Christine Berkesch Zamaere |
Abstract: Binomial D-modules are given by a binomial ideal and homogeneity operators. Combinatorial tools from toric geometry have been successful at analyzing many aspects of binomial D-modules, which carry a torus action. We will consider how to interpret taking invariants of D-modules with torus actions, with the goal of gaining a new understanding of the classical hypergeometric systems studied by, among others, Gauss, Appell, and Lauricella. This is joint work with Laura Felicia Matusevich and Uli Walther. |
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Jim Carlson |
Abstract. We define the field of periods of an algebraic variety, discuss its transcendence degree and its relation to the Mumford-Tate group, then do some computations for a special class of cubic threefolds. |

Giulio Caviglia |
Abstract: I will discuss a conjecture by Eisenbud, Green and Harris regarding the possible Hilbert functions of subschemes of complete intersections. Two special cases of this conjecture are the Cayley-Bacharach theorem and the Kruskal-Katona theorem on f-vectors of abstract simplicial complexes. I will focus on a series of sharp upper bounds for multiplicity, Betti numbers and Hilbert functions of local cohomology modules that are suggested by, and can be proved when the above conjecture is known. |

Dusty Ross |
Abstract: Two fundamental questions in Gromov-Witten theory are Ruan's crepant resolution conjecture and the Gromov-Witten/Donaldson-Thomas correspondence. I will introduce these notions and discuss recent results leading to a complete understanding of the correspondences when the targets belong to a certain class of toric orbifold. This is joint work with A. Brini, R. Cavalieri, and Z. Zong. |

Karl Schwede |
Abstract: In this talk, I will motivate the study of F-singularities, the singularities defined by Frobenius, via connection with Kodaira type vanishing theorems. We will discuss the close relationship between F-singularities and singularities like rational and log canonical singularities. Finally some recent joint work Yoshinori Gongyo and Paolo Cascini will be discussed showing uniform bounds for the equality of F-regular and log terminal singularities on surfaces of characteristic p. |

Sofia Tirabassi |
Abstract: We study infinitesimal deformations of the Brill-Noether locus W_d(C) parameterizing degree d line bundles on a smooth curve C, and of the inclusion W_d(C) ⊂ J(C) of W_d(C) in its Albanese variety, the Jacobian variety J(C) of C. We will show that if there is a deformation of W_d(C) which is not induced by its resolution of singularities C_d, the d-symmetric product of C, or if there is a deformation of W_d(C) that deforms J(C) in a direction which goes outside the Jacobian locus, then C is hyperelliptic. This is joint work with L. Lombardi |