Matematiska kollokviet

Matematiska kollokviet är en seminarieserie vid Matematiska institutionen som vänder sig till en bred matematisk publik. Alla intresserade är välkomna.

Kollokviet organiseras av Anders Björn, Milagros Izquierdo och Hans Lundmark vid avdelningarna Analys och didaktik (ANDI) och Algebra, geometri och diskret matematik (ALGD).

Tid och lokal

Seminarietiden är vanligtvis varje onsdag kl 13:15-14:15 i Hopningspunkten som ligger i B-huset, ingång 23, plan 2, Campus Valla i Linköping. Anordnas i samarbete med Seminarier i optimeringslära.

Kommande seminarier

Onsdag 19 januari 2022, Sebastián Reyes Carocca, Universidad de la Frontera, Chile

Titel: Loci of Riemann Surfaces with Automorphisms

Sammanfattning: TBA

Onsdag 23 februari 2022, Tatiana Tchemisova, University of Aveiro, Portugal

Titel: On phenomenon of Immobility in study of convex Optimization problems

We are concerned with convex problems of infinite Optimization, namely problems of convex Semi-Infinite Programming (SIP) and linear problems of Semidefinite Programming (SDP).

Semi-Infinite Programming deals with extremal problems that consist in minimization of an objective function of finitely many variables in a set described by an infinite system of constraints. SIP models appear in different fields of modern science and engineering where it is necessary to simulate a behavior of complex processes whose models contain at least one inequality constraint for each value of some parameter (for example, time) varying in a given compact domain.
In Semidefinite Programming, an objective function is minimized under the condition that some matrix valued function is positive semidefinite. When the objective function is linear and the matrix valued function is an affine combination of some symmetric matrices, we get a convex problem. There are many applications of SDP models to combinatorial optimization, control theory, approximation theory, etc.

Optimality conditions for Optimization problems are of special interest both from theoretical and practical points of view. A special attention is devoted to the results that do not need additional conditions on the constraints, so called constraint qualifications (CQ).

In the talk, we present the results on optimality and strict duality for convex Semi-Infinite Programming problems which are obtained based on a new concept of immobile indices of constraints. We show how this concept can be applied to problems of linear SDP . The main result consists in new CQ-free optimality conditions for the considered classes of Optimization problems.

Tidigare seminarierVisa/dölj innehåll

Onsdag 24 november 2021, Evgeniy Lokharu, Matematiska institutionen, Linköpings universitet

Titel: On extreme steady water waves with vorticity

Sammanfattning: Extreme steady waves are exact solutions to Euler equations in two dimensions that posses surface singularities, where the relative velocity field vanishes. Already in 1880s Sir George Stokes made a remarkable for that time conjecture about extreme waves: the surface profile at singular points has to form a sharp corner of 120 degrees. This conjecture was very influential and had determined the research direction in the field for many years. In this talk we will discuss the history behind the problem and some recent new results obtained by the authors.

Onsdag 11 mars 2020, Juha Lerhbäck, University of Jyväskylä, Finland

Titel: Quasiadditivity properties of variational capacity and Hardy-Sobolev inequalities

Sammanfattning: Capacities are outer measures and hence subadditive, but they are practically never additive. A capacity is called quasiadditive, if it satisfies a converse for the subadditivity (with a multiplicative constant) with respect to a suitable cover of the underlying set. In this talk I consider this property for the variational capacity in an open set of the Euclidean space, with respect to a Whitney cover of the open set. In particular, I will characterize a generalized (q,p)-version of the quasiadditivity using corresponding Hardy-Sobolev inequalities.

This talk is based on joint work with Juha Kinnunen and Antti Vähäkangas. 

Onsdag 4 mars 2020, Sergey Nazarov, Matematiska institutionen, Linköpings universitet, och St Petersburg, Ryssland

Titel: The Neumann Laplacian: abnormal transmission acoustic waves through narrow canals

Onsdag 26 februari 2020, Sergei Silvestrov, Mälardalens högskola, Västerås

Titel: Hom-algebra structures

Sammanfattning: In this colloquium lecture an introductory overview and open problems about Hom-algebra structures will be given with emphasize on hom-algebra generalizations of Lie algebras and associative algebras.

