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We put forth the idea that Hamilton's equations coincide with deterministic and reversible evolution. We explore the idea from five different perspectives (mathematics, measurements, thermodynamics, information theory and state mapping) and…

In this Letter we examine the Multiverse theory and how it relates to the Anthropic Principle. Under the supposition of Eternal Inflation, the String Theory Landscape (STL) has reinvigorated the discussion of the Anthropic Principle. The…

String cosmology aims at providing a reliable description of the very early Universe in the regime where standard-model physics is no longer appropriate, and where we can safely apply the basic ingredients of superstring models such as…

What are strings made of? The possibility is discussed that strings are purely mathematical objects, made of logical axioms. More precisely, proofs in simple logical calculi are represented by graphs that can be interpreted as the Feynman…

In these lectures I discuss various unsolved problems of string theory and their relations to quantum gravity, 3d Ising model, large N QCD, and quantum cosmology. No solutions are presented but some new and perhaps useful approaches are…

We construct new classes of exact cosmological solutions to five dimensional Einstein-Maxwell-dilaton theory with two coupling constants for the dilaton-Maxwell term and dilaton-cosmological constant term. All the solutions are…

We connect a possible solution for the ``cosmological constant problem'' to the existence of a (postulated) conformal fixed point in a fundamental theory. The resulting cosmology leads to quintessence, where the present acceleration of the…

In this review article we compare the recent work of Peter Lynds, "On a finite universe with no beginning or end", with that of Stephen Hawking, primarily "Quantum Cosmology, M-Theory, and the Anthropic Principle", and two foundational…

We present an elementary account of mathematical cosmology through a series of important unsolved problems. We introduce the fundamental notion of `a cosmology' and focus on the issue of singularities as a theme unifying many current,…

This talk considers possible lessons of string theory for low energy physics. These are of two types. First, assuming that string theory is the correct underlying theory of all interactions, we ask whether there are any generic predictions…

This PhD thesis deals with a number of different problems in mathematical physics with the common thread that they have probabilistic aspects. The problems all stem from mathematical studies of lattice systems in statistical and quantum…

The question of (non-)uniqueness of one-dimensional self-similar solutions to the Riemann problem for hyperbolic systems of gas dynamics in sets of multi-dimensional admissible weak solutions was addressed in recent years in several papers…

We acuminate the idea of a final theory of physics in order to analyze its logical implications and consequences. It is argued that the rationale of a final theory is the principle of sufficient reason. This implies that a final theory of…

String theory builds on the great legacy of Yukawa and Tomonaga: New degrees of freedom and control of the UV are two important themes. This talk will give an overview of some of the progress and some of the unsolved problems that…

We propose an approach to explaining why naive large quantum fluctuations are not the right estimate for the cosmological constant. We argue that the universe is in a superposition of many vacua, in such a way that the resulting…

Mathematics cannot anymore be assimilated to a linguistic game, where formal proofs are strongly differentiated with conjectural thinking, without building any category of knowledge to understand the passage (Wittgenstein's gist). Nowadays,…

The statistical physics approach to the number partioning problem, a classical NP-hard problem, is both simple and rewarding. Very basic notions and methods from statistical mechanics are enough to obtain analytical results for the phase…

We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of…

For two decades the hot big-bang model as been referred to as the standard cosmology -- and for good reason. For just as long cosmologists have known that there are fundamental questions that are not answered by the standard cosmology and…

There are now two cosmological constant problems: (i) why the vacuum energy is so small and (ii) why it comes to dominate at about the epoch of galaxy formation. Anthropic selection appears to be the only approach that can naturally resolve…