Scientific Series

Consider a discrete quantum system with a d-dimensional state space. For certain values of d, there is an elegant information-theoretic uncertainty principle expressing the limitation on one's ability to simultaneously predict the outcome of each of d+1 mutually unbiased--or mutually conjugate--orthogonal measurements. (The allowed values of d include all powers of primes, and at present it is not known whether any value of d is excluded.) In this talk I show how states that minimize uncertainty in this sense can be generated via a discrete phase space based on finite fields. I also discuss some numerically observed features of these minimum-uncertainty states as the dimension d gets very large.

Shear viscosity is a transport coefficient in the hydrodynamic description of liquids, gases and plasmas. The ratio of the shear viscosity and the volume density of the entropy has the dimension of the ratio of two fundamental constants - the Planck constant and the Boltzmann constant - and characterizes how close a given fluid is to a perfect fluid. Transport coefficients are notoriously difficult to compute from first principles. Recent progress in string theory, in particular the development of the gauge-gravity duality, has enabled one to approach this problem from a totally unexpected perspective. In my talk, I will describe the connection between the dynamics of black hole horizons (encoded in their quasinormal spectra) and the hydrodynamics of certain strongly coupled plasmas. I will comment on the relevance of this approach for the interpretation of data obtained in experiments on heavy ion collisions.

Thermodynamics places surprisingly few fundamental constraints on information processing. In fact, most people would argue that it imposes only one, known as Landauer's Principle: a process erasing one bit of information must release an amount kT ln 2 of heat. It is this simple observation that finally led to the exorcism of Maxwell's Demon from statistical mechanics, more than a century after he first appeared. Ignoring the lesson implicit in this early advance, however, quantum information theorists have been surprisingly slow to embrace erasure as a fundamental primitive. Over the past couple of years, however, it has become clear that a detailed understanding of how difficult it is to erase correlations leads to a nearly complete synthesis and simplification of the known results of asymptotic quantum information theory. As it turns out, surprisingly many of the tasks of interest, from distilling high-quality entanglement to sending quantum data through a noisy medium to many receivers, can be understood as variants of erasure. I'll sketch the main ideas behind these discoveries and end with some speculations on what lessons the new picture might have for understanding information loss in real physical systems.

In an anisotropic limit of the weakly-coupled, 2+1-dimensional non-Abelian gauge theories are equivalent to a collection of integrable 1+1-dimensional quantum field theories. This fact makes it possible to understand confinement near this limit. Using exact form factors, it is possible to study the theory away from the extreme anisotropic limit. The string tension between fundamental color sources is found. Adjoint sources are not confined. Some ideas concerning the isotropic case and the generalization to 3+1 dimensions will be discussed.

We give a communication problem between two players, Alice and Bob, that can be solved by Alice sending a quantum message to Bob, for which any classical interactive protocol requires exponentially more communication.

Theories of physics beyond the Standard Model predict the existence of relativistic strings, either as composite objects, or as fundamental constituents of matter. If they were created in the Big Bang, they would very likely still be present in the universe today. This talk reviews the thirty year history of cosmic strings, and describes the latest work which finds intriguing hints in the Cosmic Microwave Background data that the universe is filled with string.

To realize massive pions, I propose a variation of the holographic model of massless QCD using the D4/D8/D8bar-brane configuration proposed by Sakai and Sugimoto. The deformation breaks the chiral symmetry explicitly and I compute the mass of the pions and vector mesons. The observed value of the pion mass can be obtained. I also argue a chiral perturbation corresponding to the deformation.

Anthropic arguments based on selection effects for observers have been claimed to succesfully explain the measured value of the cosmological constant.In this talk I review the fundations of such claims in the context of probability theory and show that different (and equally legitimate) ways of assigning probabilities to candidate universes lead to totally different anthropic predictions. As an explicit example, I discuss a weighting scheme based on the total number of possible observations that observers can carry out over the entire lifetime of the Universe. I show that this leads to an extremely small probability for observing a value of the cosmological constant equal to or greater than what we now measure, in marked contrast with the usual result. I also discuss principles of consistent probabilistic reasoning, showing that the anthropic principle as applied in most of the literature is logically inconsistent. I conclude that current implementations of the anthropic principle display a worrysome lack of predictivity, and cannot be used to explain the value of the cosmological constant, nor, likely, any other physical parameters.

Abstract: This group of astronomical order is slowly yielding its secrets.It is the symmetry group of a rational conformal field theory. In thisintroductory talk, I will discuss the functions that constitute monstrousmoonshine and explain the importance of the monster group and itsconnections with better established parts of mathematics