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. 

Kommande seminarier

Onsdag 13 december 2023 kl 13.15-14.15, Carl Johan Casselgren, Matematiska institutionen, Linköpings universitet

Titel: Variations on Brooks' theorem on graph coloring

Sammanfattning: Brooks' classic theorem on graph coloring states that the number of colors needed for a proper coloring of a graph G is at most the maximum degree of G, unless G is a complete graph or and odd cycle. I shall discuss some variations on this theorem, including variants proved for list coloring, precoloring extension and a recent variation where some colors cannot be used on certain vertices.

Onsdag 24 januari 2024 kl 13.15-14.15, Sebastián Reyes Carocca, Universidad de Chile

Titel: TBA
Sammanfattning: TBA

Onsdag 31 januari 2024 kl 13.15-14.15, Anita Rojas, Universidad de Chile

Titel: TBA
Sammanfattning: TBA

Tidigare seminarier

                                1. Onsdag 29 november 2023 kl 13.15-14.15, Boris Khesin, University of Toronto, Kanada & Institut Mittag-Leffler

                                  Titel: Geometry behind fluids

                                  Sammanfattning: In 1966 V. Arnold suggested a group-theoretic approach to ideal hydrodynamics via the geodesic flow of the right-invariant energy metric on the group of volume-preserving diffeomorphisms of the flow domain. We describe several recent ramifications of this approach related to compressible fluids, optimal mass transport, as well as Newton's equations on diffeomorphism groups and smooth probability densities. It turns out that various important PDEs of hydrodynamical origin can be described in this geometric framework in a natural way. This is a joint work with G. Misiołek and K. Modin.

                                  Onsdag 22 november 2023 kl 13.15-14.15, Evgeniy Lokharu, Lunds universitet

                                  Titel: On the vorticity threshold for water waves with a non-favorable constant vorticity

                                  Sammanfattning: In this talk we will discuss effects of a strong non-favorable constant vorticity on the global dynamics of Stokes waves. We will prove that for constant vorticities above some threshold value the horizontal velocity on the surface is always separated from zero by a constant depending only on the vorticity. In particular this forbids formation of extreme and overhanging waves before a critical layer appears inside the fluid, first at the bottom right below the crest. This also shows that the slopes of unidirectional solutions are uniformly bounded by a small constant, provided the vorticity is large enough and is non-favorable. We also obtain a non-trivial bound for the amplitude. Our analytic results agree with and confirm the numerical analysis by Ko and Strauss (2008). This is a joint work with Miles Wheeler from Bath University, UK.

                                  Onsdag 15 november 2023 kl 13.15-14.15, Martin Bordemann, Université Haute Alsace

                                  Titel: Deformation quantization and Lie bialgebras

                                  Sammanfattning: Deformation quantization is the interpretation of quantization, i.e. the passage from `classical observables' to `quantum observables' in quantum mechanics, in terms of associative formal deformations of Poisson algebras used in classical mechanics (1978). The quantization problem for any Poisson algebra arising in differential geometry had been completely solved by the famous formality theorem by M.L.Kontsevich, 1997. In 1999, D.E.Tamarkin gave another approach to the Kontsevich formality using as a tool the (de)quantization of differental graded Lie bialgebras, a problem posed by V.G.Drinfel'd in the mid eighties and solved (at least in the finite-dimensional case) by P.I.Etingof and D.A.Kazhdan 1996. This latter work -which is not very easy to access- uses a categorical approach inspired by representation theory and heavily relies on the Drinfel'd associator (1989), a certain formal series of two noncommutating variables which is alsoquite difficult to understand.

                                  I shall report on P.Ševera's approach in Sel. Math. 22 (2016) to the quantization of Lie bialgebras which presents a large simplification of Etingof-Kazhdan's results and a true extension to the important infinite-dimensional case because he did not have to use at all certain topological dual spaces. I shall also sketch recent work of ours how the Drinfel'd associator can be unzipped. An important tool in the work of Etingof-Kazhdan, Tamarkin and Ševera. Our work is in collaboration with Andrea Rivezzi and Thomas Weigel from Milano-Bicocca.

                                  Onsdag 8 november 2023 kl 13.15-14.15, Jana Björn, Matematiska institutionen, Linköpings universitet

                                  Titel: Besov spaces on metric spaces by means of hyperbolic fillings

                                  Sammanfattning: We shall show how any compact doubling metric space Z can be seen as the boundary of a uniform (and thus well-behaved) metric space. This has consequences for the analysis and function spaces on such sets. If Z is equipped with a doubling measure, then the Besov space on Z of functions with fractional smoothness is exactly the trace of a Sobolev type space on the corresponding uniform space. Several properties of Sobolev functions (e.g. their Lebesgue points and quasicontinuity) can then be transfered to the Besov space, giving some new results also in the classical situation of Besov spaces on R^n.

