Guest lectures and seminars - Page 51

Template Model Builder (TMB) is an R-package that is well suited for performing fast inference with latent Gaussian models when the likelihood can be written as a three times differentiable function. TMB automatically differentiates the likelihood and utilizes Markov structures to efficiently integrate over latent variables with the Laplace approximation. In this seminar I will first introduce TMB and then elaborate a fish stock assessment model implemented with use of TMB that provides quota advice for approximately 25 different fish species in Europe.

A cohomology class of a smooth complex variety of dimension n has coniveau ≥c if it vanishes in the complement of a closed subvariety of codimension ≥c, and has strong coniveau ≥c if it comes by proper pushforward from the cohomology of a smooth variety of dimension ≤n−c. We show that these two notions differ in general, both for integral classes on smooth projective varieties and for rational classes on smooth open varieties. This is joint work with Olivier Benoist.

A graded Artinian Gorenstein ring A is a quotient of a polynomial ring S with the apolar ideal of a homogeneous form. The Betti numbers of the resolution of A as an S-module are invariants to the homogeneous form. In joint work with Michal and Gregorz Kapustka, Hal Schenck, Mike Stillman and Beihui Yuan, we use these Betti numbers to describe a stratification of the space of quartics in four variables.