Analysis Seminar in Crete (2013-14)

Σεμιναριο Αναλυσης

In chronological ordering

DATE TIME ROOM SPEAKER FROM TITLE COMMENT
Wed, 9 Oct 2013 13:15 B212 Mihalis Kolountzakis University of Crete Riesz bases of exponentials for some domains
Wed, 20 Nov 2013 13:15 A302 Nikos Frantzikinakis University of Crete Szemeredi's theorem with random differences
Wed, 4 Dec 2013 13:15 A302 Georgios Costakis University of Crete Rotations of hypercyclic operators with polynomial phases
Wed, 18 Dec 2013 13:15 A302 Achilles Tertikas University of Crete On the Hardy constant of non-convex planar domains I
Tue, 4 Feb 2014 11:15 A302 Artur Nicolau Universitat Autonoma de Barcelona Oscillation of Holder continuous functions
Tue, 18 Feb 2014 11:15 A302 Achilles Tertikas University of Crete On the Hardy constant of non-convex planar domains II
Tue, 25 Feb 2014 11:15 A302 Sigrid Grepstad NTNU Trondheim Multi-tiling and Riesz bases
Let $S$ be a bounded, Riemann measurable set in ${\mathbb R}^d$, and let $L$ be a lattice. By a theorem of Fuglede, if $S$ tiles ${\mathbb R}^d$ with translation set $L$, then $S$ has an orthogonal basis of exponentials. We show that, under the more general condition that $S$ multi-tiles ${\mathbb R}^d$ with translation set, $S$ has a Riesz basis of exponentials. The proof is based on Meyer’s quasicrystals. This is a joint work with Nir Lev.
Tue, 4 Mar 2014 11:15 A302 Mihalis Kolountzakis Univ. of Crete Checkerboard discrepancies
Consider the plane as a checkerboard, with each unit square colored black or white in an arbitrary manner. Suppose now that we place a piece of a curve C on that plane and that we measure the difference of the white and black length induced on the curve $C$ by the coloring of the plane. Call this the discrepancy of $C$. The main theme of this talk is that, no matter what the coloring, one can “place” the curve $C$ in such a manner that its discrepancy is “large”. For instance, if $C$ is a straight line segment which is free to move then we can always find a placement where the discrepancy is at least $\sqrt{L}$, where $L$ is the length of the segment. The problem may be stated for several families of curves with various degrees of freedom. For instance one might consider circles or circular arcs which are free to dilate and translate or free to translate only, and in many of these cases we have results that are similar to the segment case, although there are several cases where the answer really ought to be known yet our approach leaves it out. For instance, what is the discrepancy of an L-shaped union of line segments that is free to translate, dilate and rotate? It ought to be the square root of the length but we cannot prove it. Our methods use Fourier Analysis. This is joint work with Alex Iosevich and Ioannis Parissis.
Thu, 6 Mar 2014 12:15 A302 Panagiotis Mavroudis University of Crete Extremal and approximation problems for positive definite functions (PhD defence)
Tue, 11 Mar 2014 11:15 A302 Christos Papachristodoulos Some new properties of uniform convergence at a point and applications to differential equations
Tue, 18 Mar 2014 11:15 A302 Christos Sourdis Univ. of Crete Thomas-Fermi approximation for two component Bose-Einstein condensates and nonexistence of vortices for small rotation
We study minimizers of a Gross-Pitaevskii energy describing a two-component Bose-Einstein condensate confined in a radially symmetric harmonic trap and set into rotation. We consider the case of coexistence of the components in the Thomas-Fermi regime, where a small parameter conveys a singular perturbation. The minimizer of the energy without rotation is determined as the positive solution of a system of coupled PDE's for which we show uniqueness. The limiting problem (when the small parameter is 0) has degenerate and irregular behavior at specific radii, where the gradient blows up. By means of a perturbation argument, we obtain precise estimates for the convergence of the minimizer to this limiting profile, as the small parameter tends to zero. For low rotation, based on these estimates, we can show that the ground states remain real valued and do not have vortices, even in the region of small density. This is a joint work with A. Aftalion and B. Noris.
Tue, 29 Apr 2014 11:15 A302 Georgios Stylogiannis Univ. of Thessaloniki Mean Lipschitz spaces
Abstract
Tue, 10 June 2014 11:15 A302 Nikos Tsirivas University of Crete Universal Taylor series on specific compact sets

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