TASI Lectures: Particle Physics from Perturbative and Non-perturbative Effects in D-braneworlds

In these notes we review aspects of semi-realistic particle physics from the point of view of type II orientifold compactifications. We discuss the appearance of gauge theories on spacetime filling D-branes which wrap non-trivial cycles in the Calabi-Yau. Chiral matter can appear at their intersections, with a natural interpretation of family replication given by the topological intersection number. We discuss global consistency, including tadpole cancellation and the generalized Green-Schwarz mechanism, and also the importance of related global $U(1)$ symmetries for superpotential couplings. We review the basics of D-instantons, which can generate superpotential corrections to charged matter couplings forbidden by the global $U(1)$ symmetries and may play an important role in moduli stabilization. Finally, for the purpose of studying the landscape, we discuss certain advantages of studying quiver gauge theories which arise from type II orientifold compactifications rather than globally defined models. We utilize the type IIa geometric picture and CFT techniques to illustrate the main physical points, though sometimes we supplement the discussion from the type IIb perspective using complex algebraic geometry.Comment: 35 pages. Based on lectures given by M.C. at TASI 2010. v2: added references, fixed typo

USING NATURE AS BOTH MENTOR AND MODEL: ANIMAL WELFARE RESEARCH AND DEVELOPMENT IN SUSTAINABLE SWINE PRODUCTION

Livestock Production/Industries,

The Bing-Borsuk and the Busemann Conjectures

We present two classical conjectures concerning the characterization of manifolds: the Bing Borsuk Conjecture asserts that every $n$-dimensional homogeneous ANR is a topological $n$-manifold, whereas the Busemann Conjecture asserts that every $n$-dimensional $G$-space is a topological $n$-manifold. The key object in both cases are so-called {\it generalized manifolds}, i.e. ENR homology manifolds. We look at the history, from the early beginnings to the present day. We also list several open problems and related conjectures.Comment: We have corrected three small typos on pages 8 and

Set-partition tableaux and representations of diagram algebras

The partition algebra is an associative algebra with a basis of set-partition diagrams and multiplication given by diagram concatenation. It contains as subalgebras a large class of diagram algebras including the Brauer, planar partition, rook monoid, rook-Brauer, Temperley-Lieb, Motzkin, planar rook monoid, and symmetric group algebras. We give a construction of the irreducible modules of these algebras in two isomorphic ways: first, as the span of symmetric diagrams on which the algebra acts by conjugation twisted with an irreducible symmetric group representation and, second, on a basis indexed by set-partition tableaux such that diagrams in the algebra act combinatorially on tableaux. The first representation is analogous to the Gelfand model and the second is a generalization of Young's natural representation of the symmetric group on standard tableaux. The methods of this paper work uniformly for the partition algebra and its diagram subalgebras. As an application, we express the characters of each of these algebras as nonnegative integer combinations of symmetric group characters whose coefficients count fixed points under conjugation

Detecting codimension one manifold factors with the piecewise disjoint arc-disk property and related properties

We show that all finite-dimensional resolvable generalized manifolds with the piecewise disjoint arc-disk property are codimension one manifold factors. We then show how the piecewise disjoint arc-disk property and other general position properties that detect codimension one manifold factors are related. We also note that in every example presently known to the authors of a codimension one manifold factor of dimension $n\geq 4$ determined by general position properties, the piecewise disjoint arc-disk property is satisfied