Department of Mathematics and Systems Analysis

Current

Lectures, seminars and dissertations

* Dates within the next 7 days are marked by a star.

Tuomas Hytönen (Aalto)
True and fake generalized eigenvectors of infinite matrices
* Tuesday 02 April 2024,   10:15,   M3 (M234)
In von Neumann's formulation of Quantum Mechanics, physical observables are represented by self-adjoint operators in some Hilbert space. The spectrum of the operator is interpreted as the set of possible outcomes of a measurement of the observable, which is perhaps the most important physical prediction of this mathematical model. In Physics literature, especially on the introductory level, a somewhat heuristic approach to studying the spectrum is sometimes employed: "generalized eigenvectors" outside the original Hilbert space are acceptable, unless they are too wild to be "physical". The aim of the talk is to provide a rigorous justification of such heuristics under certain conditions, but also to show that these heuristics may miserably fail in some situations.

Jonas Tölle
Nonlinear (stochastic) PDEs with singular diffusivity
Tuesday 09 April 2024,   10:15,   M140
In this talk, we shall discuss properties of solutions to parabolic deterministic (and stochastic) partial differential equations with singular nonlinear divergence-type diffusivity with zero Dirichlet boundary conditions on a bounded Euclidean domain. As these kinds of equations usually lack good coercivity estimates in higher spatial dimensions, we choose to address the general well-posedness question by variational weak energy methods. Examples include the (stochastic) singular $p$-Laplace equation, the multi-valued (stochastic) total variation flow and the (stochastic) curve shortening flow. We shall present improved pathwise regularity results and decay estimates for a general class of singular divergence-type PDEs. We shall also address the stochastic case, where the equation is perturbed by additive Gaussian noise. Based on joint works with Benjamin Gess (Leipzig and Bielefeld), Wei Liu (Xuzhou), Florian Seib (Berlin), and Wilhelm Stannat (Berlin).
Seminar on analysis and geometry

Lauri Särkiö
Very weak solutions to parabolic p-Laplace systems
Wednesday 10 April 2024,   10:15,   M3 (M234)
Seminar on analysis and geometry

Kevin Nguyen
On sales lead optimization of personal insurance covers with multi-armed bandit algorithms (MSc thesis presentation)
Wednesday 10 April 2024,   15:15,   M2 (M233)

Joaquín de la Barra
Mid-term evaluation
Tuesday 16 April 2024,   14:30,   M3 (M234)

Ivy Woo
TBA
Tuesday 16 April 2024,   15:15,   M2 (M233)
ANTA Seminar / Hollanti et al.

Kim Myyryläinen
TBA
Wednesday 17 April 2024,   10:15,   M3 (M234)
Seminar on analysis and geometry

Anna-Mariya Otsetova
Axisymmetric capillary water waves with vorticity and swirl connecting to static unduloid configurations
Wednesday 24 April 2024,   10:15,   M3 (M234)
We study steady axisymmetric water waves with general vorticity and swirl, subject to the influence of surface tension. Explicit solutions to such a water wave problem are static configurations where the surface is an unduloid, that is, a periodic surface of revolution with constant mean curvature. We prove that to any such configuration there connects a global continuum of non-static solutions by means of a global implicit function theorem and topological degree theory. To prove this, the key is strict monotonicity of a certain function describing the mean curvature of an unduloid and involving complete elliptic integrals. From this point of view, this paper is an interesting interplay between water waves, geometry, and properties of elliptic integrals. This is a joint work with Jörg Weber (University of Vienna) and Erik Wahlén (Lund University).
Seminar on analysis and geometry

Lauri Särkiö
TBA/Midterm review
Wednesday 15 May 2024,   11:15,   M3 (M234)

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