Written reports should be about 20 pages long.  Plan on 20 minutes for your oral presentation.  This should not be just a show and tell, nor the result of reading a single authorative, technical article.  You will be required present a technical topic in a way that you understand it, and not focussed entirely on detail, to an audience essentially unfamiliar with the technical details of your topic.

Suggested topics

Black hole perturbations: theory and analysis
Black hole stability: theory and results (John Rotter)
Black hole thermodynamics (Analis Lawrence)
Conserved quantities in general relativity
Cosmology: Big bang nucleosynthesis and the role of neutrinos
Cosmology: Role of gravitation in large scale structure (Huanbo Sun)
Experimental tests of General Relativity (Fatemeh Taherasghari)
Gravitational waves from throughout the universe: implications for measurement
Gravitational waves
sources and rates for LIGO (Tanmaya Mishra)
Gravitational waves
sources and rates for LISA
Hamiltonian formulation of general relativity
Holographic theory, and emergent gravity as an entropic force (Liu Tao)
Holographic theory on the cosmological scale 
viability, constraints and implications (LingQin Xue)
Initial value formulation (Daniel Brotherton)
Newman-Penrose spinor formalism
Numerical relativity methods (Daniel George)
Post-Newtonian Theory (Jinye Yang)
Recent numerical relativity results
Spinning black hole mergers: potential for new tests of General Relativity? (Sourath Ghosh)
The Hubble constant: discrepant "measurements"? (Shubhagata Bhaumik)
The inflationary theory of primordial cosmological perturbations (Alexander Hipp)
Theory and detection of primordial gravitational waves (Farshad Kamalinejad)