Polygon Seminar. NOTE: Seminar is in the room G.73, Franklin-Wilkins, WATERLOO CAMPUS of King's College London. http://www.kcl.ac.uk/campuslife/campuses/waterloo/Waterloo.aspx

I shall explain why there is symmetry enhancement near black hole and brane horizons. I shall also present some applications which include the classification of AdS backgrounds in supergravity.

Is there a consistent patching for double manifolds? I shall demonstrate that the solution of the strong section condition leads to exact 3-form field strengths. I shall also prove that the consistency of the examples presented so far depends on the choice of the atlas, and so they are not general covariant. Then I shall suggest a new construction which resolves some of the puzzles and possibly specifies the appropriate spaces up to homotopy.