Exterior differential systems, Lie algebra cohomology, and the rigidity of homogenous varieties

These are expository notes from the 2008 Srni Winter School. They have two purposes: (1) to give a quick introduction to exterior differential systems (EDS), which is a collection of techniques for determining local existence to systems of partial differential equations, and (2) to give an exposition of recent work (joint with C. Robles) on the study of the Fubini-Griffiths-Harris rigidity of rational homogeneous varieties, which also involves an advance in the EDS technology.Comment: To appear in the proceedings of the 2008 Srni Winter School on Geometry and Physic

Collider Searches for Extra Dimensions

Searches for extra spatial dimensions remain among the most popular new directions in our quest for physics beyond the Standard Model. High-energy collider experiments of the current decade should be able to find an ultimate answer to the question of their existence in a variety of models. Until the start of the LHC in a few years, the Tevatron will remain the key player in this quest. In this paper, we review the most recent results from the Tevatron on searches for large, 1/TeV-size, and Randall-Sundrum extra spatial dimensions, which have reached a new level of sensitivity and currently probe the parameter space beyond the existing constraints. While no evidence for the existence of extra dimensions has been found so far, an exciting discovery might be just steps away.Comment: To appear in Proceedings of SLAC Summer Institute, 2004. An extended version of the talk given on behalf of the CDF and D0 Collaboration

Searches for Extra Spatial Dimensions with the CMS Detector at the LHC

The success of the first three years of operations of the LHC at center-of-mass energies of 7 and 8 TeV radically changed the landscape of searches for new physics beyond the standard model and our very way of thinking about its possible origin and its hiding place. Among the paradigms of new physics that have been probed quite extensively at the LHC, are various models that predict the existence of extra spatial dimensions. In this review, the current status of searches for extra dimensions with the CMS detector is presented, along with prospects for future searches at the full energy of the LHC, expected to be reached in the next few years.Comment: Invited review on behalf of the CMS Collaboration in a special issue of Modern Physics Letters A on models with extra spatial dimension

Collider Searches for Extra Spatial Dimensions and Black Holes

Searches for extra spatial dimensions remain among the most popular new directions in our quest for physics beyond the Standard Model. High-energy collider experiments of the current decade should be able to find an ultimate answer to the question of their existence in a variety of models. We review these models and recent results from the Tevatron on searches for large, inverse-TeV-size, and Randall-Sundrum extra spatial dimensions. The most dramatic consequence of low-scale (~1 TeV) quantum gravity is copious production of mini-black holes at the LHC. We discuss selected topics in the mini-black-hole phenomenology.Comment: Invited talk given at the 13th Lomonosov International Conference on Elementary Particle Physics, Moscow, Russia, August 23-29, 200