Free boundary problems are today considered to be one of the most important directions in the mainstream analysis of partial differential equations, with an abundance of applications to real world problems. In the last two decades, various new ideas, techniques and methods have been developed and important challenging problems in physics, engineering, industry, finance and other areas have arisen, with systems biology and medicine representing particularly rich sources of new applications. The study of free boundary problems is an extremely broad topic due to the abundance of applications and this breadth presents challenges as well as opportunities.
Aims & Objectives
This applied focus half day afternoon event formed part of the Isaac Newton Institute Free Boundary Problems and Related Topics research programme and was embedded within a major international conference in the area. It brought together leading expertise in multiple disciplines across biology and medicine which require mathematical modelling and computation involving free boundaries, interfaces and related concepts. The programme was structured to assist in identifying the common challenges that have the greatest potential for research, knowledge transfer, public policy and commercial impact.
A key aim of this event was to highlight how recent developments, particularly with regard to computation and modelling, impact on the use of mathematics in areas such as:
- Cancer treatment
- Computer assisted surgery
- Wound healing
- Cell biology and imaging
- Regenerative medicine
- Bacterial infections
The talks also explored how new theories are being developed and highlighted the mathematical models which are being created to aid understanding and lead to advances in technologies and treatments and how these translate to possible end user applications. There were also opportunities for networking and investigation of potential collaborations and the afternoon finished with a facilitated discussion session, followed by a drinks reception.