                                  Onsdag 1 november 2023 kl 13.15-14.15, Sondre Tesdal Galtung, NTNU, Trondheim, Norge & Institut Mittag-Leffler

                                  Titel: A variational discretization of the Camassa–Holm equation, and a non-conservative traveling wave

                                  Sammanfattning: Since its derivation in the context of shallow-water waves, the Camassa–Holm (CH) equation has attracted much attention owing to its many interesting mathematical properties, e.g., being completely integrable, as well as exhibiting wave-breaking in finite time even for smooth initial data. In this talk we will consider a discretization of the CH equation based on variational principles in Lagrangian coordinates, which has been shown to converge to so-called conservative solutions. These are solutions which satisfy an additional balance law for the energy density of the equation, ensuring that the total energy is conserved globally in time.

                                  The corresponding numerical method in a periodic domain performs well for several traveling-wave reference solutions typical for the CH literature, e.g., the well-known peakons, and even for reference solutions involving wave-breaking and energy concentration. However, when “challenged” to apply our method to less standard traveling waves, known as stumpons, we were led to some unexpected results. Based on this observation, we prove that stumpons are non-conservative and hence not suitable for approximation with our numerical method.

                                  Onsdag 4 oktober 2023 kl 13.15-14.15, Vladimir Tkachev, Matematiska institutionen, Linköpings universitet

                                  Titel: Metrized algebras with involutions and their applications

                                  Sammanfattning: A metrized algebra is an algebra with an associative (i.e. Killing type) bilinear form. I shall give an overview of our recent results on metrized algebras with involutions. These algebras include (or relate to) many classically known classes of non-associative algebras, both commutative and non-commutative.

                                  I shall discuss a new subclass of metrized algebras, the so-called quasi-composition algebras, a generalization of the well-known class of composition algebras (in particular, Hurwitz algebras). Some quasi-composition algebras appear as appropriate (Pettersons type) isotopies of certain Lie algebras. In general, any quasi-composition algebra with anisotropic bilinear form satisfies the constant rank condition (a natural generalization of the classically known concept of division algebras).

                                  The most intriguing fact is that quasi-composition algebras appear unexpectedly in connections with a completely different story, the minimal cone algebras (aka Hsiang algebras). It turns out that the “tripling” of a metrized algebra A is a Hsiang algebra if and only if A is a quasi-composition algebra (the tripling is an appropriate generalization of the Cayley-Dickson doubling construction). My talk is based on the joint work with Daniel J. Fox (Universidad Politécnica de Madrid).

                                  Onsdag 20 september 2023 kl 13.15-14.15, Lionel Lang, Högskolan i Gävle

                                  Titel: Galois groups of systems of polynomial equations

                                  Sammanfattning: Abstract (pdf)

                                  Onsdag 6 september 2023 kl 13.15-14.15, Mats Ehrnström, NTNU, Trondheim, Norge & Institut Mittag-Leffler 

                                  Titel: Mathematics in Water Waves

                                  Sammanfattning: In this colloquium talk, we give a brief overview of the fundamentals of mathematics for water waves. Starting from a linear equation, what governs the evolution of a wave, and what is the relationship between a travelling and a time-dependent solution? Linear theory alone turns out to be insufficient in this setting, as it neither explains or captures how waves break. That naturally leads us to the concept of a solitary wave, and equations for water waves that better balance the effects of nonlinearity and dispersion. This includes the system of Euler equations and its model equations. Finally, we turn to a specific instance – the Whitham equation – showing how a seemingly simple-looking equation captures several of the most intriguing features of the full water-wave problem.

                                  Onsdag 7 juni 2023 kl 13.:15-14:15, Antti Perälä, Umeå universitet

                                  Titel: Harmonic analysis for operators on holomorphic function spaces

                                  Sammanfattning: Techniques from harmonic analysis and probability can be used to solve problems related to concrete operators on spaces of holomorphic functions. In this talk, I will explain some common techniques such as Carleson measures, area functions, factorization and Kahane-Khinchine inequalities for systems of Rademacher functions. They will be applied to study Volterra type integration operators acting between Bergman and Hardy spaces. This talk is partially based on a joint work with Santeri Miihkinen, Jordi Pau and Maofa Wang.

                                  Torsdag 1 juni 2023 kl 15.15-16.15, Johan Richter, Blekinge tekniska högskola

                                  Titel: Some non-associative versions of Hilbert’s basis theorem

                                  Sammanfattning: The classical Hilbert’s basis theorem says that if R, an associative and unital ring, is left (right) Noetherian then so is R[x]. This theorem has several associative generalizations, notably to Ore extensions. In this talk I will describe non-associative versions of Hilbert’s basis theorem. Interestingly, the non-associative case contains asymmetries between the left and right Noetherian property, not found in the associative case.

