Events and Seminars

Past Events and Seminars

2023

6 December: Christmas Workshop in Mathematical Modelling and Analysis

Niklas Lundström, Umeå university, Millions of Growth Estimates for Subsolutions of Nonlinear PDEs

Abstract: In L22 sharp growth estimates for subsolutions in halfspaces of fully nonlinear PDEs on the form F(x,u,Du,D^2u) = 0 were proven through a characterization built upon solutions of certain ODEs. 

In this talk, we show how to generalize the main theorem of L22 to hold under weaker assumptions and derive several sharp Phragmen-Lindelöf-type theorems (growth estimates for subsolutions) as corollaries.

Suprokash Hazra, Mid Sweden University, Truncated Tube Domains with Multi-Sheeted Envelope of Holomorphy

Abstract: We define the envelope of holomorphy of a general Riemann domain over C^n and discuss the schlichtness of it with some examples. Next, we address a group of problems raised by J. Noguchi and M. Jarnicki/P. Pflug, namely whether the envelopes of holomorphy of truncated tube domains are always schlicht, that is subdomains of \C^n. By providing a counter-example diffeomorphic to 4-ball we then discuss an answer to the above problem jointly obtained by Egmont Porten and the author. Finally, we discuss a sufficient condition for schlichtness in complex dimension two.

Jonatan Vallin, Umeå university, Error Estimates for Implicit Approximation of Hypersurfaces using Deep ReLU Nets

Abstract: We develop a geometric approximation theory applicable in the classification setting for deep feed-forward neural networks with ReLU activations. Given a hypersurface in Rd represented as a level-set of a C2-function φ, we show that a deep real-valued fully-connected ReLU network of width, d+1 can implicitly construct an approximation as its zero contour - the decision boundary. Our proof is constructive and relies on a geometrical analysis of ReLU layers.

Kevin Kamm, Umeå university, On the Impact of Feeding and Biological Cost in Aquaculture Valuation

Abstract: We study the effect of stochastic feeding and biological costs on animal-based commodities with particular focus on aquaculture. More specifically, we use soybean futures to infer on the stochastic behaviour of salmon feed, which we assume to follow a Schwartz-2-factor model and use a host-parasite model to estimate mortality induced by salmon lice. We compare the decision of harvesting salmon using a decision rule assuming either deterministic or stochastic feeding costs/ mortality. We show that the harvesting decision based on this new and more realistic model can lead to a significant increase of revenue, while the additional computational costs are negligible.

29 November: A weighted Bernstein-Walsh-Siciak theorem with polynomials associated to convex sets

Speaker: Bergur Snorrason, University of Iceland

Abstract: We generalize the Bernstein-Walsh-Siciak theorem on polynomial approximation to the case where the standard polynomial ring is replaced by a subring consisting of all polynomials with exponents restricted to sets $mS$, where $S$ is a compact convex subset of $\mathbb{R}^n_+$ with $0 \in S$ and $m = 0, 1, 2, 3, ...,$ and uniform estimates of error in the approximation are replaced by weighted uniform estimates with respect to an addmissible weight function.

27 November: Norm attaining vectors in Hilbert spaces

Speaker: Konstantinos Bampouras, Norwegian University of Science and Technology

Abstract: We will define what a norm attaining vector and Hilbert point are and state two theorems giving equivalent relations. We are going to investigate such vectors in the setting of Hankel operators on Hardy spaces in the polydisc. This talk is based on a recent work with Ole Fredrik Brevig (U. of Oslo).

22 November: The dawn of cooperation: unicellular-multicellular evolutionary branching driven by resource limitations

Speaker: Adriano Bonforti, Umeå University/IceLab

Abstract: Multicellular life forms have evolved many times on our planet, suggesting that this is a common evolutionary innovation. Multiple advantages have been proposed for the emergence of multicellularity (MC). In our research we address the problem of how the first precondition for MC, namely ‘stay together’, might have occurred under spatially limited resources exploited by a population of unicellular agents. Using a minimal model of evolved cell–cell adhesion among growing and dividing cells that exploit a localized resource with a given size, we show that a transition occurs at a critical resource size separating a phase of evolved multicellular aggregates from a phase where unicellularity (UC) is favoured. The two phases are separated by an intermediate domain where both UC and MC can be selected by evolution. This model provides a minimal approach to the early stages that were required to transition from individuality to cohesive groups of cells associated with a physical cooperative effect: when resources are present only in a localized portion of the habitat, MC is a desirable property as it helps cells to keep close to the available local nutrients.

