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Wydział Matematyki, Informatyki i Mechaniki Uniwersytetu Warszawskiego

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Seminar of Mathematical Physics Equations Group

Weekly research seminar


Coordinator

Room

5070

List of talks

  • 2024-01-25, 12:30, 5070

    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 propose the particle approximation of the solution with operator splitting technique...

  • 2024-01-18, 12:30, 5070

    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 behaviour has been lead by Bernard and Rivière in...

  • 2024-01-11, 12:30, 5070

    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. In this talk, I will review the history of this problem, culminating with Bethuel'...

  • 2023-11-30, 12:30, 5070

    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 levels. Due to the low regularity of kinetic solutions, we introd...

  • 2023-11-23, 12:30, 5070

    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 may deduce the sharp Harnack estimate. In recent year...

  • 2023-11-09, 12:30, 5070

    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 of the art of PDEs on such structures. ...

  • 2023-10-26, 12:30, 5070

    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 (Faber's approach), we us...

  • 2023-10-19, 12:30, 5070

    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, applying the direct  method of...

  • 2023-06-01, 12:30, 5070

    Martin Ostoja-Starzewski (University of Illinois at Urbana-Champaign, USA)

    Tensor Random Fields

    See attached file ...

    Abstract

  • 2023-05-25, 12:30, 5070

    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 for a particular scenario. By examining various counterexamples and a simpler case, we demons...

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