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
Zagadnienie brzegowo-początkowe dla pewnego liniowego nielokalnego równania ewolucyjnego
Maciej Tadej (Uniwersytet Wrocławski)

Seminarium odbędzie się stacjonarnie w sali 602 w Instytucie Matematycznym
z transmisją online:
https://teams.microsoft.com/l/meetup-join/19%3a134b9d79248e41f3a3fcf68e67de2052%40thread.tacv2/1654087227607?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
Optimality of impulse control problem in refracted Lévy model with Parisian ruin and transaction costs
Adam Kaszubowski (Uniwersytet Wrocławski)
We will consider optimal dividend problem for a company, whose underlying process is modeled by the spectrally negative Lévy process. We will assume that after each payment there will be a transaction cost implied and as a result cumulative dividend process will be a pure jump process. Therefore, instead of the traditional barrier or refracted payment strategy, we will consider so-called impulse strategy. In addition, when the controlled risk process will be below zero there will be an additional drift imposed to save the process from falling into a Parisian-type ruin. This will imply that the controlled risk process will be driven by the refracted-type SDE. Our aim will be to concentrate on proving the optimality of the impulse strategy with the use of standard steps of the Verification Lemma. We will show how and when natural assumptions arise and how they are connected with the scale functions. The talk is based on the joint work with Irmina Czarna.
, 601
From the Steinhaus property to the Laczkovich one
Eliza Jabłońska (AGH)
, 606
Testowanie stochastycznego uporządkowania dwóch funkcji przeżycia, II.
Grzegorz Wyłupek
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