Title: The Waldschmidt constant

Abstract:  A (projective) variety V is a set of common zeros of the polynomials in an ideal I that is generated by homogenous polynomials. Given the generators of the ideal I,  one would like to know the minimum degree of a polynomial F such that each point of V is a root of f of a given multiplicity, say k. As this is often a difficult problem one studies first the corresponding question for large k. This leads to the Waldschmidt constant, which gives an asymptotic answer to the problem.

If I is a an ideal that is generated by squarefree monomials, then the Waldschmidt constant can be expressed as the optimal solution to a linear program or as a fractional chromatic number. This leads to the new bounds and computations of the Waldschmidt constant.

No prior knowledge of monomial ideals or graph theory is assumed. All concepts will be explained in the talk.