Organizers

prof. dr hab. Grzegorz Łukaszewicz

Information

Thursdays, 12:30 p.m. , room: 5070

Research fields

Mathematical Physics and Applied Analysis

List of talks

April 18, 2024, 12:30 p.m.
Roman Korsak (SDNŚiS)
A fluid-particle interaction model
In 2011 three authors J.A. Carrillo, T. Karper and K. Travisa published the paper "On the dynamics of a fluid-particle interaction model: The bubbling regime". They discussed a model, where particles of one fluid are …
March 21, 2024, 12:30 p.m.
Armin Schikorra (University of Pittsburgh)
A nonlocal Willmore Energy
I will discuss a natural definition of a nonlocal version of the Willmore energy -- based on Caffarelli-Roquejoffre-Savin's mean curvature notion -- and their relation to the so-called tangent-point energies, with consequences for existence of …
Feb. 29, 2024, 12:30 p.m.
Paweł Jujeczko
Filamentary structure of streamers in Transient Luminous Events
The subject of the seminar will be a numerical modelling of instabilities in a weakly-ionized plasma with a use of kinetic theory plasma models. The natural phenomenon being treated is the process of branching (filamentation) …
- Filamentary structure of streamers in Transient Luminous Events - prezentation
Jan. 25, 2024, 12:30 p.m.
Matej Benko (Brno University of Technology)
Discretization of Wasserstein Gradient Flow
We consider the local model and the model with non-local interactions with linear diffusion as equivalent problems to the gradient flow along a convex functional. In the first part, the local model is considered. We …
Jan. 18, 2024, 12:30 p.m.
Dorian Martino (Université Paris Cité)
Energy quantization of Willmore surfaces with bounded index
Quantization phenomena, pioneered by Sacks-Uhlenbeck in 1981, arise in the study of compactness questions of every conformally invariant functional and requires a subtle analysis. In the context of Willmore surfaces, the first study of such …
Jan. 11, 2024, 12:30 p.m.
Antoine Detaille (Université Claude-Bernard-Lyon-I)
Strong density in Sobolev spaces to manifolds
In striking contrast with what happens to classical Sobolev spaces, the space of smooth maps with values into a compact manifold $N$ does not need to be dense in the space of $N$-valued $W^{s,p}$ maps. …
Nov. 30, 2023, 12:30 p.m.
Michał Fabisiak (doktorant SDNŚiS)
Cucker-Smale model in bounded domains
Cucker-Smale model describes the behaviour of agents aligning their velocities according to nonlocal protocol. We consider the model posed in domains with a boundary and try to justify the mean-field limit between particle and kinetic …
Nov. 23, 2023, 12:30 p.m.
Mateusz Dembny (doktorant SDNŚiS)
On differential Harnack bounds for a fractional heat equation
Consider the linear heat equation. The celebrated Li-Yau inequality states that for positive solutions we have $\bigtriangleup \log u \geq - \frac{n}{2t}$. By integrating this inequality along a straight space-time interval between two points, we …
Nov. 9, 2023, 12:30 p.m.
Łukasz Chomienia (SDNŚiP)
PDEs on low-dimensional structures: regularity and parabolic issues
By the low-dimensional structure we understand a closed subset of Euclidean space possessing some geometrical nature. The class includes, for instance, CW-complexes, families of manifolds, stratified manifolds etc. We very briefly recall the current state …
Oct. 26, 2023, 12:30 p.m.
Jarosław Duda (Institute of Computer Science and Computer Mathematics, Jagiellonian University)
Electromagnetism with built-in electric charge quantization as topological
I will discuss topological solitons starting with 1+1 dimensional sine-Gordon model. Then I will consider higher dimensional model, like topological defects with long-range e.g. Coulomb-like interactions observed in liquid crystals. To recreate electromagnetism for them …
Oct. 19, 2023, 12:30 p.m.
Benoît Van Vaerenbergh (UCLouvain)
The p-harmonic relaxation versus the Ginzburg-Landau functional
We will describe the manifold-valued harmonic extension problem of a boundary data defined on the boundary of a domain and taking values into the manifold. This extension has engineering applications, which we will present. Unfortunately, …
June 1, 2023, 12:30 p.m.
Martin Ostoja-Starzewski (University of Illinois at Urbana-Champaign, USA)
Tensor Random Fields
See attached file
- Abstract
May 25, 2023, 12:30 p.m.
Benjamin Lledos (Université Paul Sabatier, Institut de Mathématiques de Toulouse)
Some results about the uniqueness of the solutions in the calculus of variations
We want to find a framework in which we can establish the uniqueness of solutions for non-strictly convex problems in the calculus of variations. The main idea is to extend a method devised by Marcellini …
May 18, 2023, 12:30 p.m.
Mateusz Dembny (SDNŚiS)
Spiral vortex sheets and 2d Euler equation
In my talk, I will introduce Prandtl's and Kaden's spirals. Prandtl's spirals are weak solutions to the 2d Euler equation and this is a result by T. Cieslak, P. Kokocki and W.S. Ozanski. We will check whether Kaden's …
May 4, 2023, 12:30 p.m.
Michał Borowski (MIMUW)
Absence of Lavrentiev’s phenomenon and Musielak-Orlicz-Sobolev spaces
We want to study Lavrentiev’s phenomenon for a broad class of variational functionals, covering anisotropic functionals of non-standard growth. To this purpose, we consider Musielak–Orlicz–Sobolev spaces and describe how the density of regular functions guarantees …