12 research outputs found
Unitarity bounds on low scale quantum gravity
We study the unitarity of models with low scale quantum gravity both in four
dimensions and in models with a large extra-dimensional volume. We find that
models with low scale quantum gravity have problems with unitarity below the
scale at which gravity becomes strong. An important consequence of our work is
that their first signal at the Large Hadron Collider would not be of a
gravitational nature such as graviton emission or small black holes, but rather
linked to the mechanism which fixes the unitarity problem. We also study models
with scalar fields with non minimal couplings to the Ricci scalar. We consider
the strength of gravity in these models and study the consequences for
inflation models with non-minimally coupled scalar fields. We show that a
single scalar field with a large non-minimal coupling can lower the Planck mass
in the TeV region. In that model, it is possible to lower the scale at which
gravity becomes strong down to 14 TeV without violating unitarity below that
scale.Comment: 15 page
Four lectures on secant varieties
This paper is based on the first author's lectures at the 2012 University of
Regina Workshop "Connections Between Algebra and Geometry". Its aim is to
provide an introduction to the theory of higher secant varieties and their
applications. Several references and solved exercises are also included.Comment: Lectures notes to appear in PROMS (Springer Proceedings in
Mathematics & Statistics), Springer/Birkhause