Analysis Seminar in Crete (2018-19) |
Σεμιναριο Αναλυσης
Analysis Seminars in the World / Analysis seminars in Greece
DATE | TIME | ROOM | SPEAKER | FROM | TITLE | COMMENT |
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9/7/2018 | 11:15 | B201 | Agelos Georgakopoulos | University of Warwick | Analytic functions in bond percolation | |
Abstract: We consider Bernoulli bond percolation on various graphs/groups and prove that certain functions are analytic in the percolation parameter $p$. This will be an overview talk; hardly any background will be assumed. Joint work with C. Panagiotis. |
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9/19/2018 | 9:00 | B201 | Speakers | Fourier Bases 2018 | ||
Abstract: http://fourier.math.uoc.gr/fb18 | ||||||
9/20/2018 | 9:00 | B201 | Speakers | Fourier Bases 2018 | ||
Abstract: http://fourier.math.uoc.gr/fb18 | ||||||
9/21/2018 | 9:00 | B201 | Speakers | Fourier Bases 2018 | ||
Abstract: http://fourier.math.uoc.gr/fb18 | ||||||
10/30/2018 | 10:00 | A303 | George Costakis | University of Crete | Unions of numerical ranges | |
11/13/2018 | 10:00 | A303 | Themis Mitsis | University of Crete | Projection theorems for antichains | |
1/24/2019 | 11:00 | A303 | Nikos Tsirivas | University of Ioannina | Computation of the acceleration in the uniform circular motion | |
Abstract: In physics circular motion is a movement of an object along the circumference of a circle or rotation along a circular path. It can be uniform, with constant angular rate of rotation and constant speed, or non-uniform with a changing rate of rotation. The rotation around a fixed axis of a three-dimensional body involves circular motion of its parts. The equations of motion describe the movement of the center of mass of a body. Examples of circular motion include: an artificial satellite orbiting the Earth at a constant height, a ceiling fan's blades rotating around a hub, a stone which is tied to a rope and is being swung in circles, a car turning through a curve in a race track, an electron moving perpendicular to a uniform magnetic field, and a gear turning inside a mechanism. Since the object's velocity vector is constantly changing direction, the moving object is undergoing acceleration by a centripetal in the direction of the center of rotation. Without this acceleration, the object would move in a straight line, according to Newton's laws of motion. In this talk we derive the formula of acceleration of the uniform circular motion using direct computation (the argument seems to be not widely known). The talk will be targeted towards undergraduate and graduate students. |
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2/12/2019 | 10:00 | A303 | Vasiliki Evdoridou | The Open University | Singularities of inner functions and entire maps of finite order | |
Abstract: Let $f$ be a transcendental entire function of finite order and $U$ an unbounded, invariant connected component of the Fatou set of $f$. We can associate an inner function, $g$ say, to the restriction of $f$ to $U$. We show that for two classes of entire functions whose set of singular values is bounded, the number of singularities of $g$ on the unit circle is at most twice the order of $f$. This is joint work with N. Fagella, X. Jarque and D. Sixsmith. |
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2/19/2019 | 10:00 | A303 | Vassili Nestoridis | University of Athens | Mergelyan approximations in several complex variables and a new algebra of functions | |
3/13/2019 | 10:00 | A303 | Georgios Costakis | University of Crete | Dynamics of linear operators and similarity transformations | |
4/3/2019 | 10:00 | A303 | Rachel Greenfeld | Bar Ilan University | Fuglede's spectral set conjecture for convex polytopes | |
Abstract: A set $\Omega \subset \mathbb{R}^d$ is called spectral if the space $L^2(\Omega)$ admits an orthogonal basis of exponential functions. In 1974, B. Fuglede conjectured that spectral sets could be characterized geometrically as sets which can tile the space by translations. Although this conjecture inspired extensive research, the precise connection between the notions of spectrality and tiling is still not clear. In the talk I will survey the subject, and discuss some recent results, joint with Nir Lev, where we focus on the conjecture for convex polytopes. | ||||||
4/17/2019 | 10:00 | A303 | Yurii Lyubarskii | NTNU Norway | Exponential Basis in Convex Polygons | |
Abstract: Let $D$ be a convex polygon in the plane which is symmetric with respect to the origin. We offer a construction of a Riesz basis in $L^2(D)$ of the form $\{\exp(i\langle x, \lambda \rangle)\}_{\lambda \in \Lambda}$, where $\Lambda$ is a sequence of points in $\mathbb R ^2$. The construction is based on solution of interpolation problem in the corresponding space of entire functions. This is a joint work with A. Rashkovskii. |
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5/28/2019 | 11:00 | A303 | Christos Pelekis | Institute of Mathematics, Czech Academy of Sciences | A continuous analogue of Erdos' $k$-Sperner theorem | |
Abstract: A chain in the unit $n$-cube is a set $C\subset [0,1]^n$ such that for every $\mathbf{x}=(x_1,\ldots,x_n)$ and $\mathbf{y}=(y_1,\ldots,y_n)$ in $C$ we either have $x_i\le y_i$ for all $i\in [n]$, or $x_i\ge y_i$ for all $i\in [n]$. We show that the $1$-dimensional Hausdorff measure of a chain in the unit $n$-cube is at most $n$, and that the bound is sharp. Given this result, we consider the problem of maximising the $n$-dimensional Lebesgue measure of a measurable set $A\subset [0,1]^n$ subject to the constraint that it satisfies $H^1(A\cap C) \leq \kappa$ for all chains $C\subset [0,1]^n$, where $\kappa$ is a fixed real number from the interval $(0,n]$. We show that the measure of $A$ is not larger than the measure of the following optimal set: \[ A^{\ast}_{\kappa} = \left\{ (x_1,\ldots,x_n)\in [0,1]^n : \frac{n-\kappa}{2}\le \sum_{i=1}^{n}x_i \le \frac{n+ \kappa}{2} \right\} \, . \] Our result may be seen as a continuous counterpart to a theorem of Erdos, regarding $k$-Sperner families of finite sets. Joint work with Themis Mitsis and Vaclav Vlasak | ||||||
6/12/2019 | 10:00 | A303 | George Androulakis | Univ. of South Carolina | The role of entropy in quantum communications | |
Abstract: We will review the properties of quantum entropy and indicate its uses in quantum communications. | ||||||
7/3/2019 | 11:15 | A303 | Mate Matolcsi | Renyi Institute | Fuglede's conjecture for convex bodies | |
Abstract: We prove that a convex body $K$ tiles $\mathbb{R}^n$ if and only if it is spectral, i.e. the space $L^2(K)$ has an orthogonal basis of exponentials. The proof relies on a construction of a so-called "diffraction measure" and a corresponding weak tiling property for $K$. Joint work with Nir Lev. |
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