Seminars

18-01-2017 11:15
, C-11 PWr (Wydział Matematyki), sala 2.11
Mixed norm estimates for generalized radial spherical means
Adam Nowak (IM PAN)
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.
23-04-2021 15:30
, https://lu-se.zoom.us/j/65067339175
A precise high-dimensional asymptotic theory for AdaBoost
Pragya Sur, Harvard University
This talk will introduce a precise high-dimensional asymptotic theory for AdaBoost on separable data, taking both statistical and computational perspectives. We will consider the common modern setting where the number of features p and the sample size n are both large and comparable, and in particular, look at scenarios where the data is separable in an asymptotic sense. Under a class of statistical models, we will provide an (asymptotically) exact analysis of the generalization error of AdaBoost, when the algorithm interpolates the training data and maximizes an empirical L1 margin. On the computational front, we provide a sharp analysis of the stopping time when boosting approximately maximizes the empirical L1 margin. Our theory provides several insights into properties of Boosting; for instance, the larger the dimensionality ratio p/n, the faster the optimization reaches interpolation. At the heart of our theory lies an in-depth study of the maximum L1-margin, which can be accurately described by a new system of non-linear equations; we analyze this margin and the properties of this system, using Gaussian comparison techniques and a novel uniform deviation argument. Time permitting, I will present a new class of boosting algorithms that correspond to Lq geometry, for q>1, together with results on their high-dimensional generalization and optimization behavior. This is based on joint work with Tengyuan Liang.
08-04-2021 10:30
, zoom.us (kontakt: wiktor.ejsmont@gmail.com)
V-monotoniczne centralne twierdzenie graniczne, cz. 4
Adrian Dacko
W referacie zostanie zaprezentowana dokładna postać V-monotonicznego standardo- wego rozkładu gaussowskiego (a konkretnie jego gęstości, gdyż jest to miara absolutnie ciągła względem miary Lebesgue’a na prostej). Wyjdziemy od funkcji tworzącej momenty, która została uzyskana w pracy „V-monotone independence”, a następnie skonstruuje- my analityczne rozszerzenie transformaty Cauchy’ego do górnej półpłaszczyzny. Ze wzoru odwrócenia Stieltjesa otrzymamy gęstość, przy okazji udowadniając bezatomowość miary.
http://www.math.uni.wroc.pl/dgt/
26-04-2021 15:15
, Teams
Stabilność singularnych rozwiązań układu Naviera-Stokesa
Grzegorz Karch (Uniwersytet Wrocławski)
26-02-2020 16:15
, 602
Amenability and definability
Krzysztof Krupiński (University of Wrocław)
The general motivation standing behind this research is to understand relationships between dynamical and model-theoretic properties of definable [topological] groups and between dynamical properties of groups of automorphisms of first order structures and model-theoretic properties of the underlying theories. More specifically, our goal is to understand model-theoretic consequences of various notions of amenability.

Among the notions of amenability that we are interested in are: definable amenability of a definable group, classical amenability of a topological group, and, more generally, [weak] definable topological amenability of a definable topological group. We also introduce and study amenable theories.

The consequences of amenability that we obtain are the appropriate versions of G-compactness: for first order theories this is the equality of Lascar strong types and Kim-Pillay strong types; for definable [topological] groups this is the equality of suitably defined connected components $G^{000}$ and $G^{00}$ of the group $G$ in question.

Among our main technical tools, of interest in its own right, is an elaboration on and strengthening of the Massicot-Wagner version of the stabilizer theorem, and also some results about measures and measure-like functions.

My series of talks will be based on my preprint “Amenability and definability” joint with Ehud Hrushovski and Anand Pillay. In the first series of talks, I will focus on the context of definable [topological] groups; the second series will be devoted to our new notion of amenable theory.
22-04-2021 12:15
, zoom (kontakt: michal.krawiec@math.uni.wroc.pl)
Ruin probability for Discrete and Continuous Gaussian Risk Models
Grigori Jasnovidov (Université de Lausanne)
In this presentation we focus on computation of the asymptotics of the ruin probabilities of Gaussian processes under the discrete time setup. We also study some properties of the Pickands constants appearing in the asymptotics.
13-04-2021 17:00
, zoom.us (contact pborod@math.uni.wroc.pl)
On zero-dimensional subspaces of Eberlein compacta
Witold Marciszewski (University of Warsaw)
Let us recall that a compact space K is Eberlein compact if it can be embedded into some Banach space X equipped with the weak topology. Our talk will be devoted to the known problem of the existence of nonmetrizable compact spaces without nonmetrizable zero-dimensional closed subspaces. Several such spaces were obtained using some additional set-theoretic assumptions. Recently, P. Koszmider constructed the first such example in ZFC. We investigate this problem for the class of Eberlein compact spaces. We construct such Eberlein compacta, assuming the existence of a Luzin set. We also show that it is consistent with ZFC that each Eberlein compact space of weight greater than $\omega_1$ contains a nonmetrizable closed zero-dimensional subspace. The talk is based on the paper "On two problems concerning Eberlein compacta":
06-06-2019 12:15
, 606
Testowanie stochastycznego uporządkowania dwóch funkcji przeżycia, II.
Grzegorz Wyłupek
Subskrybuj Seminars