3:45PM: Divisors on matroids and their volumesChristopher EurThe classical volume polynomial in algebraic geometry measures the volumes of ample (and nef) divisors on a smooth projective variety. We introduce an analogous volume polynomial for matroids, and give a complete combinatorial formula. For a realizable matroid, we thus obtain an explicit formula for the classical volume polynomial of the associated wonderful compactification. We then define an invariant called the volume of a matroid as a particular specialization of its volume polynomial, and discuss its algebrogeometric and combinatorial properties in connection to graded linear series on blowups of projective spaces.

5:00PM: The Excess intersection formulaRitvik RamkumarWe will give examples of situations where intersections do not have the expected dimension. We will describe the excess intersection formula which allows us to compute the portion of the intersection that has the expected dimension. Time permitting we will compute the Chow ring of a blowups along smooth subschemes.