15 November: Solving dynamic contracts using Nevanlinna-Pick and Wiener-Hopf methods

Speaker: Bart Taub, University of Glasgow

Abstract: We explore the impact of a constraint restricting the switching of an input process in optimal control. We motivate the model with an application to risk-sharing contracts in which the no-switching constraint is equivalent to no-defection constraints. We bring several techniques to bear to determine and analyse the solution: state space methods, Nevanlinna-Pick interpolation, Wiener-Hopf methods, and the fundamental equivalence of H∞ and H2 control as established by Sideris. Our fundamental finding is that the switching constraint is equivalent to an H∞ constraint. The effect of the constraint is to add a pole to the optimal control in addition to the pole arising naturally from the basic problem, and this affects the persistence of the output process.

8 November: Finite Parts of Certain Divergent Integrals and Their Dependence on Regularization Data

Speaker: Ludvig Svensson, Chalmers University of Technology and University of Gothenburg

Abstract: Let $X$ be a reduced complex space of pure dimension. We consider divergent integrals of certain forms on $X$ that are singular along a subvariety defined by the zero set of a holomorphic section of some holomorphic vector bundle $E \rightarrow X$. We consider two different regularizations of such integrals, both depending on a choice of smooth Hermitian metric on $E$. Given such a choice, for each of the two regularizations there is a natural way to define a finite part of the divergent integral, and I will explain that they coincide. Furthermore, I'll present an explicit formula for the dependence on the choice of metric of the finite part, and briefly talk about how it was obtained.

1 November: The steady water-wave problem

Speaker: Kristoffer Varholm, Norwegian University of Science and Technology (Mittag-Leffler participant)

Abstract: The motion of fluids has been an incredibly rich source of mathematics over the preceding (soon to be) three centuries. In this talk, we will focus on the smaller, but still vast, topic of steady water waves. These are waves that propagate at constant speed, with no change of form. I will attempt to give a gentle introduction to a neighborhood of my own research.

25 October: Some results related to the weighted conformal invariance property

Speaker: Alejandro Mas, University of Valencia

Abstract: Let $\varphi$ be an automorphism of the unit disc $\mathbb{D}$ and let  $W_{\varphi}^{\alpha}$ be the weighted composition operator, acting on a Banach space of analytic functions in the unit disc, defined by $W_{\varphi}^{\alpha} f= (f \circ \varphi)(\varphi')^{\alpha}$ with $\alpha>0$. We observe that many common examples of Banach spaces of analytic functions like Korenblum growth classes, Hardy spaces, standard weighted Bergman and certain Besov spaces are invariant under these operators. Thus, the main goal of this talk will be to present a general approach to the spaces that satisfy this weighted conformal invariance property. Among other things, we will identify the largest and the smallest as well as the ``unique'' Hilbert space satisfying this property for a given $\alpha >0$. These results are part of a joint work together with Professor Alexandru Aleman.

18 October: Modelling a Regional Electric Aviation PSO-Network in the Kvarken Region

Speaker: Jonas Westin, Umeå University

Abstract: In many regions worldwide, steps are taken towards using electric-powered aircraft for regional air transport. In sparsely populated regions with long distances, such as the Kvarken Region in northern Scandinavia, electric regional aviation may both have a potential to improve intraregional accessibility and reduce emissions compared to traditional air transport. Around the world, flight services often operate on commercial bases where airlines choose flight routes based on profitability. As a consequence, regions and routes with low or insufficient passenger demand might be excluded from the commercial flight service market. In the European Union, Public Service Obligation (PSO) is a tool for subsidizing air routes in regions where commercial air services are considered unprofitable by airlines.

This purpose of the paper is to analyze the economic potential to create electric regional air networks in the Kvarken region with support of subsidies based on the PSO-system. The optimization model is an integrated flight scheduling and fleet assignment model that creates a schedule that meets a set of PSO-requirement windows while minimizing the operating and social costs of the network.

In the model, a fixed planning period is divided into a number of discrete time steps, each corresponding to a possible departure time (e.g. every 15 or 30 minutes). The movement of aircrafts and passengers is represented by a directed graph where each vertex in the graph corresponds to a possible departure time from an airport. The model has two layers; a flight layer and a service layer. The arcs in the flight layer represent potential aircraft movements between airports, including ground arcs representing aircraft staying on the ground. The edges in the service layer correspond to possible movements of passengers in the network. Both layers share the same vertices, and every arc in the flight layer is linked to a corresponding edge in the service layer for passengers using a flight on that arc. The capacity of each edge in the service layer depends on the number of aircraft on the corresponding arc in the flight layer multiplied by the passenger capacity of aircraft type.

Charging time is an important factor for the turnaround time for electric aviation. We model different charging strategies using combined flight arcs that allows aircrafts to choose arcs with multiple stops. Since a combined flight arc in the flight layer traverses multiple airports, it is connected to multiple edges in the service layer. The model is built in Matlab and solved using Gurobi.

We use the model to analyze a case study of electric aviation in the Kvarken Region. We compare the impact of different network configurations and investigate how different charging times impact fleet size and evaluates the compatibility of existing Swedish PSO regulations with electric aviation solutions.

