Seminaria

, 605
Short remark on dimension-free estimates for discrete maximal functions over lq balls: small scale
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
A partial quantum CW-complex structure for even-dimensional quantum real projective spaces
Atul Gothe (Uniwersytet Warszawski)
A CW-complex is a topological space which can be built up inductively by attaching n-balls $B^n$ along their boundary (n-1)-spheres $S^{n-1}$. Quantum CW-complexes generalise the classical construction by dualising the pushouts of the topological spaces to pullbacks of C*-algebras and allowing the C*-algebras to be noncommutative. We construct such a family of CW-complexes, viz the even-dimensional quantum real projective spaces $(RP^{2n}_q)$, using the formalism of graph algebras.
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
O integracji i dezintegracji miar w równaniach różniczkowych
Marek Kryspin (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
Functional Central Limit Theorem for the simultaneous subgraph count of dynamic Erdős-Rényi random graphs
Nikolai Kriukov (University of Amsterdam)
In this talk we consider a dynamic Erdős-Rényi random graph with independent identically distributed edge processes. Our goal is to describe the joint evolution of count of different subgraphs. Central result of this talk is joint functional convergence of the subgraph counts to a specific multidimensional Gaussian process, which holds under mild assumptions on the edge processes, most notably a Lipschitz-type condition.
, 605
Distributivity and antichain number of algebra Borel modulo closed measure zero sets
Aleksander Cieślak (PWr)
We will investigate \(\sigma\)-ideals on polish spaces generated by closed sets and the two related cardinal invariants. To do so we will analyse the construction of Hurewicz schema from the theorem of Solecki saying that if J is generated by closed sets then every J-positive analytic set contains a J-positive \(G_\delta\) set.
06-06-2019 12:15
, 606
Testowanie stochastycznego uporządkowania dwóch funkcji przeżycia, II.
Grzegorz Wyłupek
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