We will start with presenting the basic notions of (co)homomology of simplical complexes (which requires only basic linear algebra over the field of order 2) and then we will indicate its relevance for several topics in computer science and combinatorics: 1) Property testing. 2) Quantum error correcting codes (where triangulation of some 4-dim hyperbolic manifolds lead to such codes with unexpected parameters) 3) High dimensional expanders. 4) Random simplical complexes.
For this talk I'll discuss uniformization of Riemann surfaces via Kleinian groups. In particular question of conformability by Hasudorff dimension spectrum. I'll discuss and pose some questions which also in particular will imply a conjecture due to Bers.