                                  Onsdag 17 maj 2023 kl 13:15-14:15 Tapio Rajala, University of Jyväskylä, Finland

                                  Titel: Sobolev and BV extension sets

                                  Sammanfattning: When are Sobolev or BV functions (functions of bounded variation) defined on a subset of the Euclidean space extendable to the whole space without increasing the Sobolev norm by more than a constant multiplicative factor? Partial answers to this question have been given by various people. For example, from the works of Calderón (1961) and Stein (1970) we know that Lipschitz domains have this property. More generally, this holds also for all uniform domains as was later shown by Jones in 1981.

                                  Lipschitz domains form a nice class of subsets in Euclidean spaces in the sense that any domain can be approximated from inside and from outside by them. Uniform domains provide a nice class even in the metric space setting if we assume the validity of a local Poincaré inequality and measure doubling. On one hand, in these spaces uniform domains are extensions sets for Sobolev and BV functions and, on the other hand, arbitrary domains can be approximated by uniform domains.

                                  In this talk, we will first briefly look at how far uniform domains are from general Sobolev extension domains in the special case of the Euclidean plane, how one produces the extension from uniform domains, and how one constructs uniform domains. At the end of the talk, we will look at the case of BV extensions and how bounded domains can be approximated from inside by closed BV extension sets even without assuming local Poincaré inequalities or measure doubling.

                                  Onsdag 10 maj 2023 kl 13:15-14:15 Stephen Gardiner, University College Dublin, National University of Ireland

                                  Titel: Extension theorems for harmonic functions which vanish on cylindrical and conical surfaces

                                  Sammanfattning: The Schwarz reflection principle provides a simple formula for extending a harmonic function h on a plane domain through a relatively open subset E of the boundary on which h vanishes, provided E is a line segment. A related formula holds when E is a circular arc, or even an analytic arc. In three dimensions, however, Ebenfelt and Khavinson have shown that reflection formulae for harmonic functions hold only for hyperplanes and spheres. This talk will explore what can still be said in higher dimensions by considering cylindrical and conical surfaces. (Joint work with Hermann Render.)

                                  Onsdag 10 maj 2023 kl 15.15-16.15 Björn Gustafsson, KTH

                                  Titel: Laplacian growth on branched Riemann surfaces

                                  Sammanfattning: : I will try to explain parts of the contents of a book (Springer Lecture Notes, 2021) with the above title, and coauthored by Yu-Lin Lin. It all started as a research project with the aim of proving global in time existence of simply connected solutions of a moving boundary problem for Hele-Shaw flow with a point source (Laplacian growth). If the initial domain, in the complex plane, has complicated geometry one cannot really expect such global existence, unless one allows the solution to spread on a branched Riemann surface above the complex plane. And even allowing that, there are a lot of technical difficulties to be solved along the way. We did solve some of them, but there remained a final gap in the proof, even at the time of publication of the book. However, very recently, S. Gardiner and T. Sjödin were able to fill the gap (a paper in Analysis and Mathematical Physics, 2022), hence we believe that the proof of the mentioned result is now complete.

                                  Tisdag 2 maj 2023 kl. 13.15-14.15 Yuval Roichman, Bar-Ilan University

                                  Titel: Cyclic descents, toric Schur functions and higher Lie characters

                                  Sammanfattning: The study of descents of permutations may be traced back to Euler, and is fundamental to contemporary algebraic combinatorics and its applications.
                                  A cyclic extension of this notion was introduced in the late 20th century. The talk will focus on aspects of descents and cyclic descents for permutations and for standard Young tableaux. Following an axiomatization of the notion of a cyclic descent extension, we will characterize sets of combinatorial objects for which such an extension exists. The main results concern sets of standard Young tableaux of a fixed shape and sets of permutations of a fixed cycle type, i.e., conjugacy classes. Proofs of both results are algebraic and not constructive, and involve Postnikov toric Schur functions, Gromov-Witten invariants and a treatment of the classical Thrall problem on higher Lie characters.

                                  Based on joint works with Ron Adin, Pál Hegedüs and Vic Reiner.

                                  Onsdag 26 april 2023 kl 13:15-14:15 Jonas Bergman Ärlebäck och Peter Frejd, Matematiska institutionen, Linköpings universitet

                                  Titel: Teaching and learning statistic at the secondary level - some results and insights from a research project

                                  Sammanfattning: In this presentation, we will report and discuss findings from a research project on teaching and learning statistics in grades 7 to 12. We will focus on some central themes that emerged during the research, including students' understanding of statistical concepts, teacher pedagogical choices and materials, and students' development of statistical thinking. Additionally, we will discuss challenges that teachers and students face when teaching and learning statistics, and strategies for overcoming them. Finally, we will provide examples of pedagogical tools that can help teachers teach statistics more effectively and support students in developing a deeper understanding of statistical concepts and principles.

                                  Onsdag 19 april 2023 kl 13:15-14:15 Natan Kruglyak, Matematiska institutionen, Linköpings universitet

                                  Titel: Fredholm Operators on Interpolation Scales

                                  Sammanfattning: The theory of linear bounded Fredholm operators from a Banach space to another Banach space is well-known and has very important applications in analysis, especially in integral equations and PDE’s. In the talk the theory of Fredholm operators on scales of interpolation spaces will be discussed and recent results, obtained jointly with I. Asekritova and M. Mastylo, will be presented.

