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Events - Page 6

Time and place: , room 1259 (Abels Utsikt) - Niels Henrik Abels hus

Doctoral candidate Bjørn Skauli at the Department of Mathematics will be defending the thesis Rationality Properties of Some Hypersurfaces and Complete Intersections for the degree of Philosophiae Doctor.

Time and place: , Niels Henrik Abels hus, 9th floor

Constructing fast solution schemes often involves deciding which errors are acceptable and which approximations can be made for the sake of computational efficiency. Herein, we consider a mixed formulation of Darcy flow in porous media and take the perspective that the physical law of mass conservation is significantly more important than the constitutive relationship, i.e. Darcy's law. From this point of view, we propose an inexact solution technique that nevertheless guarantees local mass conservation. The method is based on first solving the mass balance equation and then computing a solenoidal correction using the curl of a potential field. We extend the method to flows in fractured porous media and present numerical experiments that indicate the efficiency of the scheme.

Time and place: , NHA B1120

Fano manifolds are complex projective manifolds having positive first Chern class. The positivity condition on the first Chern class has far reaching geometric and arithmetic implications. For instance, Fano manifolds are covered by rational curves, and families of Fano manifolds over one dimensional bases always admit holomorphic sections. In recent years, there has been some effort towards defining suitable higher analogues of the Fano condition. Higher Fano manifolds are expected to enjoy stronger versions of several of the nice properties of Fano manifolds.

In this talk, I will discuss higher Fano manifolds which are defined in terms of positivity of higher Chern characters. After a brief survey of what is currently known, I will present recent joint work with Carolina Araujo, Roya Beheshti, Kelly Jabbusch, Svetlana Makarova, Enrica Mazzon and Nivedita Viswanathan, regarding toric higher Fano manifolds. I will explain a strategy towards proving that projective spaces are the only higher Fano manifolds among smooth projective toric varieties.

Time and place: , Abels utsikt, Niels Henrik Abels Hus,12th floor

For millennia, origami and kirigami artists have used folds and cuts to create beautiful shapes from a simple sheet of paper. I will describe our recent scientific attempts to catch up with these remarkably imaginative arts phrased as inverse problems in physical geometry that aim to control the shape and rigidity of a thin surface. Using discrete operations that vary the number, size, orientation and coordination of folds and cuts, I will show how to create piecewise isometric kirigami and origami tessellations and control their local and global morphology and mechanical response, mixing experimental, computational and theoretical approaches.

Time and place: , NHA B1119
Enriched enumerative geometry is a new area in which we take results in enumerative geometry over the complex numbers and refine them to give results over any base field. The "refinements" in question recover the classical results over algebraically closed fields but may also include arithmetic information about the base field. In this talk, I'll give an overview of a proof of an enriched refinement of the Yau-Zaslow formula for counting rational curves on K3 surfaces. Joint work with Jesse Pajwani.
Time and place: , NHA 723 and Online
Time and place: , Abels Utsikt (NHA 1259)
Time and place: , NHA 723 and Online
Time and place: , NHA107

QOMBINE seminar by Eric Bedos (UiO)

Time and place: , Niels Henrik Abels hus, 9th floor

After a brief introduction to the main physical characteristics of tsunami events, the recently developed Iterative Filtering technique is presented and applied to the decomposition of tsunami signals from pressure and tide gauges. It is shown how these signals are successfully decomposed into components of different physical origins. Then, the time-frequency representation of these time series is obtained by using the IMFogram algorithm, which computes instantaneous amplitudes and frequencies for the previously obtained components. Finally, possible applications to tsunami science are discussed, such as possible applications to real time detection in early warning context.

Time and place: , Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor

Estimates of environmental extremes are needed for a multitude of applications. For example, buildings, roads, bridges and dams must be designed to withstand extreme precipitation and flooding events of a certain size. Obtaining such estimates requires a combination of statistical theory and environmental process understanding to overcome data deficiencies: data on extremes are by definition sparse and regulations often require estimates for events that have yet to be observed. We will present approaches to obtain consistent estimates across spatial locations and accumulation periods, and discuss a few open questions on this topic. 

