07-06-2023 10:15
, 602
Hyperbolic spaces and weighted estimates
Sheldy Ombrosi (Universidad Complutense de Madrid)
In 1981 Strömberg proved that the center Hardy-Littlewood maximal operator $M$ is of the weak-type $(1,1)$ in the context of Hyperbolic spaces. In fact his result actually is in a more general context (non-compact symmetric spaces). For $p>1$ boundedness results were previously obtained by Stein and Clerk. The main difficulty in the Hyperbolic setting is the exponential growth of the measure of a ball in terms of its radio.This difficulty has generated that, to the best of our knowledge, no general theory of weights has been developed in this context. In this talk using ideas of the discrete setting ($k$-trees) due to Naor and Tao we will show that it is possible to obtain a Fefferman-Stein endpoint weighted estimate generalizing the result of Strömberg. Moreover, we also obtain (sharp) sufficient (geometric) conditions in a weight $w$ for the weak and strong estimates of $M$ in the spaces $L^p(w)$ for $p>1$. The talk is based on a joint work with J. Antezana.
24-01-2019 14:15
, 603
Operator śladu na obszarach Jordana
Krystian Kazaniecki (Uniwersytet Warszawski)
Streszczenie. W latach pięćdziesiątych Gagliardo wykazał, że dla obszaru $\Omega$ z regularnym brzegiem operator śladu z przestrzeni Sobolewa $W^1_1(\Omega)$ do przestrzeni $L^1(\partial \Omega)$ jest surjekcją. Zatem naturalne jest pytanie o istnienie prawego odwrotnego operatora do operatora śladu. Petree udowodnił, że w przypadku półpłaszczyzny $\mathbb{R}x\mathbb{R}_{+}$ nie istnieje prawy odwrotny operator do operatora śladu. Podczas referatu przedstawię prosty dowód twierdzenia Petree, który wykorzystuje tylko pokrycie Whitney'a danego obszaru oraz klasyczne własności przestrzeni Banacha. Następnie zdefiniujemy operator śladu z przestrzeni Sobolewa $W^1_1(K)$, gdzie $K$ jest płatkiem Kocha. Przez pozostałą część mojego referatu skonstruujemy prawy odwrotny do operatora śladu na płatku Kocha. W tym celu scharakteryzujemy przestrzeń śladów jako przestrzeń Arensa-Eelsa z odpowiednią metryką oraz skorzystamy z twierdzenia Ciesielskiego o przestrzeniach funkcji hölderowskich.
15-10-2021 15:30
Entropy Weighted Regularisation: A General Way to Debias Regularisation Penalties
Olof Zetterqvist (University of Gothenburg/Chalmers)
Lasso and ridge regression are well established and successful models for variance reduction and, for the lasso, variable selection. However, they come with a disadvantage of an increased bias in the estimator. In this seminar, I will talk about our general method that learns individual weights for each term in the regularisation penalty (e.g. lasso or ridge) with the goal to reduce the bias. To bound the amount of freedom for the model to choose the weights, a new regularisation term, that imposes a cost for choosing small weights, is introduced. If the form of this term is chosen wisely, the apparent doubling of the number of parameters vanishes, by means of solving for the weights in terms of the parameter estimates. We show that these estimators potentially keep the original estimators’ fundamental properties and experimentally verify that this can indeed reduce bias.
01-06-2023 10:15
, 603
Symetryzatory na grupie hyperoktahedralnej B(n) (inaczej permutacje znakowane) z zastosowaniami do modeli przestrzeni Focka typuB
Marek Bożejko (Uniwersytet Wroclawski)
W referacie opiszemy zachowanie się symetryzatorów postaci $$P(\alpha,q) (x) = \alpha^{l_{1}(x)} q^{l_{2}(x))},$$ dla pewnych naturalnych długości $l(i) ,i=1,2$, na grupie $B(n)$ . Zbadamy kiedy te symetryzatory sa odwracalne i podamy zastosowania do konstrukcji nowych przestrzeni Focka. Podamy zwiazki z przestrzeniami q-Focka i przestrzeniami t-Focka,ktore badalismy z Januszem Wysoczanskim. Beda tez problemy z tej tematyki. Praca wspolna z Wiktorem Ejsmontem.
27-02-2023 14:15
, HS
Virtual combination of relatively quasiconvex subgroups and separability properties
Ashot Minasyan
Quasiconvex subgroups are basic building blocks of hyperbolic groups, and relatively quasiconvex subgroups play a similar role in relatively hyperbolic groups. If $Q$ and $R$ are relatively quasiconvex subgroups of a relatively hyperbolic group $G$ then the intersection $Q \cap R$ will also be relatively quasiconvex, but the join $\langle Q,R \rangle$ may not be. I will discuss criteria for the existence of finite index subgroups $Q’ \leqslant_f Q$ and $R’ \leqslant_f R$ such that the ``virtual join’’ $\langle Q’, R’ \rangle$ is relatively quasiconvex. This is closely related to separability properties of $G$ and I will present applications to limit groups, Kleinian groups and fundamental groups of graphs of free groups with cyclic edge groups. The talk will be based on joint work with Lawk Mineh.
22-05-2023 15:15
, 603
Geometric structure of 2D Navier-Stokes flows
Lorenzo Brandolese (Univ. Lyon 1)
25-05-2023 12:15
, 606
Inference for the multivariate coefficients of variation in factorial designs
Łukasz Smaga (Uniwersytet im. Adama Mickiewicza)
14-06-2023 14:15
, HS
Towards model theory of hyperfields
Piotr Błaszkiewicz
Hyperfields play a special role in the model theory of the henselian valued fields of mixed characteristic. They are used, in the form of so called $RV$-sorts, to provide numerous results, such as relative quantifier elimination. These particular objects are well known and well understood by the model theorists following the subject, however there is no model theory developed for the general theory of hyperfields. The goal of this talk is to look at the theory of hyperfields in general. We shall investigate some natural model theoretical questions one needs to ask when approaching this theory. We will focus on the question of the possibility of first order axiomatization of the class of Krasner factor hyperfields, and provide some partial results based on the work The hyperring of adèle classes of Alain Connes and Caterina Consani.
29-06-2023 13:15
, 603
The Classical Laplace Distribution: Fundamental Properties, Extensions, and Applications
Tomasz J. Kozubowski (University of Nevada, Reno)
We review basic facts about the classical Laplace distribution and its asymmetric generalization. Both distributions naturally arise in connection with random summation and quantile regression settings, and offer an attractive and flexible alternative to the normal (Gaussian) distribution in a variety of setting, where the assumptions of symmetry and short tail are too restrictive. The growing popularity of the Laplace-based models in recent years is due to their fundamental properties, which include a sharp peak at the mode, heavier than Gaussian tails, existence of all moments, infinite divisibility, and, most importantly, random stability and approximation of geometric sums. Since the latter arise quite naturally, these distributions provide useful models in diverse areas, such as biology, economics, engineering, finance, geosciences, and physics. We review fundamental properties of these models, which give insight into their applicability in these areas, and discuss their various extensions, including Laplace-based time series and stochastic processes. This is a joint work with K. Podgorski.
13-06-2023 17:15
, room A.4.1 C-19 (Politechnika Wrocławska)
Remarks and questions on hyperspaces of knots: Borel complexity and local contractibility
Paweł Krupski (Politechnika Wrocławska)
06-06-2019 12:15
, 606
Testowanie stochastycznego uporządkowania dwóch funkcji przeżycia, II.
Grzegorz Wyłupek
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