# Seminars

18-01-2017 11:15
, C-11 PWr (Wydział Matematyki), sala 2.11
Mixed norm estimates for generalized radial spherical means
24-01-2019 14:15
, 603
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.
18-06-2021 15:30
, https://lu-se.zoom.us/j/65067339175
Geometry of Model Pattern Recovery by Penalized and Thresholded Estimators
Patrick Tardivel (University of Burgundy)
LASSO, SLOPE, OSCAR, Fused LASSO, Clustered LASSO, generalized LASSO… are popular penalized estimators for which the penalty term is a polyhedral gauge. This presentation focuses on the model pattern recovery of β; namely recovering the subdifferential of a polyhedral gauge at β, where β is an unknown parameter of regression coefficients. For LASSO, when the penalty term is the ℓ1 norm, the model pattern of β only depends on the sign of β and sign recovery via LASSO estimator is actually a well known topic in the literature. Furthermore, this presentation shows that the notion of model pattern recovery is relevant for many examples of polyhedral gauge penalty. Specifically, we introduce the “path condition”: a necessary condition for model pattern recovery, via a penalized least squares estimator, with a probability larger than 1/2. One may relax this later condition using “thresholded” penalized least squares estimators; a new class of estimators generalizing thresholded LASSO. Indeed, we show that the “accessibility condition”, a condition weaker than the “path condition”, is asymptotically sufficient for model pattern recovery. It is well known that penalized estimators can be not uniquely defined and, actually, the theory of model pattern recovery is closely related to the important issue of uniqueness. In this presentation we also introduce a necessary and sufficient condition for the uniform uniqueness of penalized least squares estimators.

## Dyskretna analiza harmoniczna i niekomutatywna probabilistyka

Dane kontaktowe:
czwartek
10:15
12:00
602
10-06-2021 10:30
, zoom.us (kontakt: wiktor.ejsmont@gmail.com)
Signed reflection function in type B as a character and applications
Maciej Dołęga
W moim odczycie wprowadzimy pojęcie znakowanej funkcji odbić, która uogólnia funkcję odbić na grupie typu B poprzez rozróżnienie krótkich i długich odbić. Podamy charakteryzację dodatnio-określonych znakowanych funkcji odbić i zastosujemy ją do konstrukcji nowych relacji komutacji i nowych klas operatorów Gaussowskich. Ponadto pokażemy, że momenty tych operatorów można wyrazić jawnym kombinatorycznym wzorem, który można zinterpretować jako dwuparametrowe uogólnienie stowarzyszonych wielomianów Hermite'a badanych przez Askey'ego--Wimpa oraz Kerova.
http://www.math.uni.wroc.pl/dgt/
14-06-2021 15:15
, Teams
Układ paraboliczno-eliptyczny modelujący biologiczne kanały jonowe
Lucjan Sapa (AGH)
na podstawie pracy: http://doi.org/10.1016/j.jde.2021.04.030
26-02-2020 16:15
, 602
Amenability and definability
Krzysztof Krupiński (University of Wrocław)
The general motivation standing behind this research is to understand relationships between dynamical and model-theoretic properties of definable [topological] groups and between dynamical properties of groups of automorphisms of first order structures and model-theoretic properties of the underlying theories. More specifically, our goal is to understand model-theoretic consequences of various notions of amenability.

Among the notions of amenability that we are interested in are: definable amenability of a definable group, classical amenability of a topological group, and, more generally, [weak] definable topological amenability of a definable topological group. We also introduce and study amenable theories.

The consequences of amenability that we obtain are the appropriate versions of G-compactness: for first order theories this is the equality of Lascar strong types and Kim-Pillay strong types; for definable [topological] groups this is the equality of suitably defined connected components $G^{000}$ and $G^{00}$ of the group $G$ in question.

Among our main technical tools, of interest in its own right, is an elaboration on and strengthening of the Massicot-Wagner version of the stabilizer theorem, and also some results about measures and measure-like functions.

My series of talks will be based on my preprint “Amenability and definability” joint with Ehud Hrushovski and Anand Pillay. In the first series of talks, I will focus on the context of definable [topological] groups; the second series will be devoted to our new notion of amenable theory.
17-06-2021 12:15
, zoom (kontakt: michal.krawiec@math.uni.wroc.pl)
Proportional Parisian Reinsurance with many-fBm inputs
Pavel Levlev (Université de Lausanne)
Consider the proportional reinsurance process with two (or more) companies sharing one risk process, modeled by large number of independent fractional Brownian motions. There are recent results on classical, joint and “at least one” ruin for this process, whereas the Parisian ruin seems to have not been studied before. In the talk I shall address the exact first order asymptotics in this case, which is motivated by a recent paper “Proportional reinsurance for fractional Brownian risk model” by Krzysztof Kępczyński.
08-06-2021 17:00
, zoom.us (contact pborod@math.uni.wroc.pl)
Infinitary continuous logic and descriptive set theory
Maciej Malicki (IMPAN)
There are deep connections between model theory of the infinitary logic and descriptive set theory: Scott analysis, the López-Escobar theorem or the Suzuki theorem are well known examples of this phenomenon. In this talk, I will present results of a research devoted to generalizing these connections to the setting of continuous infinitary logic and Polish metric structures. In particular, I will discuss a continuous counterpart of a theorem of Hjorth and Kechris characterizing essential countability of the isomorphism relation on a given Borel class of countable structures. As an application, I will give a short model-theoretic proof of a result of Kechris saying that orbit equivalence relations induced by continuous actions of locally compact Polish groups are essentially countable. This is joint work with Andreas Hallbäck and Todor Tsankov.
06-06-2019 12:15
, 606
Testowanie stochastycznego uporządkowania dwóch funkcji przeżycia, II.
Grzegorz Wyłupek