11 October: Numerical approximation of McKean-Vlasov SDE via stochastic gradient descent

Speaker: Ankush Agarwal, University of Glasgow

Abstract: The McKean-Vlasov SDEs are a class of SDEs that describe the evolution of particles interacting with a population of other particles, where the dynamics of the system are influenced by the empirical measure of the particles. Typically, the numerical resolution of these equations involves the simulation of interacting particle systems, which can be computationally expensive and computationally challenging, especially in high-dimensional settings. In this paper, we explore an alternative method for the numerical resolution of McKean-Vlasov SDEs that does not rely on the simulation of interacting particle systems. Specifically, we investigate the use of Stochastic Gradient Descent (SGD), which has recently emerged as a powerful tool for high-dimensional optimization problems in machine learning. We propose a novel algorithm that combines a discretization scheme with SGD to efficiently and accurately approximate the solution of McKean-Vlasov SDEs. We present numerical experiments that demonstrate the effectiveness and efficiency of our approach, even in high-dimensional state spaces.

4 October: On Wolff’s theorem for Békollé-Bonami weights

Speaker: Adrián Llinares, Umeå University

Abstract: In a famous but unpublished preprint, Wolff characterized the restrictions of Muckenhoupt Ap weights to subsets of the unit circle. In this seminar, we will show a way to extend this theorem to Békollé-Bonami weights. These families of weights could be understood as an analogous version of the Ap classes for the disk, although they are in general more ill-behaved. All of the tools, definitions, similarities and differences will be introduced, so it will be a (mostly) self-contained talk.

25 September: Jouni Rättyä, University of Eastern Finland

Abstract: In this talk we consider Carleson measures for weighted Bergman spaces starting with classical radial weights and then passing through radial doubling weights to non-radial ones. Recall that the q-Carleson measures for a space X of analytic functions in the unit disc are the non-negative Borel measures \mu that the identity operator from X to L^q_\mu is bounded.

20 September: Complete metric space structure on the finite energy spaces of big cohomology classes

Speaker: Prakhar Gupta, University of Maryland

Abstract: Complete metric space structures on the finite energy spaces in the Kähler case have found various applications. These metrics in the L^{1} energy case were used in finding the Kähler-Einstein metrics. In this talk, I'll discuss that by using different methods, we can construct a complete metric space structure on the finite energy spaces when the cohomology class is merely big.

6 September: SYZ mirror symmetry for A_n singularity

Speaker: Hang Yuan, Northwestern University

Abstract: We study the Strominger-Yau-Zaslow (SYZ) conjecture, which provides a geometric framework for mirror symmetry in Calabi-Yau manifolds. We propose a mathematically precise statement for SYZ fibration duality based on a toy local model for integrable systems in symplectic and non-archimedean contexts. We explain the globalization of this toy model using quantum correction data. A focus will be given to a down-to-earth example of our SYZ duality, addressing the transition between the smoothing and crepant resolution of A_n singularity, accompanied by certain geometric phenomena related to the braid group action.

23 August: Wind power – a short introduction for non-experts

Speaker: Cecilia Karlsson, University of Borås

Abstract: In this talk we will take a non-technical look at wind power plants, focusing on parts that can be of importance if one wants to model the power output from an existing wind farm.

This talk will be given by a mathematician, from a mathematician’s point of view, and not by an expert in wind power production.

14 June: Breaking the Dimensional Chains

Speaker: Per Åhag, Umeå University

Abstract: Do you find yourself ensnared in the monotonous dread of your daily routine as if trapped eternally in the same dimension? Grasp a steaming mug of coffee and prepare to embark on a chilling odyssey that hails from the shadowy era of the 80s with the rise of an enigmatic field of symplectic topology. This journey is not one we embark on alone, but it is a collaborative endeavor of Rafał Czyż, Håkan Samuelsson Kalm, and Aron Persson.

Allow us to navigate you through the spine-chilling realm of analytical nightmares, steering unerringly toward the black flame. Brace yourself for an encounter with Krein and his disciples, and delve into the clandestine complexities in Banach's work. We are a faction yearning for rebellion, audaciously standing up to the oppressive mainstream perspectives of Fréchet. Our journey teeters on the brink of a cataclysmic conflict within the world of topology, but Henri Cartan is set to intervene. Ready to make the ultimate sacrifice, he promises to ignite a powerful resurgence that will guide us back onto our dark path.

Prepare to discover how it casts a looming shadow over the monotony of your daily existence. Rest assured, we have stashed away sugary treats for the brave souls who dare to participate. So, summon your courage, step into obscurity with us, and prepare to unveil a new realm of possibilities.

