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• 1.
Champlain College.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
Quaternionic modular forms and exceptional sets of hypergeometric functions2015In: International Journal of Number Theory, ISSN 1793-0421, Vol. 11, no 2, p. 631-643Article in journal (Refereed)

We determine the exceptional sets of hypergeometric functions corresponding to the(2, 4, 6) triangle group by relating them to values of certain quaternionic modular formsat CM points. We prove a result on the number fields generated by exceptional values, and by using modular polynomials we explicitly compute some examples.

• 2.
Karlstad University, Faculty of Health, Science and Technology (starting 2013).
Karlstad University, Faculty of Health, Science and Technology (starting 2013). Stockholm University. Stockholm University. Stockholm University.
Growth Histories in Bimetric Massive Gravity2012In: Journal of Cosmology and Astroparticle Physics, ISSN 1475-7516, E-ISSN 1475-7516, no 12, article id 021Article in journal (Refereed)

We perform cosmological perturbation theory in Hassan-Rosen bimetric gravity for general homogeneous and isotropic backgrounds. In the de Sitter approximation, we obtain decoupled sets of massless and massive scalar gravitational fluctuations. Matter perturbations then evolve like in Einstein gravity. We perturb the future de Sitter regime by the ratio of matter to dark energy, producing quasi-de Sitter space. In this more general setting the massive and massless fluctuations mix. We argue that in the quasi-de Sitter regime, the growth of structure in bimetric gravity differs from that of Einstein gravity.

• 3.
Karlstad University, Faculty of Technology and Science, Department of Mathematics.
Half-Space Problem for the Discrete Boltzmann Equation: Condensing Vapor Flow in the Presence of a Non-condensable Gas2012In: Journal of statistical physics, ISSN 0022-4715, E-ISSN 1572-9613, Vol. 147, no 6, p. 1156-1181Article in journal (Refereed)

We consider a non-linear half-space problem related to the condensation problem for the discrete Boltzmann equation and extend some known results for a single-component gas to the case when a non-condensable gas is present. The vapor is assumed to tend to an assigned Maxwellian at infinity, as the non-condensable gas tends to zero at infinity. We assume that the vapor is completely absorbed and that the non-condensable gas is diffusively reflected at the condensed phase and that the vapor molecules leaving the condensed phase are distributed according to a given distribution. The conditions, on the given distribution, needed for the existence of a unique solution of the problem are investigated. We also find exact solvability conditions and solutions for a simplified six+four-velocity model, as the given distribution is a Maxwellian at rest, and study a simplified twelve+six-velocitymodel.

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• 4.
Department of Physics, Nanjing University, 22 Hankou Road, Nanjing, 210093, China.
Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering. Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering.
RCFT with defects: Factorization and fundamental world sheets2012In: Nuclear Physics B, ISSN 0550-3213, E-ISSN 1873-1562, Vol. 863, p. 213-259Article in journal (Refereed)

It is known that for any full rational conformal field theory, the correlation functions that are obtained bythe TFT construction satisfy all locality, modular invariance and factorization conditions, and that there isa small set of fundamental correlators to which all others are related via factorization – provided that theworld sheets considered do not contain any non-trivial defect lines. In this paper we generalize both resultsto oriented world sheets with an arbitrary network of topological defect lines.

• 5.
Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering.
Karlstad University, Faculty of Technology and Science, Department of Physics and Electrical Engineering.
Modular invariant Frobenius algebras from ribbon Hopf algebra automorphisms2012In: Journal of Algebra, ISSN 0021-8693, E-ISSN 1090-266X, Vol. 363, p. 29-72Article in journal (Refereed)

For any finite-dimensional factorizable ribbon Hopf algebra H and any ribbon automorphism of H, we establish the existence of thefollowing structure: an H-bimodule Fω and a bimodule morphism Zω from Lyubashenko’s Hopf algebra object K for the bimodulecategory to Fω. This morphism is invariant under the natural actionof the mapping class group of the one-punctured torus on thespace of bimodule morphisms from K to Fω. We further showthat the bimodule Fω can be endowed with a natural structureof a commutative symmetric Frobenius algebra in the monoidalcategory of H-bimodules, and that it is a special Frobenius algebra iff H is semisimple.The bimodules K and Fω can both be characterized as coends ofsuitable bifunctors. The morphism Zω is obtained by applying amonodromy operation to the coproduct of Fω; a similar constructionfor the product of Fω exists as well. Our results are motivated by the quest to understand the bulkstate space and the bulk partition function in two-dimensionalconformal field theories with chiral algebras that are not necessarily semisimple

• 6.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
The discriminant 10 Shimura curve and its associated Heun functions2016In: Bulletin of the London Mathematical Society, ISSN 0024-6093, E-ISSN 1469-2120, Vol. 48, p. 957-967Article in journal (Refereed)

The Shimura curve of discriminant 10 is uniformized by a subgroup of an arithmetic $(2,2,2,3)$ quadrilateral group. We derive the differential structure of the ring of modular forms for the Shimura curve and relate the ring generators to explicit Heun functions for the quadrilateral group. We also show that the Picard–Fuchs equation of the associated family of abelian surfaces has solutions that are modular forms. These results are used to completely describe the exceptional sets of the Heun functions, and we show how to find examples like $Hl\left(\frac{27}{2},\frac{7}{36}; \frac{1}{12},\frac{7}{12},\frac{2}{3},\frac{1}{2}; -\frac{96}{25}\right)=\frac{2^{1/2}5^{2/3}}{3^{4/3}}.$

• 7.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science (from 2013).
Concordia University, Canada.
Differential equations and expansions for quaternionic modular forms in the discriminant 6 case2012In: LMS Journal of Computation and Mathematics, ISSN 1461-1570, E-ISSN 1461-1570, Vol. 15, p. 385-399Article in journal (Refereed)

We study the differential structure of the ring of modular forms for the unit group of the quaternion algebra over Q of discriminant 6. Using these results we give an explicit formula for Taylor expansions of the modular forms at the elliptic points. Using appropriate normalizations we show that the Taylor coefficients at the elliptic points of the generators of the ring of modular forms are all rational and 6-integral. This gives a rational structure on the ring of modular forms. We give a recursive formula for computing the Taylor coefficients of modular forms at elliptic points and, as an application, give an algorithm for computing modular polynomials.

• 8.
Karlstad University, Faculty of Health, Science and Technology (starting 2013), Department of Mathematics and Computer Science.
My First Meetings with Konstantin Oskolkov2013In: Recent Advances in Harmonic Analysis and Applications: In honor of Konstantin Oskolkov / [ed] Dmitriy Bilyk, Laura De Carli, Alexander Petukhov, Alexander M. Stokolos, Brett D. Wick, Springer, 2013, 1, Vol. 25, p. 27-29Chapter in book (Refereed)

This note tells about our first meetings with Konstatin Oskolkov. We discuss also optimal estimates of the rate of convergence of Fourier series obtained by Oskolkov in 1975.

• 9.
Karlstad University.
Representations of finite groups2017Independent thesis Basic level (degree of Bachelor), 10 credits / 15 HE creditsStudent thesis

Representation theory is concerned with the ways of writing elements of abstract algebraic structures as linear transformations of vector spaces. Typical structures amenable to representation theory are groups, associative algebras and Lie algebras. In this thesis we study linear representations of finite groups. The study focuses on character theory and how character theory can be used to extract information from a group. Prior to that, concepts needed to treat character theory, and some of their ramifications, are investigated. The study is based on existing literature, with excessive use of examples to illuminate important aspects. An example treating a class of p-groups is also discussed.

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