Seminaria

18-01-2017 11:15
, C-11 PWr (Wydział Matematyki), sala 2.11
Mixed norm estimates for generalized radial spherical means
Adam Nowak (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.
05-12-2019 14:15
, 603
Statistical challenges in mass spectrometry data analysis: shared peptides
Mateusz Staniak
Mass spectrometry (MS) is one of the most important technologies for study of proteins. MS experiments generate massive amounts of complex data which require advanced pre-processing and careful statistical analysis. In bottom-up approach to MS, peptides - smaller segments of proteins - enter the mass spectrometer and thus measurements are made on a peptide level. Because of this, one of the problems in protein quantification based on MS is the presence of peptides that can be assigned to multiple proteins. Such peptides are referred to as shared or degenerate peptides. Since it is not obvious how to assign the abundance of shared peptides to proteins, they are often discarded from the analysis. This leads to a loss of a substantial amount of data. In this talk, I will first present the basics of Mass Spectrometry data analysis. Then, I will review existing methods for handling shared peptides. I will finish with a summary of our progress on improving methodology of protein quantification with shared peptides and related statistical challenges. The talk is based on an ongoing collaboration with Tomasz Burzykowski (Hasselt University) and Jurgen Claesen (Belgian Nuclear Research Centre).
12-12-2019 10:15
, 602
On the best possible constants in the free Khintchine inequalities
Leonard Cadilhac
The problem of finding the best constant for Khintchine inequalities with Rademacher variables remained open for 50 years until Haagerup computed them in 1981. For free variables, the problem is still open. Partial results were obtained in 1975 by Bozejko: he found the best constant for free Khintchine inequalities in Lp when p is an even integer. In this case, the proof is of purely combinatorial nature and cannot be generalised to other values of p. In this talk, we will explain how to extend this result to p between 0 and 4. The method employed relies on complex analytic results from the theory of Free Probability
http://www.math.uni.wroc.pl/dgt/
16-12-2019 15:15
, 604
Control of the jump process in non-local mean field games
Miłosz Krupski (UWr and NTNU)
11-12-2019 16:15
, 602
Generic derivations on o-minimal structures
Antongiulio Fornasiero (University of Florence)
Let $T$ be a complete, model complete o-minimal theory extending the theory $\mathrm{RCF}$ (in some language $L$). We study derivations $\delta$ on models $M \models T$. We introduce the notion of a $T$-derivation: a derivation which is compatible with the $L(\varnothing)$-definable $\mathcal{C}^1$-functions on $M$.
The theory of $T$-models with a $T$-derivation has a model completion $\mathrm{T \delta G}$. The derivation in models $(M, \delta) \models \mathrm{T \delta G}$ behaves “generically,” it is wildly discontinuous, and its kernel is a dense elementary $L$-substructure of $M$.
If $T = \mathrm{RCF}$, then $\mathrm{T \delta G}$ is the theory of closed ordered differential fields ($\mathrm{CODF}$) as introduced by Michael Singer. We are able to recover many of the known facts about $\mathrm{CODF}$ in our setting.
Among other things, $\mathrm{T \delta G}$ has $T$ as its open core, and $\mathrm{T \delta G}$ is distal.
We also examine the case of finitely many commuting $T$-derivations.
Joint work with Elliot Kaplan.
12-12-2019 12:15
, 602
Functional limit theorems for Galton–Watson processes with very active immigration
Alexander Iksanov (Taras Shevchenko National University of Kyiv)
I am going to discuss weak convergence in the Skorokhod space of Galton–Watson processes with immigration, properly normalized, under the assumption that the tail of the immigration distribution has a logarithmic decay. It will be explained that the limits are extremal shot noise processes. Interestingly, both the behavior in mean and the survival probability (especially in the subcritical case) of the underlying Galton-Watson processes without immigration affect the asymptotics in question. The talk is based on the recent SPA paper Iksanov and Kabluchko (2018).
25-11-2019 17:15
, 604
Generalized inverse limits
Włodzimierz J. Charatonik (Missouri University of Science and Technology)
The notion of inverse limits was generalized by Ingram and Mahavier to multivalued settings. We investigate topological properties that are preserved by those generalized inverse limits. We have +theorems about local connectedness, trivial shape, arc-likeness, tree-likeness, dimension etc. The talk is illustrated by many examples.
06-06-2019 12:15
, 606
Testowanie stochastycznego uporządkowania dwóch funkcji przeżycia, II.
Grzegorz Wyłupek
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