7 May: Joint Seminar in Discrete Mathematics and Mathematical Modelling and Analysis, Modelling the Motions of Realisations of Incidence Geometries

Speaker: Joannes Vermant, Umeå University

Abstract: In structural rigidity, one studies frameworks of bars and joints in Euclidean space. Such a framework is an articulated structure consisting of rigid bars, joined together at joints around which the bars may rotate. I will present a model of articulated motions of realisations of incidence geometries that uses the terminology of graph of groups, and describe the motions of such a framework using group theory. Our approach allows to model a variety of situations, such as parallel redrawings, scenes, polytopes, realisations of graphs on surfaces, and even unique colourability of graphs. We also provide a lower bound on the dimension of the infinitesimal motions of such a framework in the special case when the underlying group is a Lie group. This is joint work with Klara Stokes.

31 May: (Strictly) pseudoconvex domains and their transformations

Speaker: Arkadiusz Lewandowski, Jagiellonian University

Abstract: We shall present the notion of pseudoconvexity in several complex variables, with emphasis put on strict pseudoconvexity. We shall discuss

the role of (strictly) pseudoconvex domains and some of their transformations.

25 May: Three nontrivial solutions for nonlinear fractional Laplacian equations

Speaker: Fatma Gamze Duzgun, Hacettepe University Turkey

Abstract: We study a Dirichlet-type boundary value problem for a pseudodifferential equation driven by the fractional Laplacian, proving the existence of three non-zero solutions. When the reaction term is sublinear at infinity, we apply spectral theory. When the reaction term is superlinear at infinity, we apply the Mountain Pass Theorem and Morse theory.

24 May 2023: Workshop in Mathematical Modelling and Analysis

Adrián Llinares, Umeå University, Contractive inclusions between spaces of analytic functions

Thomas Önskog, Statistics Sweden (SCB), Backcasting the time series of the Swedish Labour Force Survey

John Fabricius, Luleå University of Technology, Dimensional reduction of the heat equation in a thin rod with convective cooling

Fatma Gamze Duzgun, Hacettepe University, Anisotropic Sobolev embeddings and the speed of propagation for parabolic equations

17 May: Berezin transform and Toeplitz operators on polygonal domains

Speaker: Jari Taskinen, University of Helsinki

10 May: Optimal transport: Modeling, applications, and computational methods with multi-marginal graph-structure problems

Speaker: Axel RIngh, Chalmers University of Technology

Abstract: Optimal transport is a classical problem in mathematics, and the topic has seen rapid development over the last decades. In particular, there has recently been a surge of research related to applications of optimal transport in a number of different areas, as well as computational methods for numerically solving the problem. Today, the most well-known algorithm for solving the problem is arguably Sinkhorn’s method, also known by names such as the Sinkhorn-Knopp algorithm, the matrix balancing algorithm, the matrix scaling algorithm, iterative proportional fitting, and others.

In this talk, I will give a short introduction to optimal transport and to Sinkhorn’s method. I will also illustrate how different problems in, e.g., imaging, information fusion, and density optimal control can be formulated in the framework. Moreover, the underlying structure in some of these problems, such as barycenter problems, displacement interpolation problems, and multi-species density control problems, have led us to consider a generalization of the classical optimal transport problem, namely graph-structured multi-marginal optimal transport. In this talk, I will introduce this class of problems and show how Sinkhorn’s method can be extended to this problem class. However, in the multi-marginal setting, Sinkhorn’s method only partially alleviates the computational difficulty. This is because computing the corresponding projections needed in the method in a naïve fashion scales exponentially in the number of marginals. Nevertheless, I will present methods for how these projections can be efficiently compute when the underlying graph structure is, in some sense, simple. In particular, I will show how the projections can be computed in the case when the graph is a tree.

26 April: Pluripotential theory on Berkovich spaces

Speaker: Léonard Pille-Schneider, ENS Paris

Abstract: Berkovich spaces are an analog of complex manifolds/complex analytic spaces when the field of complex numbers is replaced by a non-archimedean field. They in particular enjoy nice topological properties, which contrasts with the ultrametric nature of the field. The goal of this talk is to explain how to perform (pluri)potential theory on those spaces, similar to the classical complex one. If time permits I will also present some applications to problems coming from differential geometry.

19 April: Pricing and Hedging of Financial Options using Backward Stochastic Differential Equations (BSDEs)

Speaker: Abigail Berta, Umeå University

Abstract: A financial option is a contractual agreement that grants the holder the right to buy or sell an underlying asset at a predetermined price within/at a specified time frame. Although there are analytical formulas available under certain restrictive assumptions and semi-analytical transform methods, such as the Fourier transform, that can be used when the characteristic function of the underlying asset process is known, many real-world problems are non-linear and cannot be solved analytically. Therefore, numerical methods are necessary to solve complex models and option types. The most common method used is Monte Carlo simulation, but it suffers from the curse of dimensionality when dealing with problems in multiple dimensions.