These interesting and rich algebraic structures appear for example when discretizing the differential calculus as well as in constructions of differential calculus on non-commutative spaces. In 1990’th quantum deformations of algebras, q-deformed oscillator algebras, q-deformations of Witt and Virasoro algebras and related families of algebras defined by generators and parameter commutation relations have been constructed in connection to quantum deformations and discretized models of mechanics and quantum mechanics, q-deformations of vertex operators, q-deformed conformal quantum field theory, q-deformed integrable systems, q-deformed superstrings and central extensions. Also, various quantum n-ary extensions of Nambu mechanics and related n-ary extensions of differential structures and of Lie algebras Jacobi identities have been considered. It was noticed that many of quantum algebras and q-deformed Lie algebras obey certain q-deformed versions of Jacobi identity generalizing Lie algebras Jacobi identity. Motivated by these works Hartwig, Larsson and Silvestrov in 2003 developed a general method of obtaining such deformations and generalized Jacobi identities based on general twisted derivations. This development, as well generalizations of supersymmetry, lead to development of more general algebraic structures such as quasi-Lie and Hom-Lie algebras, Hom-associative and Hom-Lie admissible algebras, Hom-Jordan algebras, Hom-Poisson algebras, Hom-Yang-Baxter equations, Hom-bialgebras, Hom-Hopf algebras, and other hom-algebra structures, as well as Hom-Nambu and Hom-Nambu Lie algebras some related n-ary Hom-algebra generalizations of Nambu algebras, associative algebras and Lie algebras and their constructions.

Onsdag 12 februari 2020, Ahmed Al-Shujary, Matematiska institutionen (MAI), Linköpings universitet

Titel: Kähler-Poisson Algebras

Sammanfattning: : In this talk, we introduce Kähler-Poisson algebras and study their basic properties. The motivation comes from differential geometry, where one can show that the Riemannian geometry of an almost Kähler manifold can be formulated in terms of the Poisson algebra of smooth functions on the manifold. It turns out that one can identify an algebraic condition in the Poisson algebra (together with a metric) implying that most geometric objects can be given a purely algebraic formulation. This leads to the definition of a Kähler-Poisson algebra, which consists of a Poisson algebra and a metric fulfilling an algebraic condition. We show that every Kähler-Poisson algebra admits a unique Levi-Civita connection on its module of inner derivations and, furthermore, that the corresponding curvature operator has all the classical symmetries. Moreover, we present a construction procedure which allows one to associate a Kähler-Poisson algebra to a large class of Poisson algebras. From a more algebraic perspective, we introduce basic notions, such as morphisms and subalgebras, as well as direct sums and tensor products. Finally, we initiate a study of the moduli space of Kähler-Poisson algebras; i.e for a given Poisson algebra, one considers classes of metrics giving rise to non-isomorphic Kähler-Poisson algebras. As it turns out, even the simple case of a Poisson algebra generated by two variables gives rise to a nontrivial classification problem.

Onsdag 29 januari 2020, Evgeniy Lokharu, Matematiska institutionen (MAI), Linköpings universitet

Titel: Nonexistence of subcritical solitary waves

Sammanfattning: We prove the nonexistence of two-dimensional solitary gravity water waves with subcritical wave speeds and an arbitrary distribution of vorticity. This is a longstanding open problem, and even in the irrotational case there are only partial results relying on sign conditions or smallness assumptions. As a corollary, we obtain a relatively complete classification of solitary waves: they must be supercritical, symmetric, and monotonically decreasing on either side of a central crest. The proof introduces a new function related to the so-called flow force which has several surprising properties. In addition to solitary waves, our nonexistence result applies to "half-solitary" waves (e.g. bores) which decay in only one direction.

This is a joint work with Vladimir Kozlov (MAI) and Miles H. Wheeler (University of Bath, UK).

Onsdag 22 januari 2020, Elina Rönnberg, Matematiska institutionen (MAI), Linköpings universitet

Seminariet arrangeras ihop med Tvärvetenskapliga seminarier på MAI.

Titel: Efficient use of hardware resources in avionic systems

Sammanfattning: A key ingredient when designing an avionic system – i. e. the electronic system of an aircraft – is to make sure that it always can be trusted. In modern integrated modular avionic systems, different aircraft functions share hardware resources on a common avionic platform. For such architectures, it is necessary to create a spatial and temporal partitioning of the system to prevent faults from propagating between different functions. One way to establish a temporal partitioning is through pre-runtime scheduling.

While the avionic systems are growing more and more complex, so is the challenge of scheduling them. Scheduling of the system has an important role when a new avionic system is developed. Typically, functions are added to the system over a period of several years and a scheduling tool is used both to determine if the platform can host the new functionality and, in case this is possible, to create a new schedule.

In this talk, I will discuss a design case from Saab Aeronautics and present an optimisation-based scheduling tool that we have developed. From an optimisation point of view, the problem can be described as a rich multiprocessor scheduling problem that also includes a communication network to be scheduled. Results are presented for practically relevant large-scale instances with up to 60 000 tasks.

Onsdag 15 januari 2020, Andrew Ross Winters, Matematiska institutionen (MAI), Linköpings universitet

Titel: My numerical scheme crashed, now what?

Sammanfattning: Numerical methods to approximate the solution of partial differential equations are a powerful tool to model problems we otherwise could not. But can they tell us something even when they fail?

We present why numerical methods can break, and how to fix them. To do so, we motivate the discussion from a physical perspective, which we then translate and inspect with the language of mathematics.

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