                                  Onsdag 19 april 2023 kl 15:15-16:15 Marie-Claude Arnaud Institut de Mathématiques de Jussieu – Paris Rive Gauche and Institut Mittag-Leffler

                                  Titel: Invariant Cantor sets for conservative dynamics

                                  Sammanfattning: Poincaré said in 1892 « ce qui nous rend ces solutions périodiques si précieuses, c'est qu'elles sont, pour ainsi dire, la seule brèche par où nous puissions essayer de pénétrer dans une place jusqu'ici réputée inabordable .» i.e. « what makes periodic solutions so valuable is that they offer the only opening through which we might try to penetrate into the fortress which has the reputation of being impregnable »

                                  However, one or several periodic orbits don’t reflect the complexity of a given dynamical system. For example, for the preserving area diffeomorphisms of a surface, there often exist close to the periodic orbits some Cantor sets that are invariant, called horseshoes and Denjoy sets.

                                  We will introduce the notions of Cantor sets, horseshoes and Denjoy sets and explain their mutual relations as well as their relations with the ambiant dynamics, through past and recent results.

                                  Onsdag 29 mars 2023 kl 13:15-14:15, Alexei Iantchenko, Malmö universitet

                                  Titel: Semiclassical surface-wave imaging and leaking modes in seismology

                                  Sammanfattning:  Semiclassical analysis can be employed to describe surface waves in an elastic half space which is quasi-stratified near its boundary. In case of isotropic medium, the surface wave decouples up to principal parts into Love and Rayleigh waves associated to scalar and matrix spectral problems, respectively. Since the mathematical features (such as spectrum, resonances) of these problems can be extracted from the seismograms, we are interested in recovering the Lamé parameters from these data.

                                  I consider two inverse problem approaches:

                                  1. semiclassical techniques using the semiclassical spectra as the data
                                  2. exact methods for Sturm-Liouville operators based on solution of the Gel'fand-Levitan equations, by using as data the discrete and continuous spectra (Weyl or Jost functions).

                                  We generalize spectral methods for Schrödinger operators to the Rayleigh problem, which is essentially not of Schrödinger type; and give comprehensive analysis of the wavenumber resonances, known in seismology as leaking modes.

                                  Onsdag 22 mars kl 13.15-14:15, Tere M-Seara, Universitat Politècnica de Catalunya and Institute Mittag-Leffler

                                  Titel: Chaos in the Three body problem

                                  Sammanfattning: Chaos in the Three body problem

                                  Onsdag 8 mars 2023 kl 13:15-14:15, Melanija Mitrović, Niš Universitet, Serbien

                                  Titel: Constructive Relational Binary Structures With Apartness – Unity Not Uniformity

                                  Sammanfattning: Seminar abstract Melanija Mitrovic (pdf)

                                  Torsdag 2 mars 2023 kl 15:15-16:15 Riikka Korte, Aaltouniversitetet, Helsingfors, Finland

                                  Titel: $JN_p$ — a generalisation of BMO

                                  Sammanfattning: In 1961, along with the well-known class of functions of bounded mean oscillation (BMO), John and Nirenberg also introduced the following variant of the BMO condition, which was subsequently used to define what is now called the John-Nirenberg space with exponent $p>1$, denoted $JN_p$. Even though the space of BMO functions has been extensively studied, the John-Nirenberg spaces have attracted more attention only recently. The nature of these function spaces is not yet well understood. For example, we know already from the work of John and Nirenberg that the $JN_p$ space lies between $L^p$ and weak $L^p$ spaces, but the first known example of a $JN_p$-function that is not $L^p$-integrable was constructed only recently. In this talk, we will discuss recent results about the John-Nirenberg spaces.

                                  Onsdag 1 mars 2023 kl 13:15-14:15, Ivan Kaygorodov, Universidade da Beira Interior, Covilhã, Portugal

                                  Titel: Transposed Poisson algebras

                                  Sammanfattning: Recently (2020), a dual notion of the Poisson algebra (transposed Poisson algebra), by exchanging the roles of the two binary operations in the Leibniz rule defining the Poisson algebra, has been introduced in the paper of Bai, Bai, Guo, and Wu. They have shown that the transposed Poisson algebra defined in this way not only shares common properties with the Poisson algebra, including the closure undertaking tensor products and the Koszul self-duality as an operad but also admits a rich class of identities. More significantly, a transposed Poisson algebra naturally arises from a Novikov-Poisson algebra by taking the commutator Lie algebra of the Novikov algebra. The talk is about new results related to transposed Poisson algebras and their relations with other types of algebraic systems.

