To Infinity and Beyond

	ALVARO LOZANO-ROBLEDO H. C. Wang Assistant Professor at Cornell University. Office: 584 Malott Hall, Email: alozano@math.cornell.edu To Infinity and Beyond! Part I: Mathematical Infinities What is infinity? What is infinite? Is there something "beyond" infinity? Are there different (bigger, smaller) infinities? A brief history of the concept of infinity. "Big" numbers, "small" numbers and zero. Zeno's paradox and Thompson's lamp. Galileo: infinity is not just another number. Other paradoxes: The Infinite Hotel. Bolzano: sets and the mathematical definition of infinite. Cantor and the transfinite numbers. Part II: Infinite Spaces and Finite Spaces Is the Universe infinite? Is it finite? What kind of infinite/ finite Universes could exist? How can we tell which type of Universe do we live in? A brief history of time and the Universe (by PBS) or NOVA - Origins of the Universe. Is the Universe infinite? What would it look like? From Digges to Einstein. Is the Universe finite? Evidence and possibilities. Universes which are half finite, half infinite. Paradoxes of the finite and infinite Universes.