Guest lectures and seminars - Page 25
OceanSun’s floating solar island consists of a hydro elastic membrane attached to a flexible torus, providing a more cost-efficient alternative with natural cooling of the panels leading to increased efficiency. The current research focuses on the seakeeping characteristics of OceanSun’s FSPV concept specifically. Wave induced loads are of particular interest, as the feasibility of offshore installation strongly depends on environmental loads. Important responses of the membrane based FSPV are identified by the development of a global model based on linear potential flow theory, and linearly pre-tensioned membrane motions. Based on theory formulated by Grøn (2022), a modal analysis is used to describe the vertical displacement of the membrane-floater system. A numerical implementation of the theory in WAMIT is compared to experimental results from model-scaled tests.
QOMBINE seminar talks by Delphine Martres (University of Oslo) and Alexander Müller-Hermes (University of Oslo)
Nakajima quiver varieties are a class of combinatorially defined moduli spaces generalising the Hilbert scheme of points in the plane, defined with the aid of a quiver Q (directed graph) and a fixed framing dimension vector f. In the 90s Nakajima used the cohomology of these varieties (in fixed cohomological degrees, and for fixed f) to construct irreducible lowest weight representations of the Kac-Moody Lie algebras associated to the underlying graph of Q. Since the action is via geometric correspondences, the entire cohomology of these quiver varieties forms a module for the same Kac-Moody Lie algebras, suggesting the question: what is the decomposition of the entire cohomology into irreducible lowest weight representations?
In this talk I will explain that this question is somehow not the right one. I will introduce the BPS Lie algebra associated to Q, a generalised Kac-Moody Lie algebra associated to Q, which contains the usual one as its cohomological degree zero piece. The entire cohomology of the sum of Nakajima quiver varieties for fixed Q and f turns out to have an elegant decomposition into irreducible lowest weight modules for this Lie algebra, with lowest weight spaces isomorphic to the intersection cohomology of certain singular Nakajima quiver varieties. This is joint work with Lucien Hennecart and Sebastian Schlegel Mejia.
Finding the optimal shape is a vivid research area and has a wide range of applications, e.g., in fluid mechanics and acoustics. Moreover, there is also a close link to image registration and image segmentation. In this talk, we consider shape optimization tasks as optimal control problems that are constrained by partial differential equations. From this perspective, state-of-the-art methods can be motivated by the choice of the metric on the set of admissible shapes. Moreover, a new approach for density based topology optimization is presented in the setting of Stokes flow. It is based on classical topology optimization and phase field approaches, and introduces a different way to relax the underlying infinite-dimensional mixed integer problem. We give a theoretically founded choice of the relaxed problems and present numerical results. Moreover, in order to show the potential of the new approach, we do a comparison to a classical approach. (joint work with Michael Ulbrich and Franziska Neumann)
A tropical curve is a graph embedded in R^2 satisfying a number of conditions. Mikhalkin's celebrated correspondence theorem establishes a correspondence between algebraic curves on a toric surface and tropical curves. This translates the difficult question of counting the number of algebraic curves through a given number of points to the question of counting tropical curves, i.e. certain graphs, with a given notion of multiplicity through a given number of points which can be solved combinatorially. To get an invariant count, real rational algebraic curves are counted with a sign, the Welschinger sign and there is a real version of the correspondence theorem. Furthermore, Marc Levine defined a generalization of the Welschinger sign that allows to get an invariant count of algebraic curves defined over an arbitrary base field. For this one counts algebraic curves with a certain quadratic form.
In the talk I am presenting work in progress joint with Andrés Jaramillo Puentes in which we provide a version Mikhalkin's correspondence theorem for an arbitrary base field, that is a correspondence between algebraic curves counted with the above mentioned quadratic form and tropical curves counted with a quadratic enrichment of the multiplicity. Then I will explain how to use this quadratic correspondence theorem to do the count of algebraic curves over an arbitrary base field.