Mathematical models based on first principles can describe the interaction between electrical, mechanical and fluid-dynamical processes occurring in the heart. This is a classical multi-physics problem. Appropriate numerical strategies need to be devised to allow for an effective description of the fluid in large and medium size arteries, the analysis of physiological and pathological conditions, and the simulation, control and shape optimisation of assisted devices or surgical prostheses. This presentation will address some of these issues and a few representative applications of clinical interest.
It is at first sight surprising that a minimizer of an integral of the calculus of variations may make the integrand infinite somewhere.
This talk will discuss some examples of this phenomenon, how it can be related to material defects, and related open questions from nonlinear elasticity and the theory of liquid crystals.
Details to follow
The so-called moonshine phenomenon relates modular forms and finite group representations. After the celebrated monstrous moonshine, various new examples of moonshine connection have been discovered in recent years. The study of these new moonshine examples has revealed interesting connections to K3 surfaces, arithmetic geometry, and string theory. In this colloquium I will give an overview of these recent developments.
The theory of metric measure spaces with Ricci curvature from below is growing very quickly, both in the "Riemannian" class RCD and the general CD one. I will review some of the most recent results, by illustrating the key identification results and technical tools (at the level of calculus in metric measure spaces) underlying these results.
The fourth QBIOX Colloquium will take place in the Mathematical Institute on Friday 10th November (5th week) and feature talks from Professor Paul Riley (Department of Pathology, Anatomy and Genetics / BHF Oxbridge Centre for Regenerative Medicine, https://www.dpag.ox.ac.uk/research/riley-group) and Professor Eleanor Stride (Institute of Biomedical Engineering, http://www.ibme.ox.ac.uk/research/non-invasive-therapy-drug-delivery/peo...).
1600-1645 - Paul Riley, "Enroute to mending broken hearts".
1645-1730 - Eleanor Stride, "Reducing tissue hypoxia for cancer therapy".
1730-1800 - Networking and refreshments.
We very much hope to see you there. As ever, tickets are not necessary, but registering to attend will help us with numbers for catering.
Please see the following link for further details and a link to register.
Paul Riley - "En route to mending broken hearts".
We adopt the paradigm of understanding how the heart develops during pregnancy as a first principal to inform on adult heart repair and regeneration. Our target for cell-based repair is the epicardium and epicardium-derived cells (EPDCs) which line the outside of the forming heart and contribute vascular endothelial and smooth muscle cells to the coronary vasculature, interstitial fibroblasts and cardiomyocytes. The epicardium can also act as a source of signals to condition the growth of the underlying embryonic heart muscle. In the adult heart, whilst the epicardium is retained, it is effectively quiescent. We have sought to extrapolate the developmental potential of the epicardium to the adult heart following injury by stimulating dormant epicardial cells to give rise to new muscle and vasculature. In parallel, we seek to modulate the local environment into which the new cells emerge: a cytotoxic mixture of inflammation and fibrosis which prevents cell engraftment and integration with survived heart tissue. To this end we manipulate the lymphatic vessels in the heart given that, elsewhere in the body, the lymphatics survey the immune system and modulate inflammation at peripheral injury sites. We recently described the development of the cardiac lymphatic vasculature and revealed in the adult heart that they undergo increased vessel sprouting (lymphangiogenesis) in response to injury, to improve function, remodelling and fibrosis. We are currently investigating whether increased lymphangiogenesis functions to clear immune cells and constrain the reparative response for optimal healing.
Eleanor Stride - "Reducing tissue hypoxia for cancer therapy"
Hypoxia, i.e. a reduction in dissolved oxygen concentration below physiologically normal levels, has been identified as playing a critical role in the progression of many types of disease and as a key determinant of the success of cancer treatment. It poses a particular challenge for treatments such as radiotherapy, photodynamic and sonodynamic therapy which rely on the production of reactive oxygen species. Strategies for treating hypoxia have included the development of hypoxia-selective drugs as well as methods for directly increasing blood oxygenation, e.g. hyperbaric oxygen therapy, pure oxygen or carbogen breathing, ozone therapy, hydrogen peroxide injections and administration of suspensions of oxygen carrier liquids. To date, however, these approaches have delivered limited success either due to lack of proven efficacy and/or unwanted side effects. Gas microbubbles, stabilised by a biocompatible shell have been used as ultrasound contrast agents for several decades and have also been widely investigated as a means of promoting drug delivery. This talk will present our recent research on the use of micro and nanobubbles to deliver both drug molecules and oxygen simultaneously to a tumour to facilitate treatment.
Coding theory revolves around the question of what can be accomplished with only memory and redundancy. When we ask what enables the things that transmit and store information, we discover codes at work, connecting the world of geometry to the world of algorithms.
This talk will focus on those connections that link the real world of Euclidean geometry to the world of binary geometry that we associate with Hamming.
A cubic polynomial equation in four or more variables tends to have many integer solutions, while one in two variables has a limited number of such solutions. There is a body of work establishing results along these lines. On the other hand very little is known in the critical case of three variables. For special such cubics, which we call Markoff surfaces, a theory can be developed. We will review some of the tools used to deal with these and related problems.
Joint works with Bourgain/Gamburd and with Ghosh
The cover of the December 2016 AMS Notices shows an eye-like region picked out by blue and red dots and surrounded by green rays. The picture, drawn by Yasushi Yamashita, illustrates Gaven Martin’s search for the smallest volume 3-dimensional hyperbolic orbifold. It represents a family of two generator groups of isometries of hyperbolic 3-space which was recently studied, for quite different reasons, by myself, Yamashita and Ser Peow Tan.
After explaining the coloured dots and their role in Martin’s search, we concentrate on the green rays. These are Keen-Series pleating rays which are used to locate spaces of discrete groups. The theory also suggests why groups represented by the red dots on the rays in the inner part of the eye display some interesting geometry.