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Matematiska Kollokviets Tidigare Seminarier Matematiska kollokviet - Linköpings universitet https://liu.se/artikel/matematiska-kollokviet 0nsdag 18 december 2019, Antonio F. Costa, UNED, Madrid, Spanien Titel: Concepts in Geometry and Topology Illustrated Using Decorations of Islamic Art Sammanfattning: Islamic art, because of its abstract character, is particularly well suited to exemplify some mathematical concepts. We'll start by remembering one of the most well- known and controversial subject: the appearance in this art of all possible euclidean planar crystalline symmetry. Other recent discoveries, as the presence of quasi-crystals, and examples of relations with mathematical concepts will also be exhibited. 0nsdag 11 december 2019, Joakim Arnlind, Matematiska institutionen, Linkopings universitet Titel: Projective modules over the noncommutative cylinder Sammanfattning: I will give an introduction to the noncommutative cylinder, which is a simple example of a non-compact noncommutative manifold. Finitely generated projective modules over a noncommutative algebra correspond to vector bundles in classical geometry, and we present explicit projectors generating the so called K-theory of the noncommutative cylinder. Furthermore, as everyone might not be familiar with the basic ideas of noncommutative geometry, I will try to motivate and explain several of the concepts as they appear in this context. 0nsdag 4 december 2019, Hans Lundmark, Matematiska institutionen, Linkopings universitet Titel: Peakon solutions of the Novikov and Geng–Xue equations Sammanfattning: Peakons (short for peaked solitons) are solutions of a particular form admitted by certain integrable partial differential equations. These solutions consist of a train of peak-shaped waves that interact with each other in a nonlinear way. The most well-known of these PDEs with peakon solutions is the Camassa–Holm shallow water equation from 1993, but there are several others, such as the Degasperis–Procesi equation and two of its close mathematical relatives which I will focus on in particular in this talk, namely the Novikov equation and the Geng–Xue equation. All these equations are similar in many respects, but they also have interesting differences, for example regarding how regular the solutions need to be, and how solutions can be continued past a singularity where some kind of breakdown occurs. Explicit formulas for the peakon solutions are known, and with their aid one can for example study in detail the kind of wave-breaking that takes place when a positive-amplitude peakon collides with a negative-amplitude antipeakon. This is particularly interesting for the Novikov equation, whose peakon-antipeakon solutions display a much wider array of behaviours than usual, including the possibility of several peakons and antipeakons travelling together in breather-like clusters. The Geng–Xue equation is interesting in a different way. It is a two-component system, with many possible inequivalent configurations depending on the order in which the peakons appear in the two components. The solution formulas describing an arbitrary configuration are very intricate and have been derived only recently, relying not Matematiska kollokviet - Linköpings universitet https://liu.se/artikel/matematiska-kollokviet only on the usual inverse spectral techniques, but also (crucially) on a certain limiting procedure for turning peakons into “ghostpeakons” with amplitude zero. This talk is based on joint works with Jacek Szmigielski, Marcus Kardell, Budor Shuaib and Andy Hone. Mcindag 25 november 2019, Yasunao Hattori, Shimane University, Japan Titel: Interaction between domain theory and topology Sammanfattning: In the talk, I will give a brief survey on the interaction between domain theory and topology. Recall that the domain theory studies order structures on (continuous) partial ordered sets (posets). A domain (= a continuous directed complete poset) D is called a computational model for a topological space X if the set M(D) of maximal elements of D with the Scott topology is homeomorphic to X . A space X is said to be domain-representable if X has a computational model. In 1981 Weihrauch and Schreiber introduced a set of formal balls for a metric space X , and showed that is a computational model for X if X is complete, i.e. every complete metric space is domain-representable. So I will suggest some results on the domain-representable spaces (in particular, the real line) and show a relationship among several topologies on the sets of (generalized) formal balls for (generalized) metric spaces. 