In this project, we aimed to numerically solve non-linear option pricing problems by utilizing Backward Stochastic Differential Equations (BSDEs). We employed Markovian BSDEs to formulate nonlinear pricing and hedging problems, which is crucial in pricing financial instruments as it enables the consideration of market imperfections and computations in high dimensions. The solutions to the processes involve conditional expectations. Thus, we employed the least squares Monte Carlo and deep neural network methods to approximate the solutions numerically.

5 April: Exponential Fermi Accelerator

Speaker: Davit Karaguylan, KTH Royal Institute of Technology (Mittag-Leffler participant)

Abstract: We consider a resonant Fermi accelerator, which is realized as a square billiard with a periodically oscillating platform. We combine tools from the theory of hyperbolic systems with singularities and probability theory to show that the set of initial conditions, for which the velocity of the particle goes to infinity, has an infinite Lebesgue measure. We also give estimates on the escape rate. This is joint work with Jing Zhou.

29 March: Large complex structure limits, polytopes and optimal transport

Speaker: Jakob Hultgren, Umeå University

Abstract: A cylindrical surface of soap film suspended between two circles will eventually snap if the circles are moved far enough apart. Similarly, if the data defining a complex algebraic manifold is adjusted in certain ways the manifold will break. Particularly severe cases of this are called large complex structure limits and these have proved to be very important both in theoretical physics (string theory, super symmetry) and algebraic geometry. A key insight of Yan Soibelman and Fields medalist Maxim Kontsevich is that large complex structure limits can be understood as the manifold collapsing onto the boundary of a polytope or, more generally, a simplicial complex. After giving a non-technical account covering some of this background I will explain that in order to get a finer understanding of it one is led to a partial differential equation on the boundary of a polytope and present the first general existence and uniqueness results for this equation (joint work with Mattias Jonsson, Enrica Mazzon and Nick McCleerey).

22 March: Leveraging concepts from stochastic simulation and machine learning for efficient Bayesian inference

Speaker: Ruth Baker, University of Oxford

Abstract: With the advent of a host of new experimental technologies, the last ten years has seen an explosion in the amount and types of quantitative data now being generated. In tandem, the mechanistic, mathematical models developed to interrogate these data have also grown in size and complexity. These detailed models have the potential to provide vital new insights into governing mechanisms. However, to achieve this goal requires meeting significant mathematical challenges in calibrating them to experimental data. In this talk, I will outline some of these challenges, and recent steps we have taken in addressing them.

15 March: Natural Almost Hermitian Structures on Conformally Foliated 4-Dimensional Lie Groups with Minimal Leaves

Speaker: Emma Andersdotter Svensson, Umeå University

Abstract: I will present my master’s thesis as well as give a brief introduction to Riemannian geometry. In the thesis, we let (G, g) be a 4-dimensional Riemannian Lie group with a 2-dimensional left-invariant, conformal foliation F with minimal leaves and adapt an almost Hermitian structure J on G to the foliation F. In 2014, S. Gudmundsson and M. Svensson showed that the corresponding Lie algebra of G must then belong to one of 20 families. In the thesis, we classify such structures J which are almost Kähler (AK), integrable (I) or Kähler (K). Hereby, we construct 16 multi-dimensional almost Kähler families, 18 integrable families and 11 Kähler families.

8 March: Random Weierstrass zeta functions

Speaker: Aron Wennman, Stockholm University

Abstract: In this talk, I will describe a construction of random meromorphic functions with prescribed simple poles with unit residues at a given stationary point process in the plane. These functions can be viewed as random analogues of the Weierstrass zeta function from the theory of elliptic functions, or equivalently as electric fields generated by an infinite random distribution of point charges.

I plan to describe for which point processes these electric fields, after subtracting the mean, become stationary, and discuss how they may be used to study the growth of the number variance (“charge fluctuations”) of stationary point processes in dilations of Jordan domains with quite irregular boundaries.

This talk is based on recent joint work with Misha Sodin and Oren Yakir (Tel Aviv)

1 March: Automorphic forms and their Fourier coefficients

Speaker: Henrik Gustafsson, Umeå University

Abstract: I will give a basic introduction to automorphic forms on reductive groups and their Fourier coefficients with respect to different unipotent subgroups. I will review a series of papers joint with Dmitry Gourevitch, Axel Kleinschmidt, Daniel Persson and Siddhartha Sahi for how these Fourier coefficients can be computed by a reduction principle. In particular, we have shown that they simplify drastically for automorphic forms in small automorphic representations, and I will give a brief overview of applications of this work to scattering amplitudes in string theory.

