Monthly Archives: May 2017

Notes of Alina Vdovina’s Cambridge lecture 31-05-2017

Expanders, Beauville surfaces and buildings 1. Expanders For a graph, Cheeger’s constant enters in the isoperimetric inequality Example. For a -regular tree, . Definition 1 An expander is a sequence of finite bounded degree graphs whose Cheeger constants are bounded … Continue reading

Notes of Viktor Schroeder’s third informal Cambridge lecture 30-05-2017

Moebius structures on boundaries, III Today’s material is taken from Jonas Beyrer’s PhD. Given a space, Bourdon’s formula often takes value 0. Nevertheless, for higher rank symmetric spaces, or for products of spaces, the restriction to the Furstenberg boundary is … Continue reading

Notes of Richard Schwartz’ sixth Cambridge lecture 26-05-2017

PETs, pseudogroup actions, and renormalisation Started by group theorist B.H. Neumann in 1959. Outer billiard around a convex polygon composes 180 degrees rotation through vertices. Theorem 1 For a kite (a quadrilateral with one axial symmetry), there exist unbounded orbits … Continue reading

Notes of Richard Schwartz’ fifth Cambridge lecture 24-05-2017

The pentagram map and discrete integrable systems Joint work with Valentin Ovsienko and Serge Tabachnikov Start with a convex polygon. Draw diagonals between vertices at distance 2, they form a smaller polygon inside. Call this the pentagram map, although the … Continue reading

Notes of Viktor Schroeder’s second informal Cambridge lecture 23-05-2017

Moebius structures on boundaries, II 1. Ptolemaic Moebius structures Recall that a Moebius structure is Ptolemaic if cross-ratios satisfy the Ptolemaic inequality, This means that takes its values in the triangle with vertices at the extra points . Examples Boundaries … Continue reading