Tendon tissue engineering aims to grow functional tissue in the lab. Tissue is grown inside a bioreactor which controls both the mechanical and biochemical environment. As tendon cells alter their behaviour in response to mechanical stresses, designing suitable bioreactor loading regimes forms a key component in ensuring healthy tissue growth.  

Linking the forces imposed by the bioreactor to the shear stress experienced by individual cell is achieved by homogenisation using multiscale asymptotics. We will present a continuum model capturing fluid-structure interaction between the nutrient media and the fibrous scaffold where cells grow. Solutions reflecting different experimental conditions will be discussed in view of the implications for shear stress distribution experienced by cells across the bioreactor.  

I will be first introducing the Polyakov loop space formalism to
gauge theories. I will also discuss how the Polyakov loop space is modified
by Planck scale corrections.  The gauge theory will be deformed by the
Planck length as the minimum measurable length in the background spacetime.
This deformation will in turn deform the Polyakov loops space. It will be
observed that this deformation can have important consequences for
non-abelian monopoles in gauge theories.

Dark matter is known to exist, but no-one knows what it is or where it came
from.  We describe a new production mechanism of particle dark matter, which
hinges on a first-order cosmological phase transition.  We then show that
this mechanism can be slightly modified to produce primordial black holes.

While solar mass and supermassive black holes are now known to exist,
primordial black holes have not yet been seen but could solve a number of
problems in cosmology.  Finally, we demonstrate that if an evaporating
primordial black hole is observed, it will provide a unique window onto
Beyond the Standard Model physics.

We revisit rough paths and signatures from a geometric and "smooth model" perspective. This provides a lean framework to understand and formulate key concepts of the theory, including recent insights on higher-order translation, also known as renormalization of rough paths. This first part is joint work with C Bellingeri (TU Berlin), and S Paycha (U Potsdam). In a second part, we take a semimartingale perspective and more specifically analyze the structure of expected signatures when written in exponential form. Following Bonnier-Oberhauser (2020), we call the resulting objects signature cumulants. These can be described - and recursively computed - in a way that can be seen as unification of previously unrelated pieces of mathematics, including Magnus (1954), Lyons-Ni (2015), Gatheral and coworkers (2017 onwards) and Lacoin-Rhodes-Vargas (2019). This is joint work with P Hager and N Tapia.