A taste of Galois theory
Madhavendra, Madhavendra Burke, Maxim
2021 UPEI Undergraduate Research Days
Abstract
2021
Physics Mathematical and Computational Sciences
The realization of Galois groups over the field of rationals has been a longstanding open question in abstract algebra since Hilbert termed it as Inverse Galois Problem in 1892. The 'problem' deals with the requirement of a rigorous proof or a general computational method to provide a one-toone correspondence between the fundamentals of symmetries in nature called groups and abstract quantities called Galois field extensions- which habitat the root systems of certain types of polynomial Show moreThe realization of Galois groups over the field of rationals has been a longstanding open question in abstract algebra since Hilbert termed it as Inverse Galois Problem in 1892. The 'problem' deals with the requirement of a rigorous proof or a general computational method to provide a one-toone correspondence between the fundamentals of symmetries in nature called groups and abstract quantities called Galois field extensions- which habitat the root systems of certain types of polynomial equations. The presenter discusses the foundations of Galois theory and elaborates further on the methods and goals which were studied and developed during the research term. Furthermore, applications to physics in terms of knot theory and spontaneous symmetry breaking in quantum systems are highlighted. Show less
