Ricerc@Sapienza

I argue that the construction of representation theorems is a powerful tool for creating novel objects and theories in mathematics, as the construction of a new representation introduces new pieces of information in a very specific way that enables a solution for a problem and a proof of a new theorem. In more detail, I show how the work behind the proof of a representation theorem transforms a mathematical problem in a way that makes it tractable and introduces information into it that it did not contain at the beginning of the process.

3-dimensional (3D) audio is the new frontier in audio technology and it is quickly taking place in many applications, from cinema to virtual reality, audio surveillance and video games. The large amount of data requires fast and compact solutions for signal processing. With this aim in view, research is moving towards the exploration of hypercomplex algebras in order to find a non-redundant and compact form for the representation of 3D audio sound fields without the loss of information.