Analysis Seminar in Crete (2015-16)

Σεμιναριο Αναλυσης

In chronological ordering

DATE TIME ROOM SPEAKER FROM TITLE COMMENT
Tue, 29 Sep 2015 13:45 A302 Themis Mitsis University of Crete Strong maximal functions and weights
Tue, 3 Nov 2015 13:15 A302 Nikos Frantzikinakis University of Crete Ergodic theorems with arithmetic weights.
Abstract: We present results with an arithmetic flavor that generalize the polynomial multidimensional Szemeredi theorem and related multiple recurrence and convergence results in ergodic theory. For instance, we show that in all these statements we can restrict the ''common difference'' to those integers that have an even (or an odd) number of distinct prime factors, or satisfy any other such congruence condition. In order to obtain these refinements we study the limiting behavior of some closely related multiple ergodic averages with weights given by appropriately chosen multiplicative functions. These averages are then analyzed using recent structural results for multiple correlation sequences and bounded multiplicative functions. This is joint work with B. Host.
Wed, 18 Nov 2015 13:15 A302 Nikolaos Pattakos University of Crete From dyadic estimates to continuous estimates in Harmonic analysis I
Abstract: A dyadic weighted estimate is going to be presented for the Martingale transform and then by the use of the Bellman function technique we will pass to an analogous estimate for continuous type operators such as the Hilbert transform and the Riesz transforms.
Wed, 2 Dec 2015 13:15 A302 Nikolaos Pattakos University of Crete From dyadic estimates to continuous estimates in Harmonic analysis II
Abstract: A dyadic weighted estimate is going to be presented for the Martingale transform and then by the use of the Bellman function technique we will pass to an analogous estimate for continuous type operators such as the Hilbert transform and the Riesz transforms.
Tue, 16 Feb 2016 13:15 A302 Jorge Antezana Univ. Nacional de la Plata and Instituto Argentino de Matemática "Alberto Calderón" Convergence of the iterated Aluthge Transform sequence for matrices
Abstract: Here in PDF.
Tue, 23 Feb 2016 13:15 A302 Elona Agora Instituto Argentino de Matemática "Alberto Calderón" Sufficient conditions for the boundedness of the Riesz transforms on Weighted Lorentz spaces
Abstract: Throughout this talk we will discuss an ongoing research on the boundedness of Riesz transforms on Weighted Lorentz spaces. We will present sufficient conditions for this boundedness in terms of the boundedness of the multi-dimensional Hardy-Littlewood maximal operator. Since the Riesz transforms are a natural generalization of the Hilbert transform in several variables, our work has been motivated by recent results on the boundedness of the Hilbert transform on the same spaces.
Tue, 15 Mar 2016 13:15 A302 Georgios Costakis University of Crete Kronecker type theorems and dynamics of matrices.
Tue, 29 Mar 2016 13:15 A302 Nikos Dafnis Technion An inequality for moments of log-concave functions on Gaussian random vectors
Abstract: We prove a sharp moment inequality for a log-concave or a log-convex function, on Gaussian random vectors. As an application we take a stability result for the classical logarithmic Sobolev inequality of L. Gross in the case where the function is log-concave.
Tue, 12 Apr 2016 13:15 A302 Agelos Georgakopoulos University of Warwick The planar Cayley graphs are effectively enumerable

Abstract:

We show [2] that a group admits a planar, finitely generated Cayley graph if and only if it admits a special kind of group presentation we introduce, called a planar presentation. Planar presentations can be recognised algorithmically. As a consequence, we obtain an effective enumeration of the planar Cayley graphs, yielding in particular an affirmative answer to a question of Droms et al. asking whether the planar groups can be effectively enumerated. This builds on the techniques of [1], where the 3-regular planar Cayley graphs have been classified.

Joint work with Matthias Hamann.

[1] A. Georgakopoulos. The planar cubic Cayley graphs. To appear in Memoirs of the AMS.
[2] Agelos Georgakopoulos and Matthias Hamann. The planar Cayley graphs are effectively enumerable. 2015. arXiv: 1506.03361.

Wed, 20 Apr 2016 10:15 A302 Mihalis Kolountzakis University of Crete Some variations of the Steinhaus tiling problem
Tue, 28 Jun 2016 13:15 A303 Jakub Konieczny University of Oxford Combinatorial properties of Nil-Bohr sets of integers
Abstract: We explore connections between two classes of sets of integers. On one hand, we have the Nil-Bohr sets, which are the natural analogues of Bohr sets in higher order Fourier analysis, and arise from dynamics on nilmanifolds. On the other hand - we have the purely combinatorial property SG*, which is a slight modification of the better known IP*. It was first observed by Host and Kra that the two classes mentioned above are closely connected, in that every SG*-set is piecewise Nil-Bohr. During the talk, a partial converse to this statement will be discussed, leading to a partial combinatorial characterisation of the class of Nil-Bohr sets. As an application, a characterisation of pre-nilsystems in terms of sets of return times will be obtained.
Tue, 5 Jul 2016 13:15 A303 Ioannis Kontoyiannis Athens Univ of Econ & Business Sumset and inverse sumset bounds for the entropy
Abstract: The development of the field of additive combinatorics in recent years has provided a collection of fascinating and deep, though elementary, tools for estimating the sizes of discrete subsets of abelian groups. Tao in 2010 connected these results with the entropy of discrete probability measures: Interpreting the entropy of a discrete random variable as the logarithm of its "effective support size", he provided a series of new inequalities for the discrete entropy. We will review this background and describe how Tao's results extend in a nontrivial way to the entropy of random elements in general abelian groups. The (somewhat surprising) key difference between the discrete and the general case is that the "functional submodularity" property of the discrete entropy needs to be replaced by the general "data processing property" of the entropy.

No background in information theory, entropy or additive combinatorics will be assumed. This is joint work with Mokshay Madiman.

Tue, 12 Jul 2016 13:15 A303 Andreas Koutsogiannis Ohio State University On the convergence of multiple correlation sequences with integer part polynomial iterates
Abstract: We will discuss known and new results on multiple correlation sequences. More specifically, we will show that multiple ergodic averages with iterates given by the integer part of real valued polynomials converge in the (uniform) mean. The key ingredient is a transference principle that enables one to deduce results for $\mathbb{Z}$-actions, from results for flows. Using the same method, we prove an extension of the multidimensional Szemerédi theorem which involves closest integer polynomials evaluated at the set of shifted primes.

All seminars

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