                                  Tisdag 28 februari 2023 kl 13:15-14:15, Sari Rogovin, Helsingfors

                                  Titel: Some remarks about the Gehring-Hayman theorem

                                  Sammanfattning: We will discuss how the Gehring-Hayman theorem, that says in simplicity that the hyperbolic geodesic on the disc in the complex plane is essentially the shortest curve, has been generalized to a tool to see for example how geometric conditions such as Gromov hyperbolicity and uniformity are linked in metric spaces. We also talk about some equivalent characterizations for the Gehring-Hayman theorem in the metric space setting.

                                  Onsdag 22 februari 2023 kl 13:15-14:15, Erik Darpö, Matematiska institutionen, Linköpings universitet

                                  1. Titel: Constructive algebra

                                    Sammanfattning: To prove the existence of an object with certain properties means to provide a finite algorithm that constructs the object and demonstrates that is has the required properties in question. This basic premise of constructive mathematics leads to a reconsideration of classical logic; in particular, the law of excluded middle, holding that every proposition is either true or false, is discarded as a general principle.

                                    In this talk, we shall have a look at the differences between constructive and classical mathematics, and introduce some of the ideas - and challenges - of doing algebra within a constructive framework.

                                  Onsdag 8 februari 2023 kl 13.15-14.15, Minhyun Kim, University of Bielefeld, Tyskland

                                  1. Titel: Wiener criterion for nonlocal Dirichlet problems

                                    Sammanfattning: We study the boundary behavior of solutions to the Dirichlet problems for nonlocal nonlinear operators. We establish a nonlocal counterpart of the Wiener criterion, which characterizes a regular boundary point in terms of the nonlocal nonlinear potential theory. This talk is based on a joint work with Ki-Ahm Lee and Se-Chan Lee.

                                2. Onsdag 25 januari 2023 kl 13:15-14:15, Kimmo Eriksson, Mälardalens universitet

                                1. Titel: Why do moral opinions change?

                                  Sammanfattning: For almost 20 years, I have done research on cultural evolution. This research uses a combination of mathematical modeling and empirical studies to understand the processes by which various aspects of culture change. In this talk I will speak on my research on contemporary evolution of moral opinions (joint work with Pontus Strimling and Irina Vartanova). I will present a model that provides novel answers to multiple questions: Why are certain moral opinions becoming increasingly popular? Why does opinion change go faster on some issues than others? Why is there so little difference in moral opinions between conservatives and liberals? Why do people who discuss more often tend to have more liberal opjnions? Why do more intelligent people tend to have more liberal opinions? Can we predict future change in moral opinions?

                              1. Torsdag 15 december 2022 kl 8:30-9:30, Christian Stump, Ruhr-Universität Bochum, Tyskland

                              1. Titel: Playing with combinatorial statistics

                              Sammanfattning: The study of permutation statistics (this is, assigning numbers to permutations) is a fundamental concept in combinatorics. Among the most important are the Mahonian and Eulerian numbers given by the number of inversions and by the number of descents. In this talk, I present examples of how to use the online Combinatorial Statistics database to systematically study permutation statistics. Most importantly, I present a generalization of these statistics to finite Coxeter groups and how to semi-automatically guess their statistical behavior. This talk is based on collaborations with Thomas Kahle and Kathrin Meier.

                              Torsdag 8 december 2022, kl 11.00-12.00, Alexandre Karassev, Nipissing University, North Bay, Kanada

                              Titel: On discrete homogeneous spaces

                              Sammanfattning: A topological space is called homogeneous if for any two points x, y of X there exists a homeomorphism f: X ->X such that  f(x) = y. We will discuss some generalizations of the notion related to discrete subsets of X. Different examples distinguishing the introduced types of homogeneity will be given.

                            1. Onsdag 7 december 2022 kl 13:15-14:15, Antonio F. Costa, UNED, Spanien

                            Titel: On one dimensional equisymmetric strata in Moduli Space

                            Sammanfattning: In this talk I am presenting results obtained in collaboration with S. Allen Broughton and Milagros Izquierdo. Moduli space M_g is the space of complex structures on surfaces of genus g. M_g admits a stratification into a finite, disjoint union of equisymmetric strata. Each stratum corresponds to a collection of surfaces whose automorphism groups act in a topologically equivalent way. There are two types of strata of complex dimension one. The first type corresponds to the surfaces that are regular coverings of the sphere branched over four points. This type of strata has been exhaustively studied in a previous work: One dimensional equisymmetric strata in moduli space, S. Allen Broughton, Antonio F. Costa, and Milagros Izquierdo, Contemporary Mathematics, Volume 776, 2022. The second type of strata corresponds to surfaces S such that S/Aut(S) has genus one. For this type of strata we first show that strata of this type exist, exhibiting some examples. We describe the geometry and topology of the strata of type 2 as Belyi curves with several punctures. As consequence we have that all strata of dimension one are Belyi curves. Finally we remark that the strata of type 2 are somewhat less frequent than those of type 1.

