Analysis Seminar in Crete (2022-23) |
Σεμιναριο Αναλυσης
Analysis Seminars in the World / Analysis seminars in Greece
9/22/2022, 11:00, Room: A303
Speaker: Andreas Koutsogiannis
( Aristotle University of Thessaloniki)
Joint ergodicity for functions of polynomial degree
Abstract: In this talk we will deal with multiple ergodic averages having iterates a common integer-valued sequence that comes from appropriate classes of functions. In particular, we are dealing with the combination of a Hardy, a tempered, and a polynomial function satisfying some growth-rate restrictions to avoid local obstructions. Joint work with S. Donoso and W. Sun.
9/29/2022, 11:00, Room: A303
Speaker: Giorgos Chasapis
(University of Crete)
On a Rademacher-Gaussian tail comparison
Abstract: Let $\varepsilon_1,\varepsilon_2,\ldots$ be independent Rademacher random variables and $g_1,g_2,\ldots$ be independent standard Gaussian random variables. Pinelis has proved that there is an absolute constant $C>0$ such that for every $n\in\mathbb{N}$, real numbers $v_1,\ldots,v_n$ and any $t>0$, $$ \mathbb{P}\left(\left|\sum_{j=1}^n v_j\varepsilon_j\right|\gtrapprox t\right)\lessapprox C\cdot \mathbb{P}\left(\left|\sum_{j=1}^n v_jg_j\right|\gtrapprox t\right). $$ We extend this Rademacher-Gaussian tail comparison to the case of complex coefficients and discuss related open problems.
Based on joint work with R. Liu and T. Tkocz.
10/13/2022, 12:00, Room: A303
Speaker: Silouanos Brazitikos
(University of Crete)
Geometric Inequalities and their Functional Analogues
Abstract: We explain connections between classical geometric inequalities, like isoperimetric or Loomis-Whitney, or Kakeya type and their functional analogues. Joint work with D. Alonso, J. Bernues and A. Carbery
10/20/2022, 11:00, Room: A303
Speaker: Grigorios Fournodavlos
(University of Crete)
On the nature of the Big Bang singularity
Abstract: 100 years ago, Friedmann and Kasner discovered the first exact cosmological solutions to Einstein’s equations, revealing the presence of a striking new phenomenon, namely, the Big Bang singularity. Since then, it has been the object of study in a great deal of research on general relativity. However, the nature of the ‘generic’ Big Bang singularity remains a mystery. Rivaling scenarios are abound (monotonicity, chaos, spikes) that make the classification of all solutions a very intricate problem. I will give a historic overview of the subject and describe recent progress that confirms a small part of the conjectural picture.
11/24/2022, 11:00, Room: A303
Speaker: Borys Kuca
(University of Crete)
Multiple ergodic averages along polynomials and joint ergodicity
Abstract: Furstenberg’s dynamical proof of the Szemerédi theorem initiated a thorough examination of multiple ergodic averages, laying the grounds for a new subfield within ergodic theory. Special attention has been paid to averages of commuting transformations with polynomial iterates owing to their central role in Bergelson and Leibman’s proof of the polynomial Szemerédi theorem. Their norm convergence has been established in a celebrated paper of Walsh, but for a long time, little more has been known due to obstacles encountered by existing methods. Recently, there has been an outburst of research activity which sheds new light on their limiting behaviour. I will discuss a number of novel results, including new seminorm estimates and limit formulas for these averages. Additionally, I will talk about new criteria for joint ergodicity of general families of integer sequences whose potential utility reaches far beyond polynomial sequences. The talk will be based on two recent papers written jointly with Nikos Frantzikinakis.
12/1/2022, 11:00, Room: A303
Speaker: Romanos Malikiosis
(Aristotle Univ. of Thessaloniki)
Covering radii of polytopes and the lonely runner conjecture
Abstract: We will present a new algorithm on computing the covering radius of a polytope, whose vertices have rational coordinates. We will then apply this algorithm to solve the first unknown case of the shifted lonely runner conjecture (the case of four runners). For this purpose, we will use the geometric reformulation of this conjecture, which was given by the speaker and Schymura in 2017, and yields an inequality involving the covering radius of a special class of zonotopes.
Such an algorithm was first given by Kannan in 1992, but ours is much faster. Moreover, the geometric reformulation of the lonely runner conjecture leads to an improvement of Tao's result in 2017, concerning the number of cases one needs to consider in order to solve the lonely runner conjecture for $\leq n$ runners (work in progress).
This is joint work with Cslovjecsek, Naszodi, Schymura.
12/8/2022, 11:00, Room: Α303
Speaker: Effie Papageorgiou
(University of Crete)
Large Sets containing no copies of a given infinite sequence
Abstract: Let $\mathbb{A}$ be a discrete, unbounded, infinite set in $\mathbb{R}$. Can we find a ``large" measurable set $E\subset \mathbb{R}$ which does not contain any affine copy $x + t\mathbb{A}$ of $\mathbb{A}$ (for any $x\in \mathbb{R}$, $t > 0$)?
If $a_n$ is a real, nonnegative sequence that does not increase exponentially, then, for any $0\leq p < 1$, we construct a Lebesgue measurable set which has measure at least $p$ in any unit interval and which contains no affine copy of the given sequence. We generalize this to higher dimensions and also for some ``non-linear" copies of the sequence. Our method is probabilistic.
Joint work with M. Kolountzakis.
12/15/2022, 11:00, Room: A303
Speaker: Mihalis Kolountzakis
(University of Crete)
Sets of full measure avoiding Cantor sets
Abstract: In relation to the Erdos similarity problem (show that for any infinite set $A$ of real numbers there exists a set of positive Lebesgue measure which contains no affine copy of $A$) we give some new examples of infinite sets which are not universal in measure, i.e. they satisfy the above conjecture. These are symmetric Cantor sets $C$ which can be quite thin: the length of the $n$-th generation intervals defining the Cantor set is decreasing almost doubly exponentially. Further, we achieve to construct a set, not just of positive measure, but of full measure not containing any affine copy of $C$. Our method is probabilistic.
Seminar organizer for 2022-23: Silouanos Brazitikos
Page maintained by Mihalis Kolountzakis.