ICTS

I will discuss the connections of matrix positivity and its preservers to multiple sub-fields of mathematics: analysis, metric geometry, combinatorics, and also downstream applications. This includes classical results by Schur, Rudin, Loewner, Karlin, and their students: FitzGerald, Horn, Pinkus,...more

In two dimensional topologically ordered matter, processes depend on gross topology rather than detailed geometry. Thinking in 2+1 dimensions, particle world lines can be interpreted as knots or links, and the amplitude for certain processes becomes a topological invariant of that link. While...more