Matematiska kollokviet

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

Titel: Classifying compact Riemann surfaces by number of symmetries
Sammanfattning: The groups of automorphisms of compact Riemann surfaces (or complex projective algebraic curves) have been extensively studied over the last decades. In this talk we shall consider compact Riemann surfaces that are uniquely determined by the property of possessing a group of automorphisms of a prescribed order. We shall discuss some recent results concerning the case in which such an order is 3g, where g is the genus. This is a joint work with Pietro Speziali (Campinas).

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 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:

semiclassical techniques using the semiclassical spectra as the data

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

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

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.

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

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?

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