Analysis Seminar, Dept. of Mathematics and Applied Math. -- Σεμινάριο Ανάλυσης

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Analysis Seminar in Crete (2024-25)

Σεμιναριο Αναλυσης

http://www.math.uoc.gr/analysis-seminar

Department of Mathematics and Applied Math

Analysis Seminars in the World / Analysis seminars in Greece

In chronological ordering

	Date	Speaker	Title
1.	Thu, 03 Oct 2024	Mate Matolcsi	The fractional chromatic number of the plane is at least 4
2.	Thu, 24 Oct 2024	Tomasz Tkocz	Two extensions of Webb’s simplex slicing
3.	Thu, 31 Oct 2024	Natalia Tziotziou	Inequalities for sections and projections of log-concave functions
4.	Thu, 05 Dec 2024	Davide Sclosa	Bounded Power Series on the Real Line
5.	Thu, 19 Dec 2024	Andreas Mountakis	On multiplicative recurrence along linear patterns
6.	Thu, 20 Feb 2025	Sha Wu	Spectrality of a measure consisting of two line segments
7.	Wed, 12 Mar 2025	Manos Spyridakis	Exponential polynomials and identification of polygonal regions from Fourier samples
8.	Thu, 10 Apr 2025	Michail Fasoulakis	New algorithms for two-player zero-sum games: from games to optimization and learning
9.	Thu, 24 Apr 2025	Borys Kuca	Joint ergodicity - 40 years on

Thu, 03 Oct 2024, 11:15, Room: A303
Speaker: Mate Matolcsi (Renyi Institute (Budapest))

The fractional chromatic number of the plane is at least 4

Abstract: We prove that the fractional chromatic number of the unit distance graph of the Euclidean plane is greater than or equal to 4. This improves a series of earlier lower bounds edging closer to 4 over the past decades. A fundamental ingredient of the proof is the notion of geometric fractional chromatic number introduced recently in connection with the density of planar 1-avoiding sets. In the proof we also exploit the amenability of the group of Euclidean transformations in dimension 2.

Thu, 24 Oct 2024, 11:15, Room: A303
Speaker: Tomasz Tkocz (Carnegie Mellon University)

Two extensions of Webb’s simplex slicing

Abstract: I shall present two refinements of Webb’s sharp upper bound on the volume of central slices of the regular simplex: stability as well as sharp bounds on $L_p$ norms.

Thu, 31 Oct 2024, 11:15, Room: Α303
Speaker: Natalia Tziotziou (NTUA-SEMFE)

Inequalities for sections and projections of log-concave functions

Abstract: We provide extensions of geometric inequalities about sections and projections of convex bodies to the setting of integrable log-concave functions. Namely, we consider suitable generalizations of the affine and dual affine quermassintegrals of a log-concave function f and obtain upper and lower estimates for them in terms of the integral $\|f\|_1$ of $f$ , we give estimates for sections and projections of log-concave functions in the spirit of the lower dimensional Busemann-Petty and Shephard problem, and we extend to log-concave functions the affirmative answer to a variant of the Busemann-Petty and Shephard problems, proposed by V. Milman.

Thu, 05 Dec 2024, 11:15, Room: A303
Speaker: Davide Sclosa (University of Crete)

Bounded Power Series on the Real Line

Abstract: The power series of $\sin(x)$ , $\exp(-\pi x^2)$ , and $\exp(1-\exp(x))$ , all converge to a bounded function on the real line. What do their coefficients have in common? In this talk, we explore this question from analytical, topological, and algebraic perspectives. For $\exp(1-\exp(x))$ , the question relates to an open problem in analytic combinatorics.

Thu, 19 Dec 2024, 11:15, Room: A303
Speaker: Andreas Mountakis (University of Crete)

On multiplicative recurrence along linear patterns

Abstract: In a recent article, Donoso, Le, Moreira and Sun studied sets of recurrence for multiplicative actions of the natural numbers and provided some sufficient conditions for sets of the form $S=\{ (an+b)/(cn+d) : n\in \mathbb{N}\}$ to be sets of recurrence for such actions. A necessary condition for $S$ to be a set of multiplicative recurrence is that for every completely multiplicative function $f$ taking values in $\mathbb{S}^1$ we have that $\liminf_{n\to \infty} |f(an+b)-f(cn+d)|=0$ . We fully characterise the integer quadruples $(a,b,c,d)$ which satisfy the latter property. Our result generalizes a result of Klurman and Mangerel concerning the pair $(n,n+1)$ , as well as some results of Donoso, Le, Moreira and Sun. This is based on joint work with Dimitrios Charamaras and Konstantinos Tsinas.

