Meeting on Algebraic Geometry and Combinatorics

UiT, Department of Mathematics and Statistics, B284, August 11 – 12, 2025
Supported by TFS project Pure Mathematics in Norway


Organizers: Marta Panizzut and Tobias Boege (UiT)

Monday, August 11

13:00	Hadleigh Frost, IAS Princenton	Matroid Cosmology: A Tale of Two Posets Abstract Cosmology is the study of the evolution of the universe through time. We define and study the combinatorics of how the universe evolves through time in a matroid setting. Fix a matroid and building set. It is well known that the nested sets define cones in a simplicial fan, the Bergman fan, whose face lattice is the poset of nested sets defined by set inclusion. By thinking differently about the nested sets as "causal orderings", we can define a different poset on the nested sets, and realize this as the face lattice of a second (non-simplicial) fan. Moreover, by combining both poset structures, we find a refinement of the Bergman fan whose face lattice captures the combinatorics of the "wavefunction of the universe".
14:30	Bernd Sturmfels, MPI MiS Leipzig	The Two Lives of the Grassmannian Abstract The Grassmannian parametrizes linear subspaces of a real vector space. It is both a projective variety (via Plücker coordinates) and an affine variety (via orthogonal projections). We examine these two representations, through the lenses of linear algebra, commutative algebra, and statistics.

Tuesday, August 12

13:00	Ettore Turatti, UiT	Terracini Loci of Veronese varieties Abstract Let X be a nondegenerate projective variety. Terracini's Lemma is a classical result that describes the tangent space to the secant varieties of X at a generic point. However, it does not characterise which points in the secant variety are generic. Therefore, an interesting question is to determine the special configurations of points for which Terracini's Lemma fails, or in other words, when zero-dimensional schemes of double points supported on X do not impose independent conditions. In this talk, we will focus on this question in the case of curves and Veronese varieties. This is joint work with Francesco Galuppi, Pierpaola Santarsiero, and Douglas Torrence.
14:30	Anaëlle Pfister, MPI MiS Leipzig	Canonical forms for non-compact hyperplane arrangement Abstract Brown and Dupont introduced a mixed Hodge theoretic definition for canonical forms of pairs of compact varieties. In a work in progress, we aim to extend this definition to affine complex hyperplane arrangements using relative homology H_n(C^n, A) and its Poincaré dual H^n_c(C^n, Rj_* j^* Q_C^n). In this talk, I will define this group and give a characterisation in terms of differential forms.