Time and place: , Niels Henrik Abels hus, 9th floor

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.

Time and place: , NHA107

QOMBINE seminar talks by Delphine Martres (University of Oslo) and Alexander Müller-Hermes (University of Oslo)

Time and place: , NHA B1020

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.

Time and place: , Niels Henrik Abels hus, 9th floor

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)

Time and place: , NHA B1120

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.

Time and place: , NHA B1119
We will discuss the recent theory of Nikulin orbifolds and orbifolds of Nikulin type in dimension 4. Nikulin orbifolds are irreducible holomorphic symplectic orbifolds which are partial resolutions of quotients of IHS manifolds of K3^[n] type. Their deformations are called orbifolds of Nikulin type. Our main aim will be the description of the first known locally complete family of projective irreducible holomorphic symplectic orbifolds of dimension 4 which are of Nikulin type. It is a family of IHS orbifolds that appear as double covers of special complete intersections (3,4) in P^6. This is joint work with Ch. Camere and A. Garbagnati.
Time and place: , NHA107

C*-algebra seminar talk by Lucas Hataishi (University of Oslo)

Time and place: , Erling Sverdrups plass, Niels Henrik Abels hus, 8th floor
Time and place: , NHA B1120

Following Givental, enumerative mirror symmetry can be stated as a relation between genus zero Gromov-Witten invariants and period integrals. I will talk about a relative version of mirror symmetry that relates genus zero relative Gromov-Witten invariants of smooth pairs and relative periods. Then I will talk about how to use it to compute the mirror proper Landau-Ginzburg potentials of smooth log Calabi-Yau pairs.

Time and place: , Abels Utsikt (NHA 1259)
Time and place: , Niels Henrik Abels hus, 9th floor

I will go through my PhD work at DTU. It is about the development of a fully-nonlinear finite difference based potential flow solver which imposes all of the fluid boundaries via an immersed boundary method. The convergence and stability of this approach is first established for various linear and nonlinear wave propagation problems. When it comes to the wave-body interaction problem, cautious attention is paid to the intersection point between free surface and body surface, and a scheme which meets the accuracy and stability requirements best is picked from several proposals. With the scheme introduced in this paper, piston type wave maker and forced heaving cylinder cases with high oscillation frequency have been simulated successfully.

Time and place: , Niels Henrik Abels hus, 9th floor

Internal solitary waves (ISWs) are underwater waves of great amplitude moving horizontally in the layered ocean. The waves induce a velocity field which is felt both at the ocean surface, throughout the entire water column, and at the bottom. When of great amplitude, the waves induce a vortex wake in the bottom boundary layer behind the wave and transport water in the vertical direction displacing, e.g., sediments from the bottom. A fundamental mechanism in the ocean ecosystem is the vertical mixing and movement of particles, e.g., biological materials. In this talk, we present numerical simulations of ISWs of depression and of large amplitude by replicating a laboratory experiment. Furthermore, we discuss the dynamics of ISW-sediment interactions and illustrate particle movements, trajectories, and particle distribution in the water column under the influence of ISWs of large amplitude.

Time and place: , Simula Research Laboratory, Kristian Augusts gate 23 and Zoom - Niels Henrik Abels hus

Doctoral candidate Eleonora Piersanti at the Department of Mathematics will be defending the thesis Parameter-robust formulation and preconditioning of poroelasticity equations for brain modelling for the degree of Philosophiae Doctor.

Time and place: , NHA B1120
Already Plücker knew that a smooth complex plane quartic curve has exactly 28 bitangents. Bitangents of quartic curves are related to a variety of mathematical problems. They appear in one of Arnold's trinities, together with lines in a cubic surface and 120 tritangent planes of a sextic space curve. In this talk, we review known results about counts of bitangents under variation of the ground field. Special focus will be on counting in the tropical world, and its relations to real and arithmetic counts. We end with new results concerning the arithmetic multiplicity of tropical bitangent classes, based on joint work in progress with Sam Payne and Kris Shaw.