Colloquium

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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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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