Analysis Seminar in Crete (201920) 
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Analysis Seminars in the World / Analysis seminars in Greece
DATE  TIME  ROOM  SPEAKER  FROM  TITLE  COMMENT 

Wednesday, October 9, 2019  10:00  A303  Nikos Frantzikinakis  University 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.  
Tuesday, October 22, 2019  12:00  A303  Kostas Panteris  University of Crete  Closed range composition operators on Besov spaces and on BMOA  
Wednesday, October 30, 2019  10:00  A303  Nikos Poursalidis  University of Crete  Structural results for multiple translational tilings (Master's thesis presentation)  
Wednesday, November 6, 2019  10:00  A302  Anastasia Mestnikova  Novosibirsk State Univ.  Free surface of an ideal fluid flow with a singular sink  
Abstract: A twodimensional steady problem of a potential freesurface 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 LeviCivita 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.  
Wednesday, November 20, 2019  10:00  A303  Romanos Malikiosis  Aristotle 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 socalled 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. 

Wednesday, December 18, 2019  10:00  A303  Maria Ntekoume  UCLA  Symplectic nonsqueezing for the Kortewegde Vries flow on the line  
Abstract: The goal of this talk is to prove that the Kortewegde 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 nonsqueezing theorem for an infinite dimensional PDE in infinite volume.


Wednesday, January 29, 2020  10:00  A303  Jim Tao  NTNU 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 Ktheory 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 McKeanSinger 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.  
Wednesday, February 26, 2020  10:00  A303  Shahaf Nitzan  Georgia 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. 

Wednesday, March 4, 2020  10:00  A303  Giannis Platis  University 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 3space 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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