Seminaria

, 605
O gęstości stanów nieograniczonych macierzy Jacobiego
Grzegorz Świderski (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
, 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
Fullness of q-Araki-Woods factors
Manish Kumar (IMPAN)
I will discuss the fullness question of q-Araki-Woods factors, as constructed by Hiai. These von Neumann algebras are non-tracial counterparts of q-Gaussian algebras, which combine the q-deformations of free-group factors due to Bożejko-Speicher, and quasi-free deformations of Shlyakhtenko. In particular, the q-Araki-Woods factors are full in all the possible cases. I will describe an approach towards the proof based on averaging methods involving certain Wick operators. This is joint work with Simeng Wang.
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
Rozwiązania stacjonarne równań typu dyfuzji-agregacji
Krzysztof Krawczyk (Uniwersytet Wrocławski)
, 604
Estymacja krzywych koncentracji
Sylwester Piątek (Politechnika Wrocławska)
, HS
Structural Ramsey theory and definability patterns
Tomasz Rzepecki
In the seminar, I will introduce the Ramsey property as defined by Hrushovski in "Definability patterns and their symmetries", and discuss how it relates to the Ramsey property for omega-categorical structures à la Kechris, Pestov and Todorčević. Then I will describe the results related to this property from the above paper, including the canonical Ramsey expansion of a complete first order theory.
, 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.
, 601
Non-meager filters
Daria Perkowska
In the talk I will consider filters on \omega in the measurability (and complexity) context. Also, one can distinguish some natural subclasses of non-meager filters. We say that a filter F is ccc if P(\omega) /F is ccc. Similarly, we say that a filter supports a measure if there is a probability measure \mu on \omega such that F = {A: \mu(A)=1}. I will show that every ultrafilter supports a measure, every measure supporting filter is ccc and every ccc filter is non-meager. So, one can think about these notions as forming some hierarchy of complexity of filters. This hierarchy is strict. Next I will show that for every ultrafilter from the forcing extension (by \mathbb{A}), there is a ground model filter F such that the ultrafilter extends F and there is an injective Boolean homomorphism \varphi: P(\omega) /F \to \mathbb{A}.
06-06-2019 12:15
, 606
Testowanie stochastycznego uporządkowania dwóch funkcji przeżycia, II.
Grzegorz Wyłupek
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