On some combinatorial formulae coming from Hessian Topology
  The interaction between combinatorics and algebraic and differential geometry is very strong. While researching a problem of Hessian topology, we came across a series of identities of binomial coefficients, which are useful for proving a topological property of certain spaces whose elements are graphs of a class of hyperbolic polynomials. These identities are proven by different methods in combinatorics. 
Adriana Ortiz-Rodr\'iguez and Federico S\'anchez-Bringas
math.CO