15 February: Determinantal point processes associated with Bergman kernels, construction and asymptotics

Speaker: Thibaut Lemoine, Université de Lille

Abstract: Determinantal point processes (DPP) are point processes whose correlation functions are expressed as the determinant of an integral kernel on the ambient space. They often appear in models of particles with repulsive interactions, such as fermions, and have been studied extensively in quantum mechanics and random matrix theory. In this talk, I will describe a class of such processes on compact Kähler manifolds, first described by Berman a decade ago, whose correlation kernel is the Bergman kernel of a positive line bundle. In particular, I will show how the asymptotic expansion of the Bergman kernel, initiated by Tian, Catlin and Zelditch in the late 90's, translates into a universality phenomenon for these DPP.

8 February: On the connectivity of branch loci of spaces of curves

Speaker: Milagros Izquierdo, Linköping University

Abstract: Since the 19th century the theory of Riemann surfaces has a central place in mathematics putting together complex analysis, algebraic and hyperbolic geometry, group theory and combinatorial methods. Since Riemann, Klein and Poincaré, among others, we know that a compact Riemann surface is a complex curve, and also the quotient of the hyperbolic plane by a Fuchsian group. In this talk we study the connectivity of the moduli spaces of Riemann surfaces (i.e in spaces of Fuchsian groups). Spaces of Fuchsian groups are orbifolds where the singular locus is formed by Riemann surfaces with automorphisms: the branch loci: With a few exceptions the branch loci is disconnected and consists of several connected components. This talk is a survey of the different methods and topics playing together in the theory of Riemann surfaces.

1 February: Adaptive evolutionary trajectories: from unicellularity to differentiated multicellularity and back again

Speaker: Hanna Isaksson, Umeå University

Abstract: There is a wide range of multicellularity that spans from simple cell clusters to plants and animals. Recent experiments show that simple forms of multicellularity can easily evolve de novo. However, the evolutionary trajectory towards increased complexity such as cell differentiation is not clear. Moreover, since these early forms of multicellularity are just a few mutations away from a unicellular ancestor, evolution might cause the groups to collapse back to unicellularity. Here we study the evolutionary trajectory from a unicellular ancestor to differentiated multicellularity in the context of an environment that periodically contains an abiotic stress. In environments where the stress is present cells are prevented from growth and die, but in environments without the stress cell populations grow exponentially. In response to this stress, cell populations may improve their fitness by either evolving multicellularity or differentiating into two phenotypes specialized to the two environmental states. Importantly both of these responses have associated costs via a time delay in switching between phenotypes or in forming multicellular groups. We use a combination of dynamical models and simulations to study the evolutionary trajectory of unicellular populations adapting to abiotic stress. We find that these trajectories are heavily influenced by historical contingency and often included iterations where complexity is repeatedly gained and lost. Thus we find that the initial selective driver for the evolution of multicellularity may not be enough to sustain it towards ever increasing complexity.

25 January: Weighted and graded pluripotential theory

Speaker: Álfheiður Edda Sigurðardóttir, University of Iceland

Abstract: The Green function has a higher dimensional version called the pluricomplex Green function. The Siciak-Zakharjuta theorem states that the pluricomplex Green function is equal to the Siciak function, which is written in terms of polynomials. The usual grading of polynomials is the smallest dilate of the unit simplex containing its support. If the unit simplex is replaced by any compact convex set, a new grading of polynomials arises and a new Siciak function. We study when a generalization of the Siciak-Zakharjuta theorem applies in this setting.

18 January: Essential positivity

Speaker: Antti Perälä, Umeå university

Abstract: We define essentially positive operators on Hilbert space as a class of self-adjoint operators whose essential spectra is contained in the nonnegative real numbers and describe their basic properties. Using Toeplitz operators and the Berezin transform, we further illustrate the notion of essential positivity in the Hardy space and the Bergman space. This is a joint work with Jani Virtanen.

2022

14/12/2022 Christmas Workshop in Mathematical Modelling and Analysis

Carl Lundholm, Umeå university
Niklas Lundström, Umeå university 
Eric Libby, Umeå university 

7/12/2022 Per-Håkan Lundow, Umeå University, The Ising model, p,q-binomials and two special functions

30/11/2022 Gohar Aleksanyan, University of Helsinki, On the regularity theory of the optimal switching problem

23/11/2022 Jan Wiegerinck, University of Amsterdam, Pluripolar hulls and fine holomorphy

16/11/2022 Christian Ewald, Umeå University, Beating the Market by Trading Energy

9/11/2022 Sebastian Throm, Umeå university, Self-similar long-time behaviour for kinetic equations

2/11/2022 Anton Frisk Kockum, Chalmers University of Technology, Quantum state and process tomography with machine learning and gradient descent

26/10/2022 Jimmy Aronsson, Chalmers University of Technology, Group- and gauge-equivariant CNNs

