3:45PM: Pushouts in algebraic geometryDavid RydhPushouts are frequently used in topology and simple to describe. In algebraic geometry on the other hand, pushouts are more unwieldy and far less utilized. In this talk I'll motivate why pushouts nevertheless constitute a powerful technique and explain the ins and outs of two fundamental classes of pushouts.

5:20PM: Linear spaces of multigraded Betti diagramsThanh VuLet S = k[x_1, ..., x_n] be the polynomial ring. For each strictly increasing sequence of integers d = (d_0 < ... < d_n), denote the difference sequence by e = (d_1  d_0, ..., d_n  d_n1). For each such d, there exists a pure free resolution of the form S(d_0)^b_0 < ... < S(d_n)^b_n which is also GL(n) equivariant, therefore has a natural multigraded structure with multigraded Betti diagram B. It turns out that all multigraded Betti diagrams of possible multigraded structures of pure free resolutions with difference sequences e are linear combination of the twists of B as announced by Floeystad. I'll explain this result and the description of the positive cone of these multigraded Betti diagrams.
