Semigroup theory is the abstract study of first-order ordinary differential equations with values in Banach spaces, driven by linear, but possibly unbounded operators. Roughly speaking, the semigroup approach in partial differential equations is to regard a time-dependent partial differential equation as an ordinary differential equation on a suitable function space.
In this talk, we outline the basics of the theory and present as well two applications to linear PDE; heat equation and second-order parabolic PDE, which is the generalization of the heat equation.
Introduction to Semigroup Theory
Apr. 08, 2015 4pm (MATH 350)
Grad Student Seminar
Braden Balentine (CU-Boulder)
X
Bell’s theorem is a fundamental and incredibly strange result that shows quantum mechanics is incompatible with theories in which probabilities in measurement arise from ignorance of pre-existing local properties. In this talk, we provide some historical background concerning the apparent inconsistencies of quantum mechanics with the physical world and provide simple and reasonably intuitive proofs of Bell’s inequality and Bell’s theorem. Little to no physics knowledge will be required and the mathematics involves simple probability arguments and some knowledge of inner-product spaces.
Bell’s Theorem and the Weirdness of Quantum Mechanics