Department of Mathematics and Systems Analysis

Current

Lectures, seminars and dissertations

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

Luis Brummet (Aalto)
Survey on complex driven Loewner chains
* Today * Tuesday 19 March 2024,   10:15,   M3 (M234)
In this talk we provide some basic facts about Loewner chains driven by both deterministic functions and stochastic processes. In the second half of the talk we provide some insights about the current development on Loewner chains driven by deterministic complex-valued functions and complex Brownian motion.

Jani Onninen (Syracuse University)
Quasiregular values
* Wednesday 20 March 2024,   10:15,   M3 (M234)
Quasiregular maps form a higher-dimensional class of maps with many similar properties to holomorphic maps, such as continuity, openness, discreteness, and versions of the Liouville and Picard theorems. In this talk, we give a pointwise definition of quasiregularity. We show that this condition yields counterparts to many fundamental properties of quasiregular maps at a single point. The studied maps have already shown to play a key part in various important 2D results. Joint work with Ilmari Kangasniemi.
Seminar on analysis and geometry

Toni Karvonen
The relation between asymptotic and worst-case settings in numerical integration
* Thursday 21 March 2024,   09:15,   M2 (M233)

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

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)
Seminar on analysis and geometry

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