# IMath Webinar Series: Rodolfo Maza and Nicki Holighaus, Dr.rer.nat.

You’re all invited to attend our webinar on **Monday, December 4, 2023 at 3:30 PM via Zoom**. Our speakers are Rodolfo Maza (from the Differential Equations Research Group) and Nicki Holighaus, Dr.rer.nat. (from the Acoustic Research Institute, Vienna, Austria, hosted by the Optimization and Approximation Research Group).

** Rodolfo Maza** (Differential Equations Group)

**Homogenization of quasilinear elliptic problems in two-component domain with interfacial resistance and weak data**

*Title:***This talk will discuss the homogenization of quasilinear elliptic problems with a jump on the interface between the two components proportional to the flux in the of order \(\varepsilon^\gamma\). Moreover, the data is presumed to be an \(L^1\) function and the matrix field is not presumed to have a restricted growth. Consequently, the concept of renormalized solution is implemented.**

*Abstract:*In the homogenization process, we employ the periodic unfolding method. The homogenized problem was afterwards identified to be a quasilinear elliptic problem with weak data for the case that the parameter \(\gamma\) is less than 1 with the exception of \(\gamma = −1\).

** Nicki Holighaus, Dr.rer.nat.** (Acoustics Research Institute, Vienna, Austria, hosted by the Optimization and Approximation Group)

**The oscillation method for continuous frames and an application to grid-like decimation of wavelet transforms**

*Title:***A continuous frame \(\Phi\) is a family of functions in a Hilbert space, indexed by a measure space \((\Lambda,\mu)\) and associated with a norm-preserving integral transform. In this talk, I will provide a short introduction to the oscillation method for continuous frames, which can be considered as a means to use geometric arguments on the space \((\Lambda,\mu)\) for constructing discrete frames from \(\Phi\), i.e., countable subsets of \(\Lambda\), such that the \(\Phi\)-induced integral transform remains norm preserving when only considered on the countable subset. For reasons of accessibility, we will restrict the discussion to Parseval (or 1-tight) continuous frames. We will then use the oscillation method to derive 2 types of grid-like discretization rules for the continuous wavelet transform, partially motivated by their ease of implementation.**

*Abstract:*