                          1. Onsdag 23 november 2022 kl 13:15-14:15, Evgeniy Lokharu, Lunds universitet 

                        Titel: Fine properties of steady water waves

                        Sammanfattning: In this talk we will discuss some recent results on two dimensional steady water waves. We will explain how the Benjamin and Lighthill conjecture can be significantly refined and will prove a new bound for the amplitude of an arbitrary Stokes wave in terms of the non-dimensional Bernoulli constant. Our result, in particular, implies the inequality a ≤ Cc^2/g, where a is the amplitude, c is the speed of the wave, and g is the gravitational constant. This fact is valid for arbitrary Stokes waves irrespectively of the amplitude with an absolute constant C. Another observation is that any extreme Stokes wave over a sufficiently deep stream has necessarily a small amplitude, provided the non-dimensional mass flux is much smaller than the depth.

                      1. Onsdag 16 november 2022 kl 13:15-14:15, Michael Felsberg, Institutionen för systemteknik, Linköpings universitet

                  Titel: Steerable 3D Spherical Neurons

                  Sammanfattning:Emerging from low-level vision theory, steerable filters found their counterpart in prior work on steerable convolutional neural networks equivariant to rigid transformations. In our work, we propose a steerable feed-forward learning-based approach that consists of neurons with spherical decision surfaces and operates on point clouds. Such spherical neurons are obtained by conformal embedding of Euclidean space and have recently been revisited in the context of learning representations of point sets. Focusing on 3D geometry, we exploit the isometry property of spherical neurons and derive a 3D steerability constraint. After training spherical neurons to classify point clouds in a canonical orientation, we use a tetrahedron basis to quadruplicate the neurons and construct rotation-equivariant spherical filter banks. We then apply the derived constraint to interpolate the filter bank outputs and, thus, obtain a rotation-invariant network. Finally, we use a synthetic point set and real-world 3D skeleton data to verify our theoretical findings. The code is available here.

                1. Onsdag 9 november 2022 kl 13:15-14:15, Mark Allen, Brigham Young University, Provo, USA och Institut Mittag-Leffler, Djursholm

                Title: Isoperimetric and Faber-Krahn Inequalities

                Abstract: In this talk we review the isoperimetric inequality and how it leads to the Faber-Krahn inequality. We will then discuss how to establish quantitative forms of these inequalities. This entails measuring how close a set is to a ball if the perimeter (or first eigenvalue of the Laplacaian) is close to that of the ball. We will conclude by showing how quantitative inequalities can be useful.

              1. Onsdag 26 oktober 2022 kl 13:15-14:15, Erik Darpö, Matematiska institutionen, Linköpings universitet 

              Titel: Quivers, path algebras and representations

              Sammanfattning: In this talk, we will have a look at quivers and their representations: what they are, what they are good for, and how they are related to (non-commutative) rings/algebras and their modules. We will speak about one of the early, seminal results in the representation theory of algebras, Gabriel's theorem, which classifies quivers with only finitely many isomorphism classes of indecomposable representations in terms of Dynkin diagrams.

            1. Fredag 21 oktober 2022 kl 13:15-14:15, János Barát, Alfréd Rényi Institute of Mathematics, Budapest, Ungern INSTÄLLT

            2. Titel: Constructions

              Sammanfattning: I will show a few episodes of my mathematical carrier in Combinatorics, where constructions played an important role. My intention is to emphasize the differences in these stories. I try to cover the following scenarios:

              1. There is a long-standing conjecture, but nobody can prove it. Can we find examples to show the statement is actually sharp?
              2. There is a statement of the non-existence of an object. This claim appears in the most renowned book of the subject. You start a collaboration and your new colleague gives you the manuscript of the proof, but you find a small inaccuracy. Can this change the entire picture?
              3. There is a difficult problem. You try to warm up with a simpler one of the same flavor. After a while you convince yourself that you grabbed the bottleneck of the question. Can a construction inspire the entire proof?

              Possibly some more, if time permits.

              Onsdag 28 september 2022 kl 13:15-14:15, Jörg-Uwe Löbus, Matematiska institutionen, Linköpings universitet

        1. Titel: Knudsen Type Group and Boltzmann Type Equation -- Boundary Shape and Boundary Conditions

          Sammanfattning: We consider certain Boltzmann type equations on a bounded physical and a bounded velocity space under the presence of both, reflective as well as diffusive boundary conditions. We introduce conditions on the shape of the physical space and on the relation between the reflective and the diffusive part in the boundary conditions such that the associated Knudsen type semigroup can be extended to time $t\in\mathbb{R}$. Furthermore, we provide conditions under which there exists a unique global solution to a Boltzmann type equation for time $t\ge 0$ or for time $t\in [\tau_0,\infty)$ for some $\tau_0<0$ which is independent of the initial value at time  $0$. Depending on the collision kernel, $\tau_0$ can be arbitrarily small.  

