Arithmetic Spacetime Geometry from String Theory

An arithmetic framework to string compactification is described. The approach is exemplified by formulating a strategy that allows to construct geometric compactifications from exactly solvable theories at $c=3$. It is shown that the conformal field theoretic characters can be derived from the geometry of spacetime, and that the geometry is uniquely determined by the two-dimensional field theory on the world sheet. The modular forms that appear in these constructions admit complex multiplication, and allow an interpretation as generalized McKay-Thompson series associated to the Mathieu and Conway groups. This leads to a string motivated notion of arithmetic moonshine.Comment: 36 page

The Einstein-Vlasov System/Kinetic Theory

The main purpose of this article is to provide a guide to theorems on global properties of solutions to the Einstein--Vlasov system. This system couples Einstein's equations to a kinetic matter model. Kinetic theory has been an important field of research during several decades in which the main focus has been on non-relativistic and special relativistic physics, i.e., to model the dynamics of neutral gases, plasmas, and Newtonian self-gravitating systems. In 1990, Rendall and Rein initiated a mathematical study of the Einstein--Vlasov system. Since then many theorems on global properties of solutions to this system have been established.Comment: Published version http://www.livingreviews.org/lrr-2011-

On the existence of topological dyons and dyonic black holes in anti-de Sitter Einstein-Yang-Mills theories with compact semisimple gauge groups

Here we study the global existence of “hairy” dyonic black hole and dyon solutions to four-dimensional, anti-de Sitter Einstein-Yang-Mills theories for a general simply connected and semisimple gauge group G, for the so-called topologically symmetric systems, concentrating here on the regular case.We generalise here cases in the literature which considered purely magnetic spherically symmetric solutions for a general gauge group and topological dyonic solutions for su(N). We are able to establish the global existence of non-trivial solutions to all such systems, both near existing embedded solutions and as the absolute value of Lambda goes to infinity. In particular, we can identify non-trivial solutions where the gauge field functions have no zeroes, which in the su(N) case proved important to stability. We believe that these are the most general analytically proven solutions in 4D anti-de Sitter Einstein-Yang-Mills systems to date

The Simplicity of Material Objects

In my dissertation, I advance and develop an unorthodox account of ordinary material objects: Aristotelian Parts Nihilism. According to my theory, ordinary material objects, strictly speaking, do not have proper parts: they are extended simples sharing the exact location of their constituting portions of matter. The present construction has two main theoretical benefits. On the one hand, it preserves the modal intuition according to which hylomorphs and their constituting portions of matter are numerically different. As a nice consequence, it allows philosophers getting rid of counterparts to account for transworld identity of objects. On the other hand, and differently from the most part of multi-thingist theories, it is fully compatible with Classical Extensional Mereology. The dissertation is divided into four chapters. In the first chapter, I revise some arguments against counterpart theory, and thus give indirect reason to prefer a standard account of transworld genuine identity. In the second chapter, I revise the major multi-thingist theories available and find them incompatible with Classical Extensional Mereology. Mereological hylomorphism is safe from this criticism, but arguably falls prey of a circularity of dependence. Then, I advance and describe Aristotelian Parts Nihilism. In the third chapter, I explore the issues with persistence and location, and show that Aristotelian Parts Nihilism fits Transdurantism well. In the fourth and last chapter, I defend the theory by some potential issues of causal overdetermination and coincidence. Importantly, I also explain how we can say ordinary material objects to be complex while still lacking proper parts

QBism and the Limits of Scientific Realism

QBism is an agent-centered interpretation of quantum theory. It rejects the notion that quantum theory provides a God’s eye description of reality and claims instead that it imposes constraints on agents’ subjective degrees of belief. QBism’s emphasis on subjective belief has led critics to dismiss it as antirealism or instrumentalism, or even, idealism or solipsism. The aim of this paper is to consider the relation of QBism to scientific realism. I argue that while QBism is an unhappy fit with a standard way of thinking about scientific realism, an alternative conception I call ”perspectival normative realism” may allow for a reconciliation

Inference to the Best Explanation as Supporting the Expansion of Mathematicians' Ontological Commitments

This paper argues that in mathematical practice, conjectures are sometimes confirmed by “Inference to the Best Explanation” (IBE) as applied to some mathematical evidence. IBE operates in mathematics in the same way as IBE in science. When applied to empirical evidence, IBE sometimes helps to justify the expansion of scientists’ ontological commitments. Analogously, when applied to mathematical evidence, IBE sometimes helps to justify the expansion of mathematicians’ ontological commitments. IBE supplements other forms of non-deductive reasoning in mathematics, avoiding obstacles sometimes faced by enumerative induction or hypothetico-deductive reasoning. Mathematical platonists can appeal to mathematicians’ use of IBE even though it cannot supply a non-circular argument for platonism. This paper offers an inductive account of why mathematical IBE tends to lead to mathematical truths, thereby addressing part of the Benacerraf/Field challenge to our knowledge of abstract mathematical entities