0nsdag 20 november 2019, Mario Natiello, Lunds universitet Titel: Winged promises or biological contamination? Modelling genetic diffusion in the RIDL- SIT technique Sammanfattning: Recently, the RIDL-SIT technology has been field-tested for control of Aedes aegypti. The technique consists of releasing genetically modified mosquitoes carrying a “lethal gene”. In 2016 the World Health Organisation (WHO) and the Pan-American Health Organization (PAHO) recommend to their constituent countries to test the new technologies proposed to control Aedes aegypti populations. However, issues concerning effectiveness and ecological impact have not been thoroughly studied so far. In order to study these issues, we develop an ecological model compatible with the information available as of 2016. It presents an interdependent dynamics of mosquito populations and food in an homogeneous setting. Mosquito populations are described in an stochastic compartmental setup in terms of reaction norms depending on the available food in the environment. The development of the model allows us to indicate some critical biological knowledge that is missing and could (should) be produced. Hybridisation levels, release numbers during and after intervention and population recovery time after the intervention as a function of intervention duration and target are calculated under different hypotheses with regard to the fitness of hybrids and compared with two field studies of actual interventions. The minimal model should serve as a basis for detaile models when the necessary information to construct them is produced. For the time being, the model shows that nature will not clean the non-lethal introgressed genes. Joint work with H.G. Solari, Buenos Aires, Argentina. 0nsdag 13 november 2019, Sara Moad Sasane, Lunds universitet Titel: Monotone smoothing splines with bounds Matematiska kollokviet - Linköpings universitet https://liu.se/artikel/matematiska-kollokviet Sammanfattning: Splines are functions that are used to interpolate between data points. We distinguish between interpolating splines and smoothing splines. Interpolating splines are curves that interpolate between the data points and at the same time are as smooth as possible. The name comes from the drawing tool wooden spline, that was previously used to construct ships and aeroplanes. Smoothing splines are used when there are measuring errors, and it is not desirable to force the curve to pass exactly through the data points. Instead, the aim is to find a smooth curve which comes close to these points while being as little bent as possible (in a sense that wíll be made precise in the talk). Monotone smoothing splines are curves that solve a similar minimization problem but where the feasible set of functions also satisfy a monotonicity condition. I will discuss this problem from a calculus of variations point of view, and show that it can be reformulated as a finite dimensional problem which can be solved with optimization techniques. 0nsdag 30 oktober 2019, Sebastian Reyes Carocca, Universidad de la Frontera CTemucoJ, Chile Titel: On Riemann surfaces and Jacobian varieties with automorphisms Sammanfattning: Let a be an integer greater than 2. A classification of compact Riemann surfaces of genus g with a(g-1) automorphisms is known under the assumption that g-1 is a prime number. In this talk we shall discuss some recent results concerning the same classification problem for a=3 and when g-1 is assumed to be the square of a prime number. We also show interesting relations which induces the corresponding group action on the associated Jacobian varieties. This is a joint work (in progress) with Angel Carocca. 0nsdag 23 oktober 2019, Erik Lindgren, Uppsala universitet Titel: Nonlinear nonlocal equations Sammanfattning: In this talk, I will discuss some classes of nonlocal or fractional partial differential equations. In particular, I will describe recent developments for fractional versions of equations such as the p-Laplace equation. 0nsdag 16 oktober 2019, Marc Mars, University of Salamanca, Spanien Titel: Kerr-de Sitter spacetime and conformal infinity Sammanfattning: In this talk I will present several results concerning the characterization of the Kerr-de Sitter spacetime in terms of the asymptotic data at null infinity. This is relatively recent joint work with Paetz and Senovilla, and partially Simon. The first part of the talk is intended to be introductory: after reviewing the Kerr-de Sitter metric and recalling standard results on the initial value problem in General Relativity, I will discuss the initial value problem at past null infinity for the EFE with positive cosmological constant, as well as the notion of asymptotic Killing initial data. In the second part I will present the characterization results at infinity of Kerr-de Sitter based on a previous local spacetime characterization of this metric. Matematiska kollokviet - Linköpings universitet https://liu.se/artikel/matematiska-kollokviet
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