“Forty-Seven Days: How Pershing’s Warriors Came of Age to Defeat the German Army in World War I (Book Review)” by Mitchell Yockelson

Review of Forty-Seven Days: How Pershing’s Warriors Came of Age to Defeat the German Army in World War I by Mitchell Yockelso

Particle Physics Implications of F-theory

We review recent progress in realizing Grand Unified Theories (GUTs) in a strongly coupled formulation of type IIB string theory known as F-theory. Our main emphasis is on the expected low-energy phenomenology of a minimal class of F-theory GUTs. We introduce the primary ingredients in such constructions, and then present qualitative features of GUT models in this framework such as GUT breaking, doublet-triplet splitting, and proton decay. Next, we review proposals for realizing flavor hierarchies in the quark and lepton sectors. We discuss possible supersymmetry breaking scenarios, and their consequences for experiment, as well as geometrically minimal realizations of F-theory GUTs which incorporate most of these features.Comment: v2: 42 pages, 3 figures, submitted to Annu. Rev. Nuc. Part. Sci, improved formatting and small clarification

Hidden symmetry of the quantum Calogero-Moser system

Hidden symmetry of the quantum Calogero-Moser system with the inverse-square potential is explicitly demonstrated in algebraic sense. We find the underlying algebra explaining the super-integrability phenomenon for this system. Applications to related multi-variable Bessel functions are also discussed.Comment: 16 pages, latex, no figure

Angular Momenta of Relative Equilibrium Motions and Real Moment Map Geometry

Chenciner and Jimenez Perez showed that the range of the spectra of the angular momenta of all the rigid motions of a fixed central configuration in a general Euclidean space form a convex polytope. In this note we explain how this result follows from a general real convexity theorem of O Shea and Sjamaar in symplectic geometry. Finally, we provide a representation theoretic description of the pushforward of the normalized measure under the real moment map for Riemannian symmetric pairs.Comment: 23 page