Student Number Theory: Character sheaves for unipotent groups & easy algebraic groups

An algebraic group is called "easy" if every geometric point is contained in the neutral connected component of its centralizer. In 2006, Boyarchenko and Drinfeld conjectured that a unipotent group is easy if and only if its L-packets of character sheaves are singletons. In 2013, Boyarchenko proved the "only if" direction. In this talk, we sketch a proof of the converse. Along the way, we give a characterization of easy algebraic groups via their Asai twisting operators. No prior knowledge of character sheaves is assumed.