PDEA Seminar: A coarse-graining theory for elliptic operators and homogenization in high contrast
- Date
- 16 October 2025, 15:15–16:00
- Location
- Ångström Laboratory, 64119 + Zoom
- Type
- Seminar
- Lecturer
- Tuomo Kuusi (University of Helsinki)
- Organiser
- Matematiska institutionen
- Contact person
- Kaj Nyström
Tuomo Kuusi (University of Helsinki) gives this seminar. Please note the unusual time for the talk. Welcome!
Abstract: I present a coarse-graining framework for divergence-form elliptic operators that provides a quantitative description of how ellipticity evolves across scales. The construction is based on a pair of coarse-grained matrices defined on spatial blocks, which encode a scale-dependent notion of ellipticity and satisfy coarse-grained analogues of classical analytic estimates such as the Poincaré and Caccioppoli inequalities.
Under simplifying assumptions, I will consequently discuss the result of [arXiv:2405.10732] that homogenization occurs within at most $C \log^2 \Theta$ dyadic length scales in the high-contrast regime, where~$\Theta$ is the ellipticity contrast. More generally, the scale-local formulation of ellipticity offers a setting in which analytic estimates can be iterated across arbitrarily many scales, pointing toward a rigorous renormalization-group perspective on elliptic homogenization.
Participate on site or via Zoom link, meeting ID: 67226102216. Ensure Zoom access by contacting the organisers in advance.
This is a seminar in the PDEs and Applications seminar series.