Analysis Seminar in Crete (2019-20)

Σεμιναριο Αναλυσης

    Department of Mathematics and Applied Math / Fourier and Functional Analysis / Previous years: 2018-19/ 2017-18/ 2016-17/ 2015-16/ 2014-15/ 2013-14/ 2012-13/ 2011-12/ 2010-11/ 2009-10/ 2008-09/ 2007-08/ 2006-07/ 2005-06/ 2004-05 / Summer 2004 / 2003-04 / 2002-03 / 2001-02 / 2000-01 / 1999-00

    Analysis Seminars in the World / Analysis seminars in Greece

In chronological ordering

10/9/2019 10:00 A303Nikos FrantzikinakisUniversity of Crete Good weights for the Erdös discrepancy problem
Abstract: The Erdös discrepancy problem, now a theorem by T. Tao, asks whether every sequence with values plus or minus one has unbounded discrepancy along all homogeneous arithmetic progressions. We establish weighted variants of this problem, for weights given either by structured sequences that enjoy some irrationality features, or certain random sequences. As an intermediate result, we establish unboundedness of weighted sums for all bounded multiplicative functions and products of shifts of such functions. A key ingredient in our analysis for the structured weights, is a structural result for measure preserving systems naturally associated with bounded multiplicative functions that was recently obtained in joint work with B. Host.
10/22/2019 12:00 A303Kostas PanterisUniversity of Crete Closed range composition operators on Besov spaces and on BMOA
10/30/2019 10:00 A303Nikos PoursalidisUniversity of Crete Structural results for multiple translational tilings (Master's thesis presentation)
11/6/2019 10:00 A302Anastasia MestnikovaNovosibirsk State Univ. Free surface of an ideal fluid flow with a singular sink
Abstract: A two-dimensional steady problem of a potential free-surface flow of an ideal incompressible fluid caused by a singular sink is considered. The sink is placed at the horizontal bottom of the fluid layer. By employing a conformal mapping, the problem is equivalently rewritten in the unit circle. With the help of the Levi-Civita technique, the problem is reformulated as an operator equation in a Hilbert space. It is proved that there exists a unique solution of the problem provided that the Froude number is greater than some particular value. The free boundary corresponding to this solution is investigated.
11/20/2019 10:00 A303Romanos MalikiosisAristotle Univ. of Thessaloniki The lonely runner conjecture
Abstract: Suppose we have $n$ runners with pairwise distinct constant speeds on a circular track of length 1. Is it true that every runner gets "lonely" some time, that is, the distance of every other runner is at least $1/n$? This is the content of the so-called Lonely Runner Conjecture, stated by Wills in 1968. We will present the history of this problem, as well as some recent results, for example by Terence Tao in 2017

We will also discuss the equivalence of this conjecture with several geometric problems, namely (a) lines in tori avoiding a smaller "copy" of the torus (b) lines avoiding a lattice arrangement of cubes (c) billiard ball movement in a cube (d) zonotopes avoiding a lattice. The results we obtain come from the zonotopal setting, the main tool being the Flatness Theorem of Khinchin and Banaszczyk's estimate.

This is partially joint work with Matthias Schymura.

12/18/2019 10:00 A303Maria NtekoumeUCLA Symplectic non-squeezing for the Korteweg--de Vries flow on the line
Abstract: The goal of this talk is to prove that the Korteweg--de Vries (KdV) flow on the line cannot squeeze a ball in $\dot H^{-\frac 1 2}$ into a cylinder of lesser radius. This is a PDE analogue of Gromov’s famous symplectic non-squeezing theorem for an infinite dimensional PDE in infinite volume.

1/29/2020 10:00 A303Jim TaoNTNU Norway A twisted local index formula for curved noncommutative four tori
Abstract: We consider the Dirac operator of a metric in a basic conformal class on the noncommutative four torus, twisted by an idempotent (representing the K-theory class of a general noncommutative vector bundle), and derive a local formula for the Fredholm index of the twisted Dirac operator. Our approach is based on the McKean-Singer index formula, and explicit heat expansion calculations by making use of Connes' pseudodifferential calculus. As a technical tool, a rearrangement lemma recently proven in our previous paper (which considers the case of noncommutative two tori) is used to handle challenges posed by the noncommutativity of the algebra and the presence of an idempotent in the calculations in addition to a conformal factor.
2/26/2020 10:00 A303Shahaf NitzanGeorgia Institute of Technology Trigonometric polynomials and Gaussian stationary processes
Abstract: We will discuss the relation between certain spectral properties of a Gaussian Stationary process (GSP) and the probability that this process remains positive over along interval. In particular we will be interested in GSP’s whose spectral measure has a gap around zero, and in the use of trigonometric polynomials to obtain in this case, a sharp estimate on the above mentioned probability.
Based on joint works with Naomi Feldheim, Ohad Feldheim, Benjamin Jaye, and Fedor Nazarov.
3/4/2020 10:00 A303Giannis PlatisUniversity of Crete Equidistant points in the Heisenberg group
Abstract: We prove that the Hausdorff and the metric (equidistant) dimension of the first Heisenberg group endowed with the homogeneous metric are both equal to 4. This is in contrast to the Euclidean 3-space where the metric dimension is 4. The proof is an explicit construction of a normalised quadruple of equidistant points in the Heisenberg group. This is a joint work with J. Kim.

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