic dynamics is the name attached to the study of automorphisms acting on a compact abelian group, from a “dynamical point of view”. In the 1970’s, motivated by the study of…
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We will give an overview of questions one might ask about the first-order theory of free groups and related groups: how much information can first-order formulas convey about these groups or their elements, what algebraic interpretation can be given for…
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Following Marty’s Theorem we present recent results about differential inequalities that imply (or not) some degree of normality. We deal with inequalities with reversed sign of inequality than that in Marty’s Theorem, i.e. |f^{(k)}(z)|> h(|f(z)|). Based on joined work with…
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Smooth parametrization consists in a subdivision of a mathematical object under consideration into simple pieces, and a parametric representation of each piece, while keeping control of high order derivatives. The main goal of this talk is to provide an overview…
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In the talk I shall describe a puzzle for children. We have a pile of stones and a graph D with n vertices. At most one stone may be placed on a vertex, so a vertex has one of two…
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Ramanujan graphs are regular graphs whose vertex adjacency matrix has “very condensed” spectrum. The latter manifests in many desired combinatorial properties, most notable of which is the fact that Ramanujan graphs are expanders, i.e. they admit high connectivity among their…
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  In the talk I will discuss classical problems concerning the distribution of square-full numbers and their analogues over function fields. The results described are  in the context of the ring Fq[T] of polynomials over a finite field Fq of q elements,…
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I will describe the theory of hyperbolic dynamical systems, and then describe a new approach to chaotic flows in dimension three, using knot theory. I’ll use this to show that, surprisingly, the famous Lorenz flow on R^3 can be related…
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