Seminaria

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.
30-01-2020 14:15
, 603
Data-Driven Kaplan-Meier One-Sided Two-Sample Tests
Grzegorz Wyłupek
In the talk, we discuss existing approaches, known from the literature, to detection of stochastic ordering of the two survival curves as well as pose and solve the novel testing problem on it. Specifically, the null hypothesis asserts the lack of the ordering, while the alternative expresses its existence. An introduced test statistic is a functional of the standardized two-sample Kaplan-Meier process sampling in a randomly selected number of the random points being the observed survival times in the pooled sample and exploits the information contained in a specially defined one-sided weighted log-rank statistic. It automatically weighs the magnitude and sign of their components becoming a sensible procedure in the considered testing problem. As a result, the corresponding test asymptoticly controls the errors of both kinds at the specified significance level α. The conducted simulation study shows that the errors are also satisfactorily controlled when sample sizes are finite. Furthermore, in the comparison to the best and most popular tests, the new solution turns out to be a promising procedure which improves them upon. A real data analysis confirms that findings.
20-02-2020 10:15
, 602
Non-Commutative Disintegration Theory: from Classical Probability to Operator Algebras
Alessio Ranallo
Operator Algebras are incredibly interesting objects: indeed their study provides insights not only for the subject itself, but also for other areas of Mathematics and Physics. One of the key concepts is certainly non commutativity. This notion is fundamental for the inves- tigations of concepts which are generalized from classical, i.e. commutative, ones. (Non-commutative) Disintegration theory arise as a method of conditioning with respect to a given subsystem and so it brings a natural Bayesian interpretation with it, which still has to be explored (in the non commutative case). In the first part we will briefly explain what is non-commutative disintegration theory and how, from a categorical perspective, it naturally arises as a generalization of Bayes theorem in the classical (finite) probability setting. We will investigate how the structures resemble each-other, i.e. what are the similarities between the classical and quantum point of view. In the second part we will explore the connection between the dictionary of non-commutative disintegration theory and the theory of operator algebras.
http://www.math.uni.wroc.pl/dgt/
27-01-2020 15:15
, 604
Concentration phenomena in a diffusive aggregation model
Piotr Biler (Uniwersytet Wrocławski)
This is the talk presenting our recent paper: https://arxiv.org/abs/2001.06218
22-01-2020 16:15
, 602
Difference sheaves and torsors
Piotr Kowalski (University of Wrocław)
I will describe some results from the joint paper with Marcin Chałupnik "Difference sheaves and torsors" (available at https://arxiv.org/abs/1912.06886). This work is not about model theory, but it is partially motivated by model theory of difference fields.

We develop sheaf theory in the context of difference algebraic geometry. We introduce categories of difference sheaves and develop the appropriate cohomology theories. As specializations, we get difference Galois cohomology, difference Picard group and a good theory of difference torsors.
06-02-2020 12:15
, 602
Structural Properties of a Conditioned Random Walk on a Multivariate Integer Lattice with Random Local Constraints
Sergey Foss (Heriot-Watt University and Novosibirsk State University and Sobolev Institute of Mathematics)
We consider a random walk on a multidimensional integer lattice with random bounds on local times, conditioned on the event that it hits a high level before its death. We introduce an auxiliary “core” process that has a regenerative structure and plays a key role in our analysis. We obtain a number of representations for the distribution of the random walk in terms of the similar distribution of the “core” process. Based on that, we prove a number of limiting results by letting the high level to tend to infinity. In particular, we generalise results for a simple symmetric one-dimensional random walk obtained earlier in the paper by Benjamini and Berestycki (2010). This is a joint work with Alexander Sakhanenko (Novosibirsk)
25-11-2019 17:15
, 604
Generalized inverse limits
Włodzimierz J. Charatonik (Missouri University of Science and Technology)
The notion of inverse limits was generalized by Ingram and Mahavier to multivalued settings. We investigate topological properties that are preserved by those generalized inverse limits. We have +theorems about local connectedness, trivial shape, arc-likeness, tree-likeness, dimension etc. The talk is illustrated by many examples.
06-06-2019 12:15
, 606
Testowanie stochastycznego uporządkowania dwóch funkcji przeżycia, II.
Grzegorz Wyłupek
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