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.
12-06-2020 14:15
, https://lu-se.zoom.us/j/65067339175
Insights and algorithms for the multivariate square-root lasso
Aaron Molstad (University of Florida)
We study the multivariate square-root lasso, a method for fitting the multivariate response (i.e. multi-task) linear regression model with dependent errors. This estimator minimizes the nuclear norm of the residual matrix plus a convex penalty. Unlike some existing methods for multivariate response linear regression, which require explicit estimates of the error covariance matrix or its inverse, the multivariate square-root lasso criterion implicitly adapts to dependent errors and is convex. To justify the use of this estimator, we establish an error bound which illustrates that like the univariate square-root lasso, the multivariate square-root lasso is pivotal with respect to the unknown error covariance matrix. Based on our theory, we propose a simple tuning approach which requires fitting the model for only a single value of the tuning parameter, e.g., does not require cross-validation. We propose two algorithms to compute the estimator: a prox-linear alternating direction method of multipliers algorithm, and an accelerated first order algorithm which can be applied in certain cases. In both simulation studies and a genomic data application, we show that the multivariate square-root lasso can outperform more computationally intensive methods which estimate both the regression coefficient matrix and error precision matrix.
12-03-2020 10:15
, 602
Uwagi na temat wspólnego promienia numerycznego dla n operatorów
Janusz Wysoczański
Klasyczny promień numeryczny operatora T:H-->H ograniczonego na przestrzeni Hilberta H jest określony jako supremum liczb ||, wziętych po wszystkich wektorach jednostkowych x w przestrzeni H. W 2009 Gelu Popescu wprowadził pojęcie wspólnego promienia numerycznego dla n operatorów RF(T(1),… ,T(n)), działających na tej samej przestrzeni Hilberta. Definicja ta jest związana z operatorami kreacji na wolnej przestrzeni Focka. W moim referacie przedstawię nowe, analogiczne, definicje i własności dwóch rodzajów promieni numerycznych dla n operatorów: 1. wspólny monotoniczny promień numeryczny RM(T(1), …, T(n)) związany z operatorami kreacji na słabo monotonicznej przestrzeni Focka oraz 2. wspólny boole’owski promień numeryczny RB(T(1), …, T(n)) związany operatorami kreacji na boole’owskiej przestrzeni Focka. Referat będzie na podstawie wspólnej pracy z Anią Wysoczańską-Kulą.
http://www.math.uni.wroc.pl/dgt/
09-03-2020 15:15
, 604
Regular and discontinuous stationary solutions to reaction-diffusion-ODE systems
Szymon Cygan (UWr)
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.
03-12-2020 12:15
, zoom (kontakt: michal.krawiec@math.uni.wroc.pl)
Limit theorems for a stable sausage
Wojciech Cygan (TU Dresden / Uni. Wrocław)
The talk concerns the limit behavior of the volume of a stable sausage defined via a $d$-dimensional rotationally invariant $\alpha$-stable process. I will present a functional central limit theorem (in the case when $d/\alpha>3 /2$) with a standard one-dimensional Brownian motion in the limit and Khintchine's and Chung’s laws of the iterated logarithm (in the case when $d/\alpha>9 /5$). This is a joint work with N. Sandrić and S. Šebek (Uni. Zagreb).
10-11-2020 17:00
, zoom.us (contact pborod@math.uni.wroc.pl)
On wide Aronszajn trees
Mirna Dzamonja (Université Panthéon Sorbonne, Paris)
Aronszajn trees are a staple of set theory, but there are applications where the requirement of all levels being countable is of no importance. This is the case in set-theoretic model theory, where trees of height and size ω1 but with no uncountable branches play an important role by being clocks of Ehrenfeucht--Fraïssé games that measure similarity of model of size ℵ1. We call such trees wide Aronszajn. In this context one can also compare trees T and T’ by saying that T weakly embeds into T’ if there is a function f that map T into T’ while preserving the strict order <_T. This order translates into the comparison of winning strategies for the isomorphism player, where any winning strategy for T’ translates into a winning strategy for T’. Hence it is natural to ask if there is a largest such tree, or as we would say, a universal tree for the class of wide Aronszajn trees with weak embeddings. It was known that there is no such a tree under CH, but in 1994 Mekler and Väänanen conjectured that there would be under MA(ω1). In our upcoming JSL paper with Saharon Shelah we prove that this is not the case: under MA(ω1) there is no universal wide Aronszajn tree. The talk will discuss that paper. The paper is available on the arxiv and on line at JSL in the preproof version DOI: 10.1017/jsl.2020.42
06-06-2019 12:15
, 606
Testowanie stochastycznego uporządkowania dwóch funkcji przeżycia, II.
Grzegorz Wyłupek
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