Weekly research seminar
Organizers
 prof. dr hab. Grzegorz Łukaszewicz
Information
Thursdays, 12:30 p.m. , room: 5070Research fields
List of talks

April 18, 2024, 12:30 p.m.
Roman Korsak (SDNŚiS)
A fluidparticle interaction model
In 2011 three authors J.A. Carrillo, T. Karper and K. Travisa published the paper "On the dynamics of a fluidparticle 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 CaffarelliRoquejoffreSavin's mean curvature notion  and their relation to the socalled tangentpoint 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 weaklyionized plasma with a use of kinetic theory plasma models. The natural phenomenon being treated is the process of branching (filamentation) …

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 nonlocal 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 SacksUhlenbeck 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 ClaudeBernardLyonI)
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)
CuckerSmale model in bounded domains
CuckerSmale 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 meanfield 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 LiYau inequality states that for positive solutions we have $\bigtriangleup \log u \geq  \frac{n}{2t}$. By integrating this inequality along a straight spacetime interval between two points, we …

Nov. 9, 2023, 12:30 p.m.
Łukasz Chomienia (SDNŚiP)
PDEs on lowdimensional structures: regularity and parabolic issues
By the lowdimensional structure we understand a closed subset of Euclidean space possessing some geometrical nature. The class includes, for instance, CWcomplexes, 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 builtin electric charge quantization as topological
I will discuss topological solitons starting with 1+1 dimensional sineGordon model. Then I will consider higher dimensional model, like topological defects with longrange e.g. Coulomblike interactions observed in liquid crystals. To recreate electromagnetism for them …

Oct. 19, 2023, 12:30 p.m.
Benoît Van Vaerenbergh (UCLouvain)
The pharmonic relaxation versus the GinzburgLandau functional
We will describe the manifoldvalued 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 OstojaStarzewski (University of Illinois at UrbanaChampaign, USA)
Tensor Random Fields
See attached file

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 nonstrictly 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 MusielakOrliczSobolev spaces
We want to study Lavrentiev’s phenomenon for a broad class of variational functionals, covering anisotropic functionals of nonstandard growth. To this purpose, we consider Musielak–Orlicz–Sobolev spaces and describe how the density of regular functions guarantees …