- Main topic: Linear algebraic groups and their associated algebraic structures, over arbitrary fields (What is a linear algebraic group?)
- Other key topics: Essential dimension, cohomological invariants, motivic decompositions of projective homogeneous varieties, and G-torsors.
- I believe it is one of the miracles of mathematics that split simple linear algebraic groups have an elegant and easy to understand classification, given by their ''root data'', which is independent of the base field (remarkably, the classification is the same for arbitrary base schemes). This classification provides a deep link between the discrete world (for example, when the base field is finite one obtains finite groups of Lie type), and the continuous world (for example, when the base field is real or complex one obtains the Lie groups).
- I am interested in taking a PhD student starting in September 2014. Students would be expected to have some familiarity with algebraic geometry. If you are interested, you can email me.