Research Seminars in Mathematics
The research seminars are in the subjects of pure, applied, and computational mathematics and are usually held at the afternoons on Fridays. All are welcome to attend!
Speaker: Massimiliano Fasi, Durham University, UK
Date: Friday, October 15, at 13.15, Zoom meeting
Title: CPFloat: A C Library for Emulating Low-Precision Arithmetic
Abstract: Low-precision floating-point arithmetic can be simulated via software by executing each arithmetic operation in hardware and rounding the result to the desired number of significant bits. For IEEE-compliant formats, rounding requires only standard mathematical library functions, but handling subnormals, underflow, and overflow demands special attention, and numerical errors can cause mathematically correct formulae to behave incorrectly in finite arithmetic. Moreover, the ensuing algorithms are not necessarily efficient, as the library functions these techniques build upon are typically designed to handle a broad range of cases and may not be optimized for the specific needs of floating-point rounding algorithms. CPFloat is a C library that offers efficient routines for rounding arrays of binary32 and binary64 numbers to lower precision. The software exploits the bit level representation of the underlying formats and performs only low-level bit manipulation and integer arithmetic, without relying on costly library calls. In numerical experiments the new techniques bring a considerable speedup (typically one order of magnitude or more) over existing alternatives in C, C++, and MATLAB. To the best of our knowledge, CPFloat is currently the most efficient and complete library for experimenting with custom low-precision floating-point arithmetic available in any language.
Speaker: Hugo U.R. Strand, Örebro University
Date: Friday, September 17, at 13.15, Zoom meeting
Title: Hands-on high-order orthogonal-polynomial methods for an integrodifferential equation
Abstract: High-order orthogonal-polynomial approximation methods and their application is still an evolving field in numerical mathematics . Recent advances has enabled extreme high-order approximations  and new algorithmic developments has opened the door for applications on integral equations .
In this talk we will present an application of these methods to the integrodifferential "Dyson" equation, that appears in the context of perturbation theory in many-body quantum physics .
 S. Olver, R.M. Slevisksy, A. Townsend, Acta Numerica pp. 573-699 (2020)
 I. Boagert, SIAM J. Sci. Comput., v36 no. 3 pp. A1008-A1026 (2014)
 N. Hale, A. Townsend, SIAM J. Sci. Comput., v36 no. 3 pp. A1207-A1220 (2014)
 X. Dong, D. Zgid, E. Gull, H.U.R. Strand, J. Chem. Phys. 152, 134107 (2020)
Speaker: Attila Szilva, Uppsala University
Date: Friday, May 7, at 13.15, Zoom meeting
Title: From elections to science of cities: an introduction to complexity
Abstract: Animals from rats to the blues whales are built up from cells arranged in networks. The topology of the underlying networks explains the so-called Kleiber’ scaling law, which states that an animal's metabolic rate scales to the ¾ power of the animal's mass (a cat having a mass 100 times that of a mouse will consume only about 32 times the energy the mouse uses). This scaling is sublinear because the power is less than 1. In the presentation, it will be shown that the infrastructure of cities (the length of electric cables or the number of gas stations) also follows universal sublinear scaling law while in socio-economic dimensions (GDP per capita, innovation, crime) cities are superlinear. They are as a result of the individual interactions proven by a large set of mobile phone data. The concept of scaling and universality is originated in statistical physics where a large complex system emerges from simple interactions, and its behavior is almost totally independent of its microscopic structure. Another examples are the democratic elections for which physics inspired models will be also discussed in the presentation.
The talk is based mostly on the books of Geoffrey West: Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies and Stefan Thurner, Rudolf Hanel and Peter Klimek: Introduction to the theory of complex systems and the paper Social influence with recurrent mobility and multiple options by Jerome Michaud and Attila Szilva published in Physical Review E 97 (6), 062313.
Speaker: Jakob Palmkvist, Örebro University
Date: Friday, April 9, at 13.15, Zoom meeting
Title: Infinite-dimensional Lie superalgebras
Abstract: I will review how the classification of simple finite-dimensional Lie algebras leads to the construction of contragredient Lie algebras, which in general are infinite-dimensional, and how these can be further generalised to contragredient Lie superalgebras. I will then explain how a modification of the construction gives rise to a new class of non-contragredient Lie superalgebras, called tensor hierarchy algebras, whose finite-dimensional members are the simple Lie superalgebras of Cartan type. Tensor hierarchy algebras have proven useful in describing gauge structures in physical models related to string theory. I will describe some of the remarkable features they exhibit.
Speaker: Maria ElGhaoui, Sorbonne University, Paris (France) and Saint Joseph University, Beirut (Lebanon)
Date: Friday, March 5, at 13.15, Zoom meeting
Title: A Trefftz Method With Reconstruction of The Normal Derivative Applied to Elliptic Equations
Abstract: There are many classical numerical methods for solving boundary value problems on general domains. The Trefftz method is an approximation method for solving linear boundary value problems arising in applied mathematics and engineering sciences. This method consists to approximate the exact solution through a linear combination of trial functions satisfying exactly the governing differential equation. One of the advantages of this method is that the number of trial functions per cell is O(m), asymptotically much less than the quadratic estimate O(m^2) for finite element and discontinuous Galerkin approximations.
For a Laplace model equation, we present a high order Trefftz method with quadrature formula for calculation of normal derivative at interfaces. We introduce a discrete variational formulation and study the existence and uniqueness of the discrete solution. A priori error estimate is then established and finally, several numerical experiments are shown
Speaker: Mårten Gulliksson, Örebro University
Date: Friday, February 5, at 13.15, Zoom meeting
Title: My Least Squares Problems
Abstract: During a period of more than 30 years I have now and then worked with different kinds of least squares problems. These include simple linear least squares in different settings but also much more abstract ill-posed nonlinear problems in Hilbert spaces. Some of the problems were applied such as, e.g., surface fitting, neural networks, and estimating elastic properties in paper. Others were more theoretical in nature involving convergence aspects of methods, perturbation theory, and sparsity. The talk will end with some open least squares problems.