Karlstad Applied Analysis Seminar (KAAS)
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Future seminars:
TALK 166
When: 12th of November 2026, 15:00-15:45
What: Decreasing Functions Without an Order: Monotonicity on General Measure Spaces
Who: Alejandro Santacruz Hidalgo, November 12, 2026
Where: 21E202 (offline) and online: https://kau-se.zoom.us/j/61616693592
On the half-line, decreasing functions appear in many places in analysis, including rearrangements, Lorentz spaces and Hardy inequalities. A key tool for working with them is the level function, which replaces a function by a decreasing one that is easier to work with. But most measure spaces have no natural order, so what should “decreasing” mean there?
In this talk we will explore one way to answer this question. The idea is to fix an ordered core, a totally ordered family of measurable sets that plays the role of the intervals (0, t). With this structure we can define core decreasing functions on a general σ-finite measure space. We will see that the main tools from the half-line still work in this setting, including the level function and down spaces, and that they lead to Hardy-type inequalities on general measure spaces. We will look at simple examples along the way. Time permitting, we will also explore some ideas for a non-commutative extension.
This is joint work with G. Sinnamon.
TALK 167
When: 1st of December 2026, 15:00-15:45
What: From Microstructure to Effective Diffusion: Pores, Mechanics and Imperfect Interfaces
Who: Elena Vilchevskaya, TU Berlin, Germany
Where: online: https://kau-se.zoom.us/j/61616693592
Evaluating transport properties in heterogeneous media requires accounting for local structural complexity, stress fields, and interfacial boundaries. In this talk, I will present a range of micromechanical modeling frameworks designed to predict effective diffusivity across these regimes.
The discussion begins with porous architectures - focusing on how pore geometry, orientation, and spatial anisotropy determine overall transport rates. Particular attention will be given to spheroidal pores and to applications involving hydrogen transport in porous materials. Moving beyond purely geometric effects, I will address mechanical coupling via stress-induced diffusion. By contrasting classical Fickian formulations with micropolar and non-local models, I will show how microstructural constraints can affect macroscopic fluxes at scales uncaptured by traditional theory.
Finally, we will look at imperfect interfaces between different phases. Using effective-field methods, I will show how an interface with finite transport resistance generates concentration jumps and reshapes effective transport tensors, generalizing this approach to broader physical contexts.
The different problems considered in the talk are connected by a common multiscale strategy: identify the relevant microstructural features, formulate their effect on the local fields, and determine how these effects are reflected in the effective macroscopic response. The examples discussed throughout the talk demonstrate how micromechanical, homogenization, and generalized continuum approaches can be combined to address diffusion problems involving complex microstructures, mechanical coupling, and imperfect phase interfaces.