The ghosts of departed quantities as the soul of computation

Sam Sanders (Belgium) gives a talk at the MCMP Colloquium titled "The ghosts of departed quantities as the soul of computation". Abstract: Using techniques from Nonstandard Analysis, we introduce omega-invariance: a new notion of computability based on infinitesimals. We show that omega-invariance can capture two central notions of computability, namely those provided by Recursion Theory and Constructive Analysis. We discuss the philosophical implications of these results.