19/10/2022 Kehe Zhu, SUNY Albany, The Bargmann transform

12/10/2022 Jakob Hultgren, Umeå University, Optimal transport, super resolution and star cluster identification

5/10/2022 Ryan O’Loughlin, University of Leeds, Symbols of compact truncated Toeplitz operators

28/9/2022 Axel Flinth, Umeå University, In Search of Projectively Equivariant Neural Networks

21/9/2022 Siyang Wang, Umeå University, Computational wave propagation by finite differences

14/9/2022 Åke Brännström, Umeå University, Introduction to adaptive dynamics

8/6/2022 Summer Workshop in Mathematical Modelling and Analysis

Pekka Nieminen, University of Turku, Review of Shapiro–Sundberg compactness problem for composition operators

Alessandro Milazzo, Uppsala University, Dynamic programming principle for classical and singular stochastic control with discretionary stopping

Jesper Singh, Umeå University, Estimates of p-harmonic functions in planar sectors

Fredrik Ohlsson, Umeå University, Equivariance versus Augmentation for Learning on the Sphere

1/6/2022 Benny Avelin, Uppsala University, Boundary behavior of the p-parabolic equation

25/5/2022 Johannes Borgqvist, University of Oxford, Occam's razor gets a new edge: the use of symmetries in model selection

18/5/2022 Andreas Granath, Umeå University, On the equivalence between the Cauchy-Riemann and the planar elastostatic equation

11/5/2022 Daniel Persson, Chalmers University of Technology, Emergent geometry and quantum gravity

4/5/2022 Marcin Sroka, Chalmers University of Technology and Jagiellonian University, Quaternionic PDEs

27/4/2022 Anders Karlsson, Uppsala University, A metric functional analysis and applications in deep learning

6/4/2022 Jonas Westin, Umeå University, Running on the beach – a dynamic analysis of Hotelling’s stability in competition

30/3/2022 Matias Vestberg, Uppsala university, Solving the Dirichlet problem for the Monge-Ampère equation using neural networks

23/3/2022 Mårten Nilsson, Faculty of engineering, Lund University, Unbounded envelopes of plurisubharmonic functions

16/3/2022 Workshop in Mathematical Modelling and Analysis

Marcus Olofsson, Umeå university, Playing games with ghosts

Per Åhag, Umeå university, Urban Cegrell - a mathematical artist

Santeri Miihkinen, Umeå university, On the exponential integrability of conjugate functions

23/2/2022 Alex Bergman, Lund University, An elementary proof of a Riesz-Thorin type Theorem for the Hardy space

16/2/2022 Rafal Czyz, Jagiellonian University, On a family of quasimetric spaces in generalized potential theory

2/2/2022 Sudeb Majee, Umeå university, An overview of PDE based approach to image restoration

2021

01/12/2021 Oleg Ivrii, Tel Aviv University, TBA, Critical values of inner functions

24/11/2021 María Martín, University of La Laguna, TBA, On the solutions of the incompressible Euler equations

27/10/2021 Fredrik Ohlson, Umeå University, Symmetries in deep learning: Group equivariant neural networks

06/10/2021 Jarno Talponen, University of Helsinki / OP Financial Group, On volatility smile and an investment strategy with European style out-of-the-money calls

29/09/2021 Antti Perälä, Umeå University, Estimating the norm of the Bergman projection

22/09/2021 Setareh Eskandari, Imam Khomeini International University/Umeå University, On some sub-Hilbert spaces in the weighted Bergman spaces

12/05/2021 Kristoffer Lindensjö, Stockholm University, How to detect a salami slicer: a stochastic controller-stopper game with unknown competition

05/05/2021 Daniel Seco, University Carlos III of Madrid, Zeros of optimal polynomial approximants in $\ell^p_A$

28/04/2021 Benny Avelin, Uppsala University, Approximation of BV functions using neural networks

21/04/2021 Malte Litsgård, Uppsala University, Degenerate Kolmogorov-type equations with rough coefficients - Potential theory and boundary regularity

07/04/2021 Hanna Isaksson, Umeå University, The consequences of budding versus binary fission on adaptation and aging in primitive multicellularity

24/03/2021 Torsten Lindström, Destabilization, stabilization, and multiple attractors in saturated mixotrophic environments,

17/03/2021 Janne Gröhn, University of Eastern Finland, Converse growth estimates for ODEs with slowly growing solutions

10/03/2021 Sauli Lindberg, Aalto University, Nonlinear versions of the open mapping theorem

24/02/2021 Petar Melentijevic, University of Belgrade, Best constants in inequalities concerning analytic and co-analytic projections and M. Riesz theorem for various function spaces

17/02/2021 Fredrik Ohlsson, Umeå University, Symmetries of differential equations and structural model selection: A biochemical example

10/02/2021 Jari Taskinen, University of Helsinki, Essential spectra of some periodic elliptic boundary value problems

