Colloquium

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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We approach the formalism of quantum mechanics from the logician point of view and treat the canonical commutation relations and the conventional calculus based on it as an algebraic syntax of quantum mechanics. We then aim to establish a geometric…
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: In 1921, Landau wrote a letter to Hardy including a proof of the inequality \begin{align*} \sum_{n=0}^{\infty}|\phi(n)-\phi(n+1)|^{p}\geq \left(\frac{p-1}{p}\right)^{p}\sum_{n=1}^{\infty}\frac{|\phi(n)|^{p}}{n^{p}} \end{align*} which holds for all finitely supported $\phi:\N_0\to\R$ such that $\phi(0)=0$ (here $1<p<\infty$ is a fixed number). This inequality was stated before…
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Periods of automorphic forms provides an important tool to classify automorphic representations and arise time and time again in problems with arithmetic origin. Motivated by that, I shall describe some of our investigation of local counterparts of these periods that…
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The free uniform spanning forest (FUSF) of an infinite connected graph G is obtained as the weak limit of uniformly chosen spanning trees of finite subgraphs of G. It is easy to see that the FUSF is supported on spanning…
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In infinite ergodic theory, distributional limits replace the absolutely normalized pointwise ergodic theorem.We’ll review the subject and then see that every random variable on the positive reals occurs as the distributional limit of some infinite ergodic transformation. We’ll consider consequences…
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