The computational demands of modern computer applications make the pursuit of high performance more critical than ever, and mobile, battery-powered devices, as well as concerns related to climate change, require high performance to co-exist with energy-efficiency. Due to physical limits, the traditional means for improving hardware performance by increasing processor frequency now carries an unacceptably high energy cost. Advances in processor fabrication technology instead allow the construction of many-core processors, where hundreds or thousands of processing elements are placed on a single chip, promising high performance and energy-efficiency through sheer volume of processing elements. Many-core devices are present in practically all consumer devices, including smartphones and tablets. As a result, the general public in developed countries interact with many-core software daily. Many-core technology is also used to accelerate safety-critical software in domains such as medical imaging and autonomous vehicle navigation. It is thus important that many-core software should be reliable. This requires reliable software from programmers, but also a reliable "stack" to support this software, including compilers that allow software to execute on many-core devices, and the many-core devices themselves. Recent work on formal verification and testing by myself and other researchers has identified serious technical problems spanning the many-core stack. These problems undermine confidence in applications of many-core technology: defective many-core software could risk fatal accidents in critical domains, and impact negatively on users in other important application areas. My long-term vision is that the reliability of many-core programming can be transformed through breakthroughs in programming language specification, formal verification and test case generation, enabling automated tools to assist programmers and platform vendors in constructing reliable many-core applications and language implementations. The aim of this five-year Fellowship is to undertake foundational research to investigate a number of open problems whose solution is key to enabling this long-term vision. First, I seek to investigate whether it is possible to precisely express the intricacies of many-core programming language using formal mathematics, providing a rigorous basis on which software and language implementations can be constructed. Second, I aim to tackle several open problems that stand in the way of effective formal verification of many-core software, which would allow developers to obtain strong guarantees that such software will operate as required. Third, I will investigate raising this level of rigour beyond many-core languages. A growing trend is for applications to be written in relatively simple, high-level representations, and then automatically translated into high-performance many-core code. This translation process must preserve the meaning of programs; I will investigate methods for formally certifying that it does. Fourth, I will formulate new methods for testing many-core language implementations, exploiting the rigorous language definitions brought by my approach to enable high test coverage of subtle language features. Collectively, progress on these problems promises to enable a *high-assurance* many-core stack. I will demonstrate one instance of such a stack for the industry-standard OpenCL language and the PENCIL high-level language, showing that high-level PENCIL programs can be reliably compiled into rigorously-defined OpenCL, integrated with verified library components, and deployed on thoroughly tested implementations from many-core vendors. Partnership with four leading many-core technology vendors, AMD, ARM, Imagination Technologies and NVIDIA, provides excellent opportunities for the advances the Fellowship makes to have broad industrial impact.