Tensor triangular geometry: Geometric study of tensor triangulated categories in algebraic geometry, stable homotopy, modular representation theory, motivic theory, noncommutative geometry.
Algebraic K-theory of quadratic forms, Witt groups in algebraic geometry.
Some videos:
A talk at a 2008 MSRI meeting, on modular representation theory.
A talk at ICM 2010, on tensor triangular geometry.
Some conferences:
Ascona: 2007 February 18-23.
Banff: 2011 June 12-17.
... to come:
Seattle: 2012 July 27 - August 5. Bristol: 2012 September 24-28. MSRI: 2012 August 27 - September 7. MSRI: 2013 January 28 - February 1. MSRI: 2013 February 11-15.