Thu, 20 Feb 2025, 11:15, Room: A303
Speaker: Sha Wu (University of Crete/Hunan University)

Spectrality of a measure consisting of two line segments

Abstract: Take an interval $[t, t+1]$ on the $x$ -axis together with the same interval on the $y$ -axis and let $\rho$ be the normalized one-dimensional Lebesgue measure on this set of two segments. Continuing the work done by Lev (2018), Lai, Liu and Prince (2021) as well as Ai, Lu and Zhou (2023) we examine the spectrality of this measure for all different values of $t$ (being spectral means that there is an orthonormal basis for $L^2(\rho)$ consisting of exponentials $e^{2\pi i (\lambda_1 x + \lambda_2 y)}$ ). We almost complete the study showing that for $-\frac12 \lt t \lt 0$ and for all $t \notin \QQ$ the measure $\rho$ is not spectral. The only remaining undecided case is the case t=-1/2 (plus space). We also observe that in all known cases of spectral instances of this measure the spectrum is contained in a line and we give an easy necessary and sufficient condition for such measures to have a line spectrum.

Joint work with Mihalis Kolountzakis.

Wed, 12 Mar 2025, 11:15, Room: A303
Speaker: Manos Spyridakis (University of Crete)

Exponential polynomials and identification of polygonal regions from Fourier samples

Abstract: Consider the set $E(D, N)$ of all bivariate exponential polynomials

$f(\xi, \eta) = \sum_{j=1}^n p_j(\xi, \eta) e^{2\pi i (x_j\xi+y_j\eta)},$ where the polynomials

$p_j \in \CC[\xi, \eta]$ have degree $ We use this in order to prove some uniqueness results about polygonal regions given a small set of samples of the Fourier Transform of their indicator function. If the number of different slopes of the edges of the polygonal region is

$\le k$ then the region is determined from a predetermined set of Fourier samples that depends only on

$k$ and the maximum number of vertices

$N$ and is of size

$O(k^2 N \log N)$ . In the particular case where all edges are known to be parallel to the axes the polygonal region is determined from a set of

$O(N \log N)$ Fourier samples that depends on

$N$ only.

Our methods are non-constructive.

Joint work with Mihalis Kolountzakis.

Thu, 10 Apr 2025, 11:15, Room: Α303
Speaker: Michail Fasoulakis (Royal Holloway, University of London)

New algorithms for two-player zero-sum games: from games to optimization and learning

Abstract: By the seminal paper of John von Neumann on the Minimax Theorem for two-player zero-sum games, this class of games became one of the most fundamental class in game theory. It is well-known that the computation of a pair of optimal solutions, Nash equilibrium, in this class can be done in polynomial-time by a number of different algorithms such as algorithms for Linear programming, first-order methods and learning algorithms. However, many of these algorithms are centralized and/or converge to an optimal solution on average. On the other hand, recent applications of zero-sum games in machine learning, particularly Generative Adversarial Networks (GANS), have created the need of new algorithms with better properties such as last-iterate convergence to an optimal solution. In this presentation, we present our two recent algorithms for computing a Nash equilibrium in these games: one gradient-based algorithm and one learning algorithm that improve the state of the art from different perspectives.

Thu, 24 Apr 2025, 11:15, Room: Α303
Speaker: Borys Kuca (Jagiellonian University, Kraków)

Joint ergodicity - 40 years on

Abstract: Abstract: Joint ergodicity is an extension of the classical notion of ergodicity to the case of several different measure-preserving actions on a probability space. Introduced in the 1980s by Bergelson and Berend, it has generated a lot of research activity ever since. In recent years, joint ergodicity has undergone a remarkable revival and been a subject of several breakthroughs. This talk will focus on my recent work (joint with S. Donoso, A. Koutsogiannis, W. Sun and K. Tsinas) in which we prove a number of new joint ergodicity results and seminorm estimates for multiple ergodic averages of commuting transformations along Hardy sequences.

All seminars

Seminar organizer for 2024-25: Silouanos Brazitikos

Page maintained by Mihalis Kolountzakis.