        2. The corresponding paper is available under here.

      1. Onsdag 21 september 2022 kl 13:15-14:15, Jonathan Nilsson, Matematiska institutionen, Linköpings universitet

    Titel: Old and new families of Lie algebra modules

    Sammanfattning: Representation theory for Lie algebras is a rich subject with connections throughout several areas of mathematics and physics. An important aspect in understanding the category of representations of a Lie algebra is to obtain a classification of its simple objects, but unfortunately such a classification seems intractable for all but the smallest Lie algebras. Nevertheless, by imposing some restrictions one can construct and classify several classes of simple modules, such as finite-dimensional modules, Whittaker modules and Gelfand-Zetlin modules. In the first part of this talk I will give an overview of several well-known families of Lie algebra modules. Then I will present my own contributions to this field, discussing modules which are free over the enveloping algebra of a Cartan-subalgebra, as well as some new families of modules for the Lie algebra of vector fields on affine varieties. The talk is partly based on joint work with Yuly Billig and Vyacheslav Futorny.

    Onsdag 24 augusti 2022 kl 13:15-14:15, Klara Stokes, Umeå universitet

    Titel: Incidence geometries with trialities from coset geometries and embeddings of graphs on surfaces

  1. Sammanfattning: Triality is a classical notion in geometry that arose in the context of the Lie groups of type D_4. Another notion of triality appears in the context of reflexible maps. In this talk I will show how to construct incidence geometries with trialities for other groups, using techniques such as gain/voltage graphs, embeddings of graphs on surfaces (maps) and as coset geometries. I will focus on the case in which the incidence geometry has a triality but no dualities. This is joint work with Dimitri Leemans.

Onsdagen 8 juni 2022, Juha Lehrbäck, Jyväskylä University

Titel: Weakly porous sets and Muckenhoupt $A_1$ distance weights

Sammanfattning: Let $E\subset\mathbb{R}^n$ and let $w(x)=d(x,E)^{-\alpha}$, where $\alpha>0$.

If $E$ is porous, then it is known that $w$ is a Muckenhoupt $A_1$ weight if and only if the Assouad dimension of $E$ is strictly less than $n-\alpha$. Since $E$ is porous if and only if the Assouad dimension of $E$ is strictly less than $n$, it follows that for all porous sets there exists some $\alpha>0$ such that $w$ is an $A_1$ weight.

In this talk, I extend this result to non-porous sets and show that $d(x,E)^{-\alpha}$ is an $A_1$ weight, for some $\alpha>0$, if and only if $E$ is \emph{weakly porous}. During the talk, I will introduce the relevant concepts and for instance give examples of some non-porous sets which are weakly porous.

This talk is based on an ongoing joint work with Carlos Mudarra and Antti Vähäkangas.

Onsdag 1 juni, Ezio Venturino, Università di Torino

Titel: Fighting alien species invasions through mathematical modeling

Sammanfattning: Recently, we have investigated the phenomenon of native populations replacement by exotic ones, focusing on accidentally or intentionally introduced
species in Italy and UK. Two major cases are of interest. American grey squirrels are gradually outcompeting the indigenous red ones both in Italy and in UK. In the latter case, the situation is worsened by the presence of a virus, carried by the aliens, for which it is harmless, but which ultimately is found lethal for the native species. In Italy the European hare is slowly forcing the extinction of the native mountain hare. The main difference in this case is that the contacts among the two occur just on the boundary region of the territories occupied by the two species. This allows us to formulate a non-classical interaction model, based on the concept of herd behavior. The latter is extended to other possible situations, showing the onset of some new features in the phase space, revealing quite different results from the classical ones.
OBS! Lokal: C3

Torsdag 19 maj 10.15-11.15, Hans Nguyen, University of Nottingham

Titel: Homological methods in random noncommutative geometry

Sammanfattning: Noncommutative geometry is a generalisation of ordinary (commutative) geometry, where also noncommutative algebras are regarded as algebras of functions of spaces. In this talk, we will focus on the so-called fuzzy spectral triples, which are a finite version of the celebrated spectral triples of Alain Connes that constitute the cornerstone of noncommutative Riemannian (spin) geometry. Since fuzzy spectral triples are fully classified, they form a good setting for studying random noncommutative geometry. In particular, their finite nature allows for a rigorous formulation and study of the path integral over the space of geometries, leading to toy-models for quantum gravity. The new aspect of our work is that we take into account the noncommutative analogue of diffeomorphism symmetries in the formulation of such path integrals, which we will implement through suitable homological methods.
Lokal: Hopningspunkten

Onsdag 18 maj 2022, Signe Lundqvist, Umeå universitet

Titel: When is a rod configuration infinitesimally rigid?

