Renormalization in Physics and Theoretical Computer Science
Yuri Manin, Northwestern University (Evanston, USA) and Max Planck Institute for Mathematics (Bonn, Germany)
2 de diciembre, 2011, 12:00 h., ICMAT, sala naranja (cartel)
(Calle Nicolás Cabrera, 15, Campus de Cantoblanco)
Resumen: In Quantum Field Theory main observables are expressed in terms of Feynmann's path integrals. They are not well defined mathematical objects, and various ways to extract from them meaningful statements involve intermediate infinite expressions and prescriptions for "subtracting" controlled infinities in order to get honest finite results.
In the mathematical theory of computability, based upon recursive functions, infinities inevitably appear as, for example, waiting time for computation of a value of a function at a point where it is not defined ("Halting Problem").
As an example of the realistic problem where (un)computability is not settled yet, I will discuss asymptotic bounds for error-correcting codes.
The main point of the talk is to suggest that in both contexts, the problem can be addressed using similar mathematical tools, first developed in Quantum Field Theory.