, 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.
, 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)
, HS
Measure doubling of small sets in SO(3,R)
Tran Chieu Minh
In a recent work, we show that if A is an open subset of SO(3,R) with sufficiently small normalized Haar measure, then \mu(A^2) >3.99 \mu(A). Our result was conjectured by Breuillard and Green around 2010 in the context of finding continuous counterparts of product theorems for groups of Lie type by Helfgott, Pyber-Szabo, and Breuillard-Green-Tao. In less precise forms, the question traces back to much earlier works of Henstock and Macbeath in the 50s. In this talk, I will discuss this result and its proof highlighting the fact that ideas from neostable group theory serve both as actual ingredients of the argument and as conceptual principles behind the stage. (Based on joint work with Yifan Jing and Ruixiang Zhang)
11-05-2023 12:15
, 603
Simulation of uniformly distributed points on some geometrical objects
Tomasz Rolski (Uniwersytet Wrocławski)
We will survey various methods for simulation of uniformly distributed points on geometrical objects. In particular we consider d-dimensional balls, d-1-dimensional spheres. Interesting and not obvious problems appear when simulating random points on ellipses or ellipsoids. We conclude with a "numerical methods" for generating random points on parametrized objects like hyper-ellipsoids.
, A.4.1 C-19 (Politechnika Wrocławska)
Totally imperfect Menger sets
Piotr Szewczak (UKSW)
A set of reals X is Menger if for any countable sequence of open covers of X one can pick finitely many elements from every cover in the sequence such that the chosen sets cover X. Any set of reals of cardinality smaller than the dominating number d is Menger and there is a non-Menger set of cardinality d. By the result of Bartoszyński and Tsaban, in ZFC, there is a totally imperfect (with no copy of the Cantor set inside) Menger set of cardinality d. We solve a problem, whether there is such a set of cardinality continuum. Using an iterated Sacks forcing and topological games we prove that it is consistent with ZFC that d
06-06-2019 12:15
, 606
Testowanie stochastycznego uporządkowania dwóch funkcji przeżycia, II.
Grzegorz Wyłupek
Subskrybuj Seminars