Tata Institute of Fundamental Research

Theory of Field $\mathbb{C} $ is Decidable

STCS Student Seminar
Speaker: Prabhat Kumar Jha
Organiser: Prerona Chatterjee
Date: Saturday, 4 Jul 2020, 16:00 to 17:00

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Abstract:  Zoom Details:
Link: https://zoom.us/j/98172222418?pwd=b0htSDQ5NDRKQ050K0d6cHJ3YnZXQT09
Meeting ID: 981 7222 2418
Password: studsem
Abstract:  Many optimization problems reduce to finding truth value of quantified formulas over real or/and complex numbers. In this talk we will cover a proof of decidability of theories of real numbers and complex numbers due to Tarski. We will begin by providing an algorithm to locate roots of multi-variable polynomials over these fields and then use quantifier elimination techniques to prove decidability. If time permits, we will discuss its applications to optimization and verification problems.
Note: There is no prerequisite from Mathematical Logic or Computability theory.