03/02/2021 Håkan Hedenmalm, KTH Royal Institute of Technology, Gaussian analytic functions and operator symbols of Dirichlet type

2020

09/12/2020 Antti Perälä, Umeå University, Integration operators from Bergman spaces to Hardy spaces of the unit ball

02/12/2020 Aron Persson, Uppsala University, On Complex Manifold-like Polyfolds

18/11/2020 Tuomas Sahlsten, University of Manchester, Delocalisation of Laplace-Beltrami eigenfunctions and quantum chaos on random surfaces

11/11/2020 Jani Virtanen, University of Reading, Schatten class Hankel operators on the Segal-Bargmann space and the Berger-Coburn phenomenon

04/11/2020 Istvan Prause, Random tilings, variational problems and harmonicity

28/10/2020 Santeri Miihkinen, The infinite Hilbert matrix on spaces of analytic functions

07/10/2020 Marcus Olofsson, Management of ROR hydro power -an optimal switching approach

2019

06/12/2019 Workshop in Mathematical Modelling and Analysis, 13.15-17.30, organised by Niklas Lundström 

17/04/2019  Åke Brännström, Eco-evolutionary modeling of diversification and speciation

10/04/2019 Tord Sjödin, Gamma distributions, generalized gamma convolutions and related problema

03/04/2019 Niklas Lundström, Estimates for viscosity solutions of nonhomogeneous fully nonlinear elliptic PDEs

2017

​24.05.2017, 14.15-15.00, Conference room, Tord Sjödin, Potential theory and polar sets in homogeneous spaces.

​17.05.2017, 14.15-15.00, MA356, Gunnar Söderbacka, Åbo akademi, Behaviour of many predators - one prey systems.

05.04.2017, 14.15-15.00, Conference room, Åke Brännström, Umeå University, Evolution of infectious diseases in seasonal environments​.

15.03.2017, 14.00-14.45, MA136, Lisa Hed, Umeå University, On m-regular domains within the Caffarelli-Nirenberg-Spruck model.

08.03.2017, 14.15-15.00, MA356, Niklas Lundström, Umeå University, How to find simple stability measures in nonlinear dynamics.

08.02.2017, 14.15-15.00, MA346, Britt-Marie Stocke, Umeå University, Matematikerna, ett broderskap?

25.01.2017, 14.15-15.00, MA378, Tord Sjödin, Umeå University, Almost everywhere differentiability of metric projection on closed sets.

10.01.2017, 14.15-15.00, MA346, Niklas Lundström, Umeå University, Construction of viscosity solutions to systems of non-local PDEs with interconnected obstacles.

2016

30.11.2016, 14.15-15.00, Conference room, Jonas Wickman, Umeå University, Evolutionary consequences of spatially heterogeneous productivity in a food web.

16.11.2016, 14.15-15.00, Conference room, Olli Toivanen, Umeå University, Generalizations of Lebesgue spaces.

02.11.2016, 14.15-15.00, Conference room, Åke Brännström, Umeå University, Branch-thinning explains the large-scale, self-similar structure of plants​.

04.05.2016, 14.15-15.00, MA346, Thomas Ernst, Uppsala University, On the borderline between analysis and algebra, or a brief overview of q-calculus.

20.04.2016, 14.15-15.00, MA346, Niklas Lundström, Umeå University, Pareto-efficient harvesting strategies for stage-structured populations.

06.04.2016, 14.15-15.00, MA356, Erik Alden, Umeå University, Familjer av momentproblem, entudighet/mångtydighet och täthetssatser.

16.03.2016, 13.15-14.00, MA346, Thomas Önskog, KTH, Time series analysis of the North Atlantic Oscillation.

03.02.2016, 14.15-15.00, MA346, Erik Alden, Umeå University, Tillräckliga villkor för entydighet/mångtydighet av momentproblem - täthetssatser. En kort historik inleder.

2015

16.12.2015, 14.15-15.00, N330, Video seminar, Structured population models in metric spaces.

02.12.2015, 14.15-15.00, MA346, Lai Zhang, Umeå University, Additive noise driven phase transitions in a plankton system.

18.11.2015, 14.15-15.00, Conference room, Jonas Wickman, Umeå University, Comparison of two evolutionary models in spatially structured populations: A system of two PDEs becoming a PDE-ODE system in a parameter limit.

04.11.2015, 14.15-15.00, N330, Magnus Lindh, Ume University, Constrained growth flips the direction of optimal phenological responses among annual plants.

21.10.2015, 14.15-15.00, Conference room, Niklas Lundström, Umeå University, The p-Laplace equation and some results of Phragmen-Lindelöf type.

07.10.2015, 14.15-15.00, MA346, Marcus Olofsson, Umeå University, An introduction to optimal switching problems.