Posted July 27, 2022
Last modified August 18, 2022
Jean Pierre Mutanguha, Institute for Advanced Study
Canonical forms for free group automorphisms
The Nielsen–Thurston theory of surface homeomorphisms can be thought of as a surface analogue to the Jordan Canonical Form. I will discuss my progress in developing a similar canonical form for free group automorphisms. (Un)Fortunately, free group automorphisms can have arbitrarily complicated behaviour. This is a significant barrier to translating arguments that worked for surfaces into the free group setting; nevertheless, the overall ideas/strategies do translate!
Posted August 8, 20229:30 am - 10:20 am Zoom (Click “Questions or Comments?” to request a Zoom link)
Lorena Bociu, North Carolina State University
Analysis and Control in Poroelastic Systems with Applications to Biomedicine
Fluid flows through deformable porous media are relevant for many applications in biology, medicine and bio-engineering, including tissue perfusion, fluid flow inside cartilages and bones, and design of bioartificial organs. Mathematically, they are described by quasi-static nonlinear poroelastic systems, which are implicit, degenerate, coupled systems of partial differential equations (PDE) of mixed parabolic-elliptic type. We answer questions related to tissue biomechanics via well-posedness theory, sensitivity analysis, and optimal control for the poroelastic PDE coupled systems mentioned above. One application of particular interest is perfusion inside the eye and its connection to the development of neurodegenerative diseases.