Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Tomographic Inverse Problems: Theory and Applications
No full textThis was the tenth Oberwolfach conference on the
mathematics of tomography. The field rests on the interplay between
the theoretical and applied; practical questions lead to new
mathematics and pure mathematics motivates new algorithms. This
workshop encompassed classical areas such as X-ray computed tomography
(CT) as well as new modalities and applications such as dynamic
imaging, Compton scattering tomography, hybrid imaging, optical
tomography or multi-energy CT and addressed inter alia the use of
methods from machine learning
Experimenting with Symplectic Hypergeometric Monