, 605
Hardy spaces for Fourier integral operators
Jan Rozendaal (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.
15-10-2021 15:30
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
Topology of Magnetized Fluid: from knot Encryption to basic Heliospheric structures
Ilan Roth (University of California Space Sciences, Berkeley)
The structures of electromagnetic fields in vacuum and in ionized matter (plasma) allow formation of various topological forms besides the standard static monopoles or propagating waves. I will survey recent applications of mathematical knot and braid theory to explicit structures used or planned for transfer of encrypted information, as well as analysis of recent unique data obtained by the first man-made spacecraft approaching the Sun to an amazing distance of 9 solar radii.
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
Estymacja i testowanie macierzy kowariancji należących do podprzestrzeni kwadratowych
Mateusz John (Politechnika Poznańska)
, 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.
, 602
Random walks in cones
Vitali Wachtel (Bielefeld University)
In this talk I am going to discuss the behaviour of walks constrained to some parts of the space. I will concentrate on two rather simple examples which however show the depth of the corresponding area of mathematics. I will begin with the classical Ballot problem, which can be seen as a walk conditioned to stay positive. I will then turn to a model for gambler's ruin problem with many players.
, 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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