Nazanin Roshandel Tavana: Computable analysis and its applications

Invitation to the Logic Seminar at the National University of Singapore

Date: Wednesday, 28 January 2015, 17:00 hrs

Room: S17#05-11, Department of Mathematics, NUS

Speaker: Nazanin Roshandel Tavana
Amirkabir University of Technology and IPM

Title: Computable analysis and its applications


Computable analysis is a branch of computability theory studying those
real functions and the related sets which can be computed by machines
such as digital computers. The increasing demand for reliable software
in scientific computation and engineering requires a sound foundation
not only of the analytic/numerical but also of the computational
aspects of real number computation. The central subject of this talk
is one of the approch of computable analysis called “Type Two Theory
of Effectivity (TTE)”. It is based on definitions of computable real
numbers and functions by A. Turing, A. Grzegorczyk and D. Lacombe.
First, computability on finite and infinite sequences of symbols is
introduced. Then, this kind of computability can be transfered to the
other sets by means of names or codes. After, the framework of
computability is settled down, we can talk about the effectiveness of
some other spaces as metric spaces. At the end, complexity of this
approach and its two applications are discussed. One application is
for effectiveness in metric model theory and the other one is in
measure theory.

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