I will
give an idea of what category theory is and how it can be successfully applied in mathematics and the mathematical sciences by means of example. The example is a notion from mathematical logic formalizing the intuitive concept of "property". The new category-theoretical
definition of this notion can physically be interpreted as a measurement. Unraveling this definition in particular categories can be regarded as defining the concept of "property" in different context, e.g. in classical, probabilistic
and quantum physics, and in each case this recovers familiar things. Disclaimer:
Up to some differences in the technical details, all of this is work of Bart Jacobs. (See arXiv:1205.3940)
Integrability has been successfully used to compute the
non-perturbative spectrum, Wilson loops and scattering amplitudes in the
AdS/CFT correspondence. Most of these results apply to N=4, D=4 SYM / strings
on AdS(5)xS(5). Strings on AdS(3)xM, where M is either
S(3)xT(4) or S(3)xS(3)xS(1), are also integrable and
potentially solvable by the same methods (Bethe ansatz, Y-system, TBA etc). An
interesting aspect of string theory on AdS(3) is a large number of parameters
that preserve integrability. One parameters, in particular, interpolates
between the integrable RR AdS(3) background and conformal NSNS background
described by a non-compact WZW model. Another interesting aspect of string
theory on AdS(3) is emergence of target-space Viraroso symmetry. I will review
how integrability arises in the AdS(3)/CFT(2) correspondence, and will describe
what is (not) know about the Bethe ansatz solution of the relevant
sigma-models.
Cosmic voids are potentially a rich source of information
for both astrophysics and cosmology. To enable such science, we produce the
most comprehensive void catalog to date using the Sloan Digital Sky Survey Data
Release 7 main sample out to redshift z = 0.2 and the Luminous Red Galaxy
sample out to z = 0.44. Using a modified version of the parameter-free void
finder ZOBOV, we fully take into account the presence of survey boundary and
masks. We discuss basic catalog statistics such as number counts and redshift
distributions, as well as describe some example data products derived from our
catalog, such as radial density profiles and projected density maps. Using this
catalog, we report on the first application of the Alcock-Paczynski test to
stacked voids in spectroscopic redshift surveys by applying the shape-fitting
procedure presented in Lavaux & Wandelt (2011) to ten void stacks out to
redshift z = 0.36. Our results are consistent with WMAP 7-year cosmological
constraints. We compare our results to alternate methods of constructing void
stacks and comment on future observational prospects.
There are many situations in cosmology that
motivate the study of scalar fields with higher-derivative actions. The best-known
such situations are probably k-inflation (with DBI-inflation being a special
case) and models based on galileon theories, but even eternal inflation and
cyclic universes provide good reasons to study such theories. After an extended
discussion of the motivations, I will show how scalar field theories with
higher derivatives can be constructed in (minimal, 4-dimensional) supergravity,
and will discuss their properties, especially in regard to their cosmological
applications.
We shall follow the
growth of probability theory and applications from the 1650s onwards, in
parallel with the development of statistical inference. Bayesian,
Neyman-Pearson hypothesis testing and Fisherian likelihood methods will all be
covered, with an emphasis on relating theory to a wide range of
applications. Practical sessions will use SciPy and feature
closed-form solutions, iterative and Monte Carlo simulation methods.
We shall follow the
growth of probability theory and applications from the 1650s onwards, in
parallel with the development of statistical inference. Bayesian,
Neyman-Pearson hypothesis testing and Fisherian likelihood methods will all be
covered, with an emphasis on relating theory to a wide range of
applications. Practical sessions will use SciPy and feature
closed-form solutions, iterative and Monte Carlo simulation methods.