Apr

19

2021

Reeb graphs and main other related graphical signatures have extensive use in applications, but only recently has there been intense interest in finding metrics for these objects. The idea is that graphical signatures such as Reeb graphs, merge trees, and contour trees encode data in both a space and a real valued function, and we want to build metrics that are sensitive to this information.

Apr

23

2021

This talk overviews certain asymptotic techniques for models that describe heterogeneous or composite materials. In particular, we focus on high contrast two-phase dispersed composites that are modeled by PDEs with rough coefficients, e.g. the case of highly conducting particles that are distributed in the matrix of finite conductivity. Furthermore, we focus on densely packed composites where particles are almost touching one another. Both scalar and vectorial cases are discussed.

Apr

26

2021

The study of which regular (i.e. symmetric) graphs can be the skeleton of a regular map (an embedding into a surface) has a long-ish history. We have theorems saying for which values of $n$ the complete graph $K_n$ is symmetrically embeddable. Ditto for $K_n,n$ and the $n$-dimensional cube.

The generalizations to HYPERgraphs and HYPERmaps are much less familiar. We will examine symmetry in these more general cases, and we will find, after a suitable introduction, that they have an unexpected charm.

Apr

26

2021

Numerical linear algebra and random matrix theory have long been coupled, going (at least) back to the seminal work of Goldstine and von Neumann (1951) on the condition number of random matrices. The connections have since gone deeper. A number of authors have noted that matrix factorization algorithms can be applied to Gaussian random matrices with an exact (distributional) characterization of the output. This includes the LU, QR and Schur factorizations and the Golub-Kahan bidiagonalization procedure.

Apr

30

2021

This presentation will be given by the team of researchers involved in progress on mathematical and computational models of biofilm at porescale including Azhar Alhammali (Imam Abdulrahman Bin Faisal University) and Oregon State University researchers Lisa Bigler, Kyla Jones, Choah Shin, and Naren Vohra, and Malgo Peszynska. The presentation will report on some of the results in two recently published papers. Our focus is on a new unconstrained close-to-singular diffusion model for biofilm phase which features an adaptively chosen singular diffusivity.