Sammanfattning: The mathematical theory of structural rigidity has a long history. In the nineteenth century, Cauchy studied rigidity of polyhedra, and Maxwell studied graph frameworks. The rigidity theory of graph frameworks has since been studied extensively. Pollaczek-Geiringer, and later Laman, proved a combinatorial characterization of the minimally rigid graphs in the plane. Combinatorial rigidity theory is also concerned with geometric realizations of other combinatorial structures. A rod configuration is a realisation of a hypergraph as points and straight lines in the plane, where the lines behave as rigid bodies. In this talk, we will discuss approaches for determining whether a given rod configuration is infinitesimally rigid. This is based on joint work with Klara Stokes and Lars-Daniel Öhman.

Onsdag 11 maj 2022, Magnus Herberthson, Matematiska institutionen, Linköpings universitet

Titel: Characterising the second order moments of diffusion tensor distributions

Sammanfattning: In magnetic resonance imaging (MRI), it is possible to probe tissue on a sub-resolution level. The signal obtain by MRI is then formed by a family of diffusion tensors, with may have certain statistical properties. In this talk we are interested in characterising the second order moment of this family, which is a forth order tensor with certain symmetries.

Onsdag 4 maj 2022, Anders Björn, Matematiska institutionen, Linköpings universitet

Titel: $p$-harmonic Green functions on metric measure spaces and growth rate exponents

Sammanfattning: On (unweighted) ${\bf R}^n$, the dimension $n$ determines (together with $p$) the Sobolev exponent $p^*=np/(n-p)$. Also the growth rate for the $p$-harmonic Green function $u(x)=|x|^{(p-n)/(p-1)}$ is given by $n$ (and $p$).

In this talk I will consider similar facts on a complete metric space equipped with a doubling measure supporting a Poincaré inequality. I will explain how one defines Sobolev spaces (so-called Newtonian spaces based on upper gradients) and $p$-harmonic functions on metric spaces. I will then spend some time on how to define, and what should be meant, by $p$-harmonic Green functions and discuss their local integrability properties.

I will also try to give a few other examples where different growth rates coming directly from the measure appear naturally and are sharp. For unweighted ${\bf R}^n$ all these growth rates coincide (and are $n$), but this is not so in general.

Onsdag 30 mars 2022, Axel Hultman, Matematiska institutionen, Linköpings universitet

Titel: Quickstep posets and inversion arrangements

Sammanfattning: Given a graph with a fixed vertex $v$, I shall demonstrate a construction of a partially ordered set whose elements are subsets of the neighbourhood of $v$. The motivation comes from the combinatorics of certain hyperplane arrangements known as inversion arrangements and their somewhat mysterious interplay with the geometry of Schubert varieties. An attempt at an overview for non-experts will be provided.

Onsdag 16 mars 2022, Daniel Fox, Universidad Politécnica de Madrid, Spanien

Titel: Partial associativity and quantitative nonassociativity

Sammanfattning: Taking seriously an apparently naive analogy between the multiplication of a not necessarily associative algebra and a covariant derivative operator leads to notions of partial and quantitative associativity modeled on various forms of curvature of a connection. Such notions identify classes of nonassociative algebras for which classification appears tractable and which include a diversity of interesting examples, including semisimple Lie algebras and their tensor products, semisimple Euclidean Jordan algebras, Griess algebras of vertex operator algebras (such as the Griess algebra of the monster finite simple group), and the algebra of metric curvature tensors with the Hamilton-Huisken product. These notions will be surveyed, focusing on the notions of projective associativity for commutative algberas and sectional nonassociativity for metrized commutative algebras,

Onsdag 9 mars 2022, Tomas Sjödin, Matematiska institutionen, Linköpings universitet

Titel: On Laplacian growth in the plane and a conjecture of Gustafsson and Lin.

Sammanfattning: The Laplacian growth process of Hele-Shaw flow in the plane in the forward direction has been extensively studied for several decades now, where both classical as well as weak solutions to the moving boundary problem has been considered.

One major issue is that classical solutions will almost always break down in finite time. In their recent book Laplacian growth on branched Riemann surfaces Gustafsson and Lin considers the possibility, in the configuration of a simply connected initial domain and a point source, of extending the classical solutions to exist for all time by lifting them to a branched Riemann surface. Unfortunately, they got stuck on a technical problem and had to develop the theory based on the validity of a conjecture. Roughly speaking the problem in their construction is that one inevitably more or less at certain points in time will get to a situation that the boundary infinitesimally moves with infinite speed at some points, and the approach of classical solutions breaks down. The conjecture was then that the solution still exists and is simply connected for some small time interval. This conjecture was answered in the positive in the recent article On a conjecture of Gustafsson and Lin concerning Laplacian growth (TS and S.J. Gardiner). In this talk we will discuss the law of motion for the Hele-Shaw process, how it can be interpreted in terms of the Riemann map and finally discuss the conjecture of Gustafsson and Lin.

Länk till publikationen 

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

Anordnas i samarbete med Seminarier i optimeringslära

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

Sammanfattning: 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.

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

Titel: Loci of Riemann Surfaces with Automorphisms

Sammanfattning: TBA

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.


Arkiv 2001-2019

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