Analysis Seminar in Crete (2021-22) |
Σεμιναριο Αναλυσης
Analysis Seminars in the World / Analysis seminars in Greece
Wednesday, October 13, 2021, 11:00, Room: A303
Speaker: Effie Papageorgiou
(University of Crete)
How many Fourier coefficients are needed?
Abstract:
We are looking at families of functions or measures on the torus (in dimension one and two) which are specified by a finite number of parameters $N$. The task, for a given family, is to look at a small number of Fourier coefficients of the object, at a set of locations that is predetermined and may depend only on $N$, and determine the object. We look at (a) the indicator functions of at most $N$ intervals of the torus and (b) at sums of at most $N$ complex point masses on the two-dimensional torus. In the first case we reprove a theorem of Courtney which says that the Fourier coefficients at the locations $0, 1, \ldots, N$ are sufficient to determine the function (the intervals). In the second case we produce a set of locations of size $O(N \log N)$ which suffices to determine the measure.
Joint work with M. Kolountzakis (U. of Crete).
Wednesday, October 27, 2021, 11:00, Room: A303
Speaker: Nikos Karamanlis
(University of Crete)
Conformal maps in weighted Bergman spaces and the Bergman number
Abstract: We will give several geometric characterizations of conformal maps in weighted Bergman spaces. These characterizations involve certain conformal invariants, as well as certain Euclidean geometric quantities and they extend some known results for Hardy spaces to weighted Bergman spaces. Moreover, we shall discuss the notion of the Bergman number which is the analogue of the Hardy number for weighted Bergman spaces.
Wednesday, November 3, 2021, 11:00, Room: A303
Speaker: Themis Mitsis
(University of Crete)
A geometric approach to the distance-set problem
Abstract: In the problem of the distance set we are seeking a lower bound for the "size" of the set of all distances between points of a set $A$ as a function of the "size" of the set $A$. While all approaches are using the Fourier Transform, I will describe a naive geometric method, which, without giving optimal results, can give non-trivial information.
Wednesday, November 10, 2021, 11:00, Room: A303
Speaker: Camille Labourie
(University of Cyprus)
Calibrations for a free-discontinuity problem with Robin condition
Abstract: Here
Wednesday, December 8, 2021, 11:00, Room: A303
Speaker: Mihalis Kolountzakis
(University of Crete)
The size of a common tile of several lattices
Abstract:
Old and new results will be described on the following question: if $T$ is a common set of coset representatives for the subgroups $G_i$ of the abelian group $G$, all of them of the same index, how large must $T$ be? This will be discussed under various assumptions and several notions of what it means to be large.
The $G_i$ are mostly lattices in Euclidean spaces, and $T$ is mostly assumed to be measurable, but not always. Several open questions, of varying levels of difficulty will be presented.
Wednesday, January 12, 2022, 11:00, Room: A303
Speaker: Nikos Karamanlis
(University of Crete)
A characterization of the unit disk and the harmonic measure doubling condition
Abstract: Suppose $D$ is a bounded Jordan domain in the plane. A well known theorem by Jerison and Kenig states that the boundary of $D$ is a quasicircle if and only if both $D$ and its complement are doubling domains with respect to the harmonic measure. This theorem fails if we only assume that $D$ is a doubling domain. We show that if $D$ is a doubling domain with constant $c = 1$, then it must be a disk.
Thursday, February 3, 2022, 11:00, Room: A303
Speaker: Nikos Frantzikinakis
(University of Crete)
Furstenberg systems of sequences and applications
Abstract: Furstenberg systems are measure preserving systems that are used to model the statistical behavior of bounded sequences of complex numbers. I will give a variety of examples of such systems and briefly explain how their dynamical properties can be used to prove multiple recurrence results that for the moment do not seem to be attainable by more traditional techniques. To make this more interactive, feel free to bring your favorite sequence and we'll see if we can say something interesting about the corresponding Furstenberg system.
Thursday, March 31, 2022, 11:00, Room: A303
Speaker: Kostantinos Tsinas
(University of Crete)
Multiple ergodic averages along sequences of polynomial growth
Abstract: Our problem is to determine the limiting behavior of multiple ergodic averages, where the iterates involve sequences that arise from smooth, well-behaved functions and which do not grow faster than polynomials. We show that under some suitable linear independence assumptions, the corresponding averages converge (in the $L^2$ sense ) to the product of the integrals of the involved functions in ergodic systems. Our approach relies on some recent joint ergodicity results and some new seminorm estimates for multiple ergodic averages in our setting.
Thursday, May 26, 2022, 11:00, Room: A303
Speaker: Leonidas Daskalakis
(Rutgers University)
Quantitative forms of pointwise convergence of Ergodic Averages
Abstract: In this talk, we will describe a standard two-step procedure for establishing pointwise convergence of Ergodic Averages. We will apply that procedure for a wide class of non-conventional ergodic averages and we will use quantitative forms of pointwise convergence to carry out those two steps and establish pointwise convergence on $L^1$. (Notably, we will disprove a conjecture of Rosenblatt–Wierdl.)
Thursday, June 16, 2022, 11:00, Room: A303
Speaker: Andreas Mountakis
(University of Warwick)
TBA
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