Seminaria

, 605
Spacing problem of Robert and Sargos
Jakub Niksiński (UWr)
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.
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.
, 604
O C*-algebrach grafów topologicznych, część 1
Mariusz Tobolski (Uniwersytet Wrocławski)
C*-algebry grafów topologicznych to klasa C*-algebr uogólniająca algebry Cuntza, algebry Cuntza-Kriegera, C*-algebry grafowe oraz produkty krzyżowe pochodzące od homeomorfizmu danej przestrzeni. Z każdą taką algebrą stowarzyszony jest graf topologiczny zdefiniowany przez Katsurę a ich konstrukcja opiera się na pracy Pimsnera i uogólnionej przestrzeni Focka. W referacie przedstawię najważniejsze definicje, przykłady oraz rezultaty teorii C*-algebr grafów topologicznych. W drugiej części opowiem o wynikach uzyskanych wspólnie z Atulem Gothe (Uniwersytet Warszawski) oraz Johnem Quiggiem (Uniwersytet Stanu Arizona), gdzie udowadniamy jak sklejanie grafów topologicznych prowadzi do pullbacku ich C*-algebr, co uogólnia wcześniejsze rezultaty dla grafów dyskretnych oraz pewne twierdzenie Robertsona-Szymańskiego dla tej klasy algebr.
27-02-2023 14:15
, HS
Virtual combination of relatively quasiconvex subgroups and separability properties
Ashot Minasyan
Quasiconvex subgroups are basic building blocks of hyperbolic groups, and relatively quasiconvex subgroups play a similar role in relatively hyperbolic groups. If $Q$ and $R$ are relatively quasiconvex subgroups of a relatively hyperbolic group $G$ then the intersection $Q \cap R$ will also be relatively quasiconvex, but the join $\langle Q,R \rangle$ may not be. I will discuss criteria for the existence of finite index subgroups $Q’ \leqslant_f Q$ and $R’ \leqslant_f R$ such that the ``virtual join’’ $\langle Q’, R’ \rangle$ is relatively quasiconvex. This is closely related to separability properties of $G$ and I will present applications to limit groups, Kleinian groups and fundamental groups of graphs of free groups with cyclic edge groups. The talk will be based on joint work with Lawk Mineh.
, 602
Nonlocal operators with Neumann conditions
Krzysztof Bogdan (Politechnika Wrocławska)
, 604
Sufficient Dimension Reduction in Regression and Classification: An overview and recent results for matrix-valued predictors
Efsthathia Bura (TU Vienna)
, HS
Bohr compactification and type-definable connected component of modules, rings and semidirect product of groups
Mateusz Rzepecki
For a model M and a topological space C we say that a map f: M -> C is definable if for any two disjoint closed sets in C their preimages by f are separable by a definable set. For a definable structure N in a model M we say that f is a definable compactification of N if f is a compactification of N and f is a definable map. We say that a definable compactification of N is universal if every definable compactification of N factors by f via a continuous map. It turns out that if N is a group (Gismatullin, Penazzi & Pillay) or a ring (Gismatullin, Jagiella & Krupiński) then N/N^{00}_M is the universal definable compactification of N, where N^{00}_M is the type-definable connected component of N over M. A module can be represented as N in two ways. The first one is a definable abelian group and a ring that is a part of the language. The second one is a definable abelian group and a definable ring. This talk: In this talk we will prove that for a definable module N (in both senses) N/N^00_M is a universal definable compactification of N (the definition of N^00_M for a module will be given). We will also analyze how N^00_M depends on the type-definable connected component of the abelian group. To do this we will prove a theorem that shows how connected components help in creating sets that are closed under commutative addition (generalization of the proof by Krzysztof Krupiński for approximate rings). Using the theorem, we will describe the type-definable connected component of modules, rings and semidirect products of groups. We will also show that in many cases of structures analyzed during this talk adding homomorphism/monomorphism/automorphism/differentiation to the structure N does not change the type-definable connected component of N. During the talk we will come across a few open questions. This is a joint work with Krzysztof Krupiński and is a part of a bigger project with Grzegorz Jagiella.
, 603
On decoupled random walks
Alexander Iksanov (Taras Shevchenko National University of Kyiv)
We call a decoupled random walk a sequence S1, S2,… of independent random variables such that, for each integer n, Sn has the same distribution as the position at time n of a standard random walk with nonnegative jumps. Similarly, we call a decoupled renewal process the counting process (N(t)) defined by the number of visits of (Sn) to the closed interval [0,t]. I shall present a functional limit theorem for (N(t)), properly translated, normalized and centered, as t goes to infinity under the assumption that the variance of S1 is positive and finite. Also, I shall discuss the asymptotic behavior of the logarithmic distribution tail of all-time minimum of Sn under various assumptions imposed on the distribution of S1. Our interest to the so defined decoupled random walks has been raised by their appearance in the particular case when S1 has an exponential distribution of unit mean in the context of infinite Ginibre point processes. The talk is based on a joint work with Gerold Alsmeyer and Zakhar Kabluchko (Muenster).
, 605
A small, badly behaved Radon-Nikodym compact space.
Arturo Martinez Celis
In this talk, we will show that a parametrized diamond implies the existence of a Radon-Nikodym compact space of small weight, and a continuous function whose image is not Radon-Nikodym, answering a question of Antonio Avilés and Piotr Koszmider.
06-06-2019 12:15
, 606
Testowanie stochastycznego uporządkowania dwóch funkcji przeżycia, II.
Grzegorz Wyłupek
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