Bruce Fontaine

My interests in mathematics are in representation theory and combinatorics, specifically the relationship between the two that can be constructed via geometry. There are many interesting open problems in this area: for instance by rephrasing combinatorial problems in geometric terms it is often possible to prove positivity of formulas. The geometry can in turn be used to categorify what the combinatorics counts. In my research I try to understand the nature of the trivial representations, or invariant vectors, in a tensor product of representations. This is a classic problem, but more recent combinatorial methods allow the use of geometry to examine the underlying structure of the representation.