Theory of Markov Semigroups
and Schrödinger Operators
Oct 6, 2017 (Fri)
9:15–11:00, 2.11 (C-11)
dr Tomasz Grzywny (Wrocław University of Science and Technology)
Heat kernels for non-symmetric Lévy processes
Oct 13, 2017 (Fri)
9:15–11:00, 2.11 (C-11)
dr Karol Szczypkowski (Wrocław University of Science and Technology)
Heat kernels for non-symmetric jump processes
Oct 20, 2017 (Fri)
9:15–11:00, 2.11 (C-11)
dr hab. Mateusz Kwaśnicki (Wrocław University of Science and Technology)
The $\ell^p$ norm of the discrete Hilbert transform
Abstract:
The discrete Hilbert transform (in one of several non-equivalent forms) is the convolution operator, acting on doubly infinite sequences, with kernel $(\pi n)^{-1} \mathbb{1}_{n \ne 0}$. Using an appropriate martingale transform and (the Bañuelos–Wang variant of) Burkholder’s inequality, we find an upper bound for the norm of this operator on the $\ell^p$ space. Combined with a well-known lower bound, this resolves a problem posed by D. Hilbert, M. Riesz and E. C. Titchmarsh, who asked whether the norms of the discrete and continuous Hilbert transforms are equal.
Joint work with Rodrigo Bañuelos, arXiv:1709.07427.
Oct 27, 2017 (Fri)
9:15–11:00, 2.11 (C-11)
dr hab. Mateusz Kwaśnicki (Wrocław University of Science and Technology)
A random walk is completely determined by distributions of $\max(X_n,0)$
Abstract:
Using standard theory of holomorphic functions, we prove the theorem stated in the title of this talk. This result resolves a conjecture of L. Chaumont and R. Doney, who gave a proof under various additional assumptions.
Nov 3, 2017 (Fri)
9:15–11:00, 2.11 (C-11)
dr Tomasz Luks (Universität Paderborn)
Multiple points for operator-stable processes
Nov 10, 2017 (Fri)
9:15–10:00, 2.11 (C-11)
dr Wojciech Rejchel (Nicolaus Copernicus University in Toruń)
Introduction to the model selection problem
10:15–12:00, 2.11 (C-11)
dr Wojciech Rejchel (Nicolaus Copernicus University in Toruń)
Monte Carlo methods in high-dimensional Ising model
Nov 17, 2017 (Fri)
9:15–11:00, 2.11 (C-11)
dr Kamil Kaleta (Wrocław University of Science and Technology)
On long-term evolution of Feynman–Kac semigroups of Lévy processes with jumps
Nov 24, 2017 (Fri)
9:15–10:00, 2.11 (C-11)
dr Karol Szczypkowski (Wrocław University of Science and Technology)
10:15–12:00, 2.11 (C-11)
prof. Alexei Kulik (Institute of Mathematics of the National Academy of Sciences of Ukraine)
Parametrix method for locally stable models, with applications to statistics and simulation
12:15–13:00, 2.11 (C-11)
prof. Tadeusz Kulczycki (Wrocław University of Science and Technology)
Dec 8, 2017 (Fri)
9:15–11:00, 2.11 (C-11)
mgr Grzegorz Żurek (Wrocław University of Science and Technology)
Green function of a one-dimensionl Lévy process with gradient perturbation
Dec 15, 2017 (Fri)
9:15–11:00, 2.11 (C-11)
dr Irmina Czarna (Wrocław University of Science and Technology)
Fluctuation theory for level-dependent Lévy processes
Jan 5, 2018 (Fri)
9:15–11:00, 2.11 (C-11)
dr hab. Tomasz Jakubowski (Wrocław University of Science and Technology)
Fractional Laplacian with Hardy potential I
Jan 12, 2018 (Fri)
10:15–11:00, 2.11 (C-11)
dr hab. Tomasz Grzywny (Wrocław University of Science and Technology)
Fractional Laplacian with Hardy potential II
11:15–13:00, 2.11 (C-11)
mgr Jacek Mucha (Wrocław University of Science and Technology)
Harmonic extension method for non-local operators
Jan 19, 2018 (Fri)
9:15–11:00, 2.11 (C-11)
dr hab. Jacek Zienkiewicz (University of Wrocław)
Probabilistic approach to quantum separation effect for Feynman–Kac semigroup
Feb 23, 2018 (Fri)
10:15–12:00, 5.05 (C-11)
dr Kamil Kaleta (Wrocław University of Science and Technology)
On strong hypercontractivity for non-local Schrödinger operators
Mar 2, 2018 (Fri)
10:15–12:00, 5.05 (C-11)
dr hab. Mateusz Kwaśnicki (Wrocław University of Science and Technology)
Bell-shaped functions
Abstract:
A probability density $f$ on $\mathbb{R}$ is bell-shaped if the $n$-th derivative of $f$ changes its sign $n$ times. One easily verifies that Gaussian and Cauchy densities are bell-shaped. In 1984 Wolfgang Gawronski published an article in Annals of Probability, where he proved that all stable densities are bell-shaped. However, there was an error in his argument: the proof was correct only when the index of stability $\alpha$ was in the set $\{2, 1, \tfrac{1}{2}, \tfrac{1}{3}, \tfrac{1}{4}, \ldots\}$. In 2015 Thomas Simon proved that the densities of stable subordinators are bell-shaped. During the talk I will discuss the article A new class of bell-shaped functions, in which all densities of EGGC (extended generalised gamma convolution) distributions are proved to be bell-shaped. As this class includes all stable distributions, the above paper extends Thomas Simon's result and fixes the error in Wolfgang Gawronski's article.
In fact, the paper A new class… deals with a slightly more general class of distributons rather than EGGC. Curiously, no distribution outside this more general class is known to have bell-shaped density.
Mar 9, 2018 (Fri)
10:15–12:00, 5.05 (C-11)
prof. Damir Kinzebulatov (Université Laval)
On the theory of the Kolmogorov operator in the spaces $L^p$ and $C_\infty$
Mar 16, 2018 (Fri)
10:15–12:00, 5.05 (C-11)
dr Grzegorz Serafin (Wrocław University of Science and Technology)
Number of isomorphic copies of a given graph in a random graph
Mar 23, 2018 (Fri)
10:15–12:00, 5.05 (C-11)
dr Krystian Bekała (University of Wrocław)
Mar 26, 2018 (Mon)
11:15–13:00, 5.05 (C-11)
dr hab. Piotr Kalita (Jagiellonian University)
One-dimensional Burgers equation with non-autonomous forcing
Apr 6, 2018 (Fri)
10:15–12:00, 5.05 (C-11)
dr Patrick Tardivel (University of Wrocław)
Sparsest solutions and sparsest approximate solutions of an underdetermined linear system of equations
Abstract:
In this presentation, we introduce a constrained problem that gives, without any condition, one of the sparsest solutions or one of the sparsest approximate solutions of an underdetermined linear system. To solve this constrained problem, we provide a numerical method and we prove its convergence.
Apr 13, 2018 (Fri)
10:15–12:00, 5.05 (C-11)
mgr Edyta Kania (University of Wrocław)
Semilinear Dirichlet problem for the fractional Laplacian
Apr 20, 2018 (Fri)
10:15–12:00, 5.05 (C-11)
mgr Tomasz Juszczyszyn (Wrocław University of Science and Technology)
Boundary decay rate for harmonic functions of non-symmetric $\alpha$-stable processes
Apr 27, 2018 (Fri)
10:15–12:00, 5.05 (C-11)
mgr Artur Rutkowski (Wrocław University of Science and Technology)
Extension theorem for non-local operators
May 18, 2018 (Fri)
10:15–12:00, 5.05 (C-11)
mgr Agnieszka Hejna (University of Wrocław)
Dunkl operators: heat kernel estimates and applications
Jun 8, 2018 (Fri)
10:15–12:00, 5.05 (C-11)
mgr Mariusz Olszewski (Wrocław University of Science and Technology)
Estimates of the transition density of the reflected Brownian motion on fractals
Jun 15, 2018 (Fri)
10:15–12:00, 5.05 (C-11)
mgr Rafał Meller (University of Warsaw)
Two-sided estimates of moments of random multilinear forms