Seminaria

, 605
Niezależne od wymiaru oszacowania dyskretnej funkcji maksymalnej dla kul l1 i dużych skal
Dariusz Kosz (PWr)
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.
, 603
Free probability of type B prime
Takahiro Hasebe (Hokkaido University)
Free probability of type $B$ was invented by Biane-Goodman-Nica, and then it was generalized by Belinschi-Shlyakhtenko and Février-Nica to infinitesimal free probability. The latter found its applications to eigenvalues of perturbed random matrices in the work of Shlyakhtenko and Cébron-Dahlqvist-Gabriel. This paper offers a new framework, called ``free probability of type $B$ prime'', which appears in the large size limit of independent unitarily invariant random matrices with perturbations. Our framework is related to boolean, free, (anti)monotone, cyclic-(anti)monotone, and conditionally free independences. We then apply the new framework to the principal minor of unitarily invariant random matrices, which leads to the definition of a multivariate inverse Markov-Krein transform. This talk is based on a joint work with Katsunori Fujie.
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.
, 603
Coupled Volterra integral equations with blowing up solutions
Wojciech Mydlarczyk (PWr)
Abstract: In the talk, coupled nonlinear Volterra type integral equations will be considered. We will focus on criteria for the existence of positive solutions, expressed in terms of the generalized Osgood condition. The global behavior of the solutions, especially the conditions when they experience blow up will be also discussed.
, 604
Causal graphs and conditional independence
Łukasz Rajkowski (Uniwersytet Warszawski)
, HS
Fields without points in a Brody hyperbolic variety.
Michał Szachniewicz
I will talk about a joint project with Vincent Jinhe Ye, about model companion of the theory of fields that do not have rational points in some fixed variety. Previously, Will Johnson and Jinhe Ye proved that if the forbidden variety is a genus greater or equal two curve, then the model companion exists. We were able to extend this result for a higher dimensional Broody hyperbolic variety V. The resulting model companion is called VXF and many results from the previous known case of curves immediately generalise. I will talk about them and about some open questions that arose in the project.
, 603
Extremes of multivariate locally-additive Gaussian random fields
Pavel Ievlev (Université de Lausanne)
In this talk, I am going to present some of my recent results in joint work with Nikolai Kriukiv on the extremes of multivariate Gaussian random fields. I will begin with the 2019 paper by K. Dębicki, E. Hashorva, and L. Wang, which laid the groundwork for further investigations in the area of multivariate Gaussian extremes. I will explain that some of the assumptions of this paper may not hold in cases that are practically important, and I will discuss how these issues can be amended by considering second-order contributions — I will clarify this terminology during the talk. Next, we will explore what is, in a sense, the simplest extension of these results from processes (indexed by R) to fields (indexed by R^n), which we refer to as 'locally-additive'. As an application of this extension, I will present an exact asymptotic result for the probability that a real-valued process first hits a high positive barrier and then a low negative barrier within a finite time horizon.
, A.4.1 C-19 (Politechnika Wrocławska)
The Nikodym property and filters on $\omega$. Part II
Tomasz Żuchowski (UWr)
In this talk we will continue studying the family $\mathcal{AN}$ of ideals on $\omega$ presented in the Part I. Recall that $\mathcal{I}\in\mathcal{AN}$ iff there exists a density submeasure $\varphi$ on $\omega$ such that $\varphi(\omega)=\infty$ and $\mathcal{I}\subseteq Exh(\varphi)$. We will present several conditions for a density ideal $\mathcal{I}$ equivalent to the fact that $\mathcal{I}\in\mathcal{AN}$. Next, we will make an analysis of the cofinal structure of the family $\mathcal{AN}$ ordered by the Katetov order $\leq_K$. We will prove that there is a family of size $\mathfrak{d}$ which is $\leq_K$-dominating in $\mathcal{AN}$, but there are no $\leq_K$-maximal elements in $\mathcal{AN}$.
06-06-2019 12:15
, 606
Testowanie stochastycznego uporządkowania dwóch funkcji przeżycia, II.
Grzegorz Wyłupek
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