Seminars

, C-11 PWr (Wydział Matematyki), sala 2.11
Mixed norm estimates for generalized radial spherical means
Adam Nowak (IM PAN)
, 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
, https://lu-se.zoom.us/j/65067339175
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
THE FUNCTORIALITY OF GRAPH ALGEBRAS AND PUSHOUT-TO-PULLBACK THEOREMS
Piotr M. Hajac (IMPAN)
Given a finite group G and a field k, there are two natural ways to construct a Hopf algebra out of it: the group ring kG and the function algebra Map(G,k). The former gives a covariant functor and the latter yields a contravariant functor. In this spirit, assigning different types of graph algebras to directed graphs leads to both covariant and contravariant functors for each type of graph algebras. Unlike in the case of groups, the difference between the covariant and the contravariant scenarios is only in the way morphisms of graphs induce homomorphisms of algebras, while the objects (graph algebras) are the same. The first aim of this talk is to show optimal assumptions on categories of directed graphs making the constructions of path algebras, Cohn path algebras and Leavitt path algebras covariantly or contravariantly functorial. Our second goal is to explain how to apply the contravariant-functoriality results to obtain optimal pushout-to-pullback theorems, i.e. to unravel when applying contravariant functors to pushouts of graphs produces pullbacks of various graph algebras. Finally, I will hint at applications of all this to the noncommutative topology of graph C*-algebras. (This talk is partially based on joint work with Mariusz Tobolski and Alexander Frei.)
http://www.math.uni.wroc.pl/dgt/
, 602/Teams
Rozwiązania stacjonarne jednowymiarowego równania agregacji-dyfuzji
Krzysztof Krawczyk (Uniwersytet Wrocławski)

Część druga. Seminarium odbędzie się stacjonarnie w sali 602 w Instytucie Matematycznym z transmisją online: https://teams.microsoft.com/l/meetup-join/19%3a134b9d79248e41f3a3fcf68e67de2052%40thread.tacv2/1653557403370?context=%7b%22Tid%22%3a%222b71bef9-3b13-4432-b5f4-1f5ac2278d0c%22%2c%22Oid%22%3a%223f605cf2-4741-4b58-9d48-89a636910c12%22%7d

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.
, 602
Selfdecomposable variables, their background driving distributions(BDDF), log-gamma variables and some graphs
Zbigniew J. Jurek (Uniwersytet Wrocławski)
Selfdecomposable variables (distributions) or Lévy class L, arise as a natural generalization of the central limit theorem. It is a quite large class and includes many classical distributions such as stable, gamma, log-gamma, t-Student, logistic, stochastic area under planar Brownian motion, Bessel-K, Bessel densities, Fisher z-distribution, etc. All class L distributions admit the random integral representation - a random integral with respect to some Lévy process Y , called as background driving Lévy process, in short BDLP. Probability distribution of Y(1) is called background driving distribution, in short: BDDF. In the lecture we will present the formulas for BDDF (and for some variables) in a such way that might be more useful for a simulation. References: [1] zjj (2022) Theory Probab. Appl. vol. 67(1), pp. 105-117; [2] zjj (2021) Mathematica Applicanda, vol. 49(2), pp. 85-109.
, 601
Sacks indestructible ultrafilters and reaping families
David Chodounsky (Czech Academy of Sciences)
Preservation of reaping families and especially ultrafilters on countable sets is a well studied theme in set theory of the reals. A. Miller proved that if an ultrafilter remains a reaping family in some forcing extension, then it has to be also Sacks indestructible. The existence of Sacks indestructible ultrafilters in ZFC is an open question. A related problem is Sacks indestructibility of reaping families which are complements of ideals. We prove that complements of most classical ideals are indestructible with one notable exception, the ideal of sets asymptotic density zero. The presented results are from an upcoming paper with O. Guzman and M. Hrusak. About 15 minutes before the seminar we invite you for coffee and a chat.
, 606
Testowanie stochastycznego uporządkowania dwóch funkcji przeżycia, II.
Grzegorz Wyłupek
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