Analysis Seminar in Crete (2014-15)

Σεμιναριο Αναλυσης

In chronological ordering

DATE TIME ROOM SPEAKER FROM TITLE COMMENT
Tue, 9 Sep 2014 12:15 A302 Elona Agora Insitituto Argentino de Matemática "Alberto Calderón" Construction of sampling sets and interpolation sets near the critical density
Abstract is here in PDF.
Tue, 23 Sep 2014 13:15 A302 Nikos Dafnis Univ. of Crete Improved Holder inequalities for correlated Gaussian random vectors
Joint work with Wei-Kuo Chen (University of Chicago), Grigoris Paouris (Texas A&M University). Available at http://arxiv.org/abs/1306.2410.

Abstract: We propose algebraic criteria that yield sharp Holder types of inequalities for the product of functions of Gaussian random vectors with arbitrary covariance structure. While our lower inequality appears to be new, we prove that the upper inequality gives an equivalent formulation for the Brascamp-Lieb inequality. Moreover, we will see that this result generalizes, Holder's inequality, Nelson's hypercontractivity as well as its reverse, and the sharp Young and revere sharp Young inequalities. Moreover we give two more applications: Prekopa-Leindler and Barthe inequality."

Tue, 30 Sep 2014 13:15 A302 Georgios Costakis Univ. of Crete Two problems on power-regular operators
Tue, 14 Oct 2014 13:15 A302 Nikos Frantzikinakis Univ. of Crete Uniformity of multiplicative functions and applications
Abstract: Multiplicative functions is a central topic in analytic number theory and studying their multiple correlation sequences quickly leads to very interesting and difficult problems. Partly motivated by applications, we study multiple correlation sequences of bounded multiplicative functions evaluated on linear forms in two variables. Extending previous work of Green, Tao, and Ziegler on the Mobius function, we were able to get a very good understanding of the asymptotic behavior of these multiple correlation sequences for arbitrary bounded multiplicative functions. The key ingredient is a hard earned structural result which roughly speaking asserts that every bounded multiplicative function can be decomposed into a sum of an approximately periodic and a random component. This structural result can also be used to give the first partition regularity results for homogeneous quadratic equations on the integers, and shows much promise for further applications.This is joint work with Bernard Host.
Tue, 18 Nov 2014 13:15 A302 Nikos Stylianopoulos Univ. of Cyprus Moment problems with applications
Abstract is here in PDF.
Fri, 27 Feb 2015 11:15 A302 Joanna Kulaga-Przymus N. Copernicus Univ. Torun B-free integers in number fields
Abstract: Recall that the Moebius function $\mu\colon \mathbb{N}\to \{-1,0,1\}$ is defined in the following way: $\mu(1)=1$, $\mu(n)=(-1)^m$ if $n$ is a product of $m$ distinct primes and $\mu(n)=0$ otherwise (thus, $\mu^2$ is the characteristic function of the so-called square-free integers). $\mu$ is of a great importance in number theory ($\sum_{n\leq N}\mu(n)=o(N)$ is equivalent to the prime number theorem and $\sum_{n\leq N}\mu(N)=O(N^{1/2+\varepsilon})$ for each $\varepsilon>0$ is equivalent to the Riemann Hypothesis). Sarnak in 2010 in his seminal paper proposed to study two dynamical systems: one related to $\mu$ and one related to its square $\mu^2$. He formulated a certain program on measure-thereoretical and topological properties of these systems. Since then his ideas were generalized in various directions. I will discuss one of such generalizations, related to the set of B-free integers in number fields. It has the advantage that the earlier settings are special cases of this one. The talk will be based on a joint work with Aurelia Bartnicka.
Tue, 3 Mar 2015 13:15 A302 Sigrid Grepstad NTNU Trondheim Sets of bounded discrepancy for multi-dimensional irrational rotation
Abstract: The equidistribution theorem for the irrational rotation of the circle may be stated by saying that the discrepancy $N(S,n) - n m(S) = o(n)$, where $S$ is any set whose boundary has measure zero, and $N(S,n)$ is the number of points falling into $S$ among the first n points in the orbit. It was discovered that for certain special sets $S$, the discrepancy actually remains bounded as n tends to infinity. Hecke and Kesten characterized the intervals with this property, called "bounded remainder intervals". In this talk I will discuss the Hecke-Kesten phenomenon in the multi-dimensional setting. This is joint work with Nir Lev.
Tue, 10 Mar 2015 13:15 A302 Christos Papachristodoulos University of Crete On universality and convergence of the Fourier series for functions in the disc algebra
Abstract: We construct functions in the disc algebra with pointwise universal Fourier series on sets which are $G_\delta$ and dense.We also see that some classes of closed sets of measure zero do not accept universal Fourier series, although all such sets accept divergent Fourier series. This is joint work with M. Papadimitrakis.
Tue, 17 Mar 2015 13:15 A302 Elona Agora University of Crete Boundedness of some classical operators on weighted Lorentz spaces
Abstract: In this talk we will discuss the characterization of the boundedness of Hardy Littlewood maximal operator $M$, and Hilbert transform $H$, on weighted Lorentz spaces. These spaces generalize both weighted Lebesgue spaces and classical Lorentz spaces. It is known that the boundedness of $M$ and $H$ on weighted Lebesgue spaces is characterized by the so-called $A_p$ Muckenhoupt class of weights, using techniques from Calderon-Zygmund theory. On the other hand, in the case of the classical Lorentz spaces the techniques comes from the theory of rearrangement invariant spaces. In particular, the obtained extension provides a unification of the aforementioned known results. Finally, we will also discuss some recent related results on the multidimensional case for $M$. The results are based on joint works with J. Antezana, M. J. Carro, and J. Soria.
Tue, 24 Mar 2015 13:15 A302 Nir Lev Bar-Ilan University On Fourier quasicrystals
Abstract: By a quasicrystal one often means a discrete distribution of masses that has a pure point spectrum. The name was inspired by the experimental discovery of quasicrystalline materials in the middle of 80s. I will present relevant background and discuss some recent results in the subject obtained in joint work with Alexander Olevskii.
Tue, 24 Mar 2015 14:15 A302 Jorge Antezana Univ. Nacional de la Plata Symmetric gaussian analytic functions in de Branges spaces
Abstract: Given an orthonormal basis $e_n$ in a de Branges space (a certain Hilbert space of entire functions), and i.i.d. random variables $a_n$ with real normal distribution $N(0,1)$, we consider the Gaussian Analytic Function (GAF): $F(z)=\sum_n a_n e_n(z)$. In this talk, after a brief introduction to more general GAFs, we will present some results on the distribution of the real zeroes of $F(z)$. The random set of zeroes of GAFs usually contain information about the underline Hilbert space used to construct it. We will see that, in the case of de Branges GAFs, this information is enough to characterize, up to some natural isomorphism, the de Branges space. We will also show some partial results on the hole probability. This talk is based on a joint work with Jordi Marzo and Jan-Fredrik Olsen.
Tue, 21 April 2015 13:15 A302 J.J.P. Veerman Portland State University Rank Driven Dynamics
Abstract: We investigate a class of models related to the Bak-Sneppen (BS) model, initially proposed to study evolution. The BS model is extremely simple and yet captures some forms of complex behavior'' such as punctuated equilibrium that is often observed in physical and biological systems. In the BS model, random numbers in $[0,1]$ (interpreted as fitnesses of agents) distributed according to some cumulative distribution function $R:[0,1]\rightarrow [0,1]$ are placed at the vertices of a graph $G$. At every time-step the lowest number and its immediate neighbors are replaced by new random numbers. We approximate this dynamics by making the assumption that the numbers to be replaced are independently distributed. We then use Order Statistics to define a dynamical system on the cumulative distribution functions $R$ of the collection of numbers. For this simplified model we can find the limiting marginal distribution as a function of the initial conditions. Agreement with experimental results of the BS model is excellent. We analyze two main cases: The exogenous case where the new fitnesses are taken from an a priori fixed distribution, and the endogenous case where the new fitnesses are taken from the current distribution as it evolves.
Tue, 12 May 2015 13:15 A302 Mihalis Kolountzakis Univ. of Crete Fourier pairs of discrete support with little structure
paper
Mon, 15 Jun 2015 10:00 A302 Thai Hoang Le Ecole Polytechnique Additive bases in groups

Abstract:

Let $\mathbb{N}$ be the set of all nonnegative integers. A set $A \subset \mathbb{N}$ is called a basis of $\mathbb{N}$ if every sufficiently large integer is a sum of $h$ elements from $A$, for some $h$. The smallest such $h$ is called the order of $A$. For example, the squares form a basis of order 4 and the primes form a basis of order 3 of $\mathbb{N}$. Erdos and Graham asked the following questions. If $A$ is a basis of $\mathbb{N}$ and $a \in A$, when is $A \setminus \{ a \}$ still a basis? It turns out that this is the case for all $a \in A$ except a finite number of exceptions. If $A \setminus \{ a \}$ is still a basis, what can we say about its order? These questions and related questions have been extensively studied. In this talk, we address these questions in the more general setting of an abelian group in place of $\mathbb{N}$. This is joint work with Victor Lambert and Alain Plagne.

Wed, 24 Jun 2015 13:15 A302 Nikolaos Tsirivas Univ. of Crete Common hypercyclic vectors for backward shift and differential operators
Tue, 14 Jul 2015 14:15 A303 Grigoris Paouris Texas A & M Univ. Bounding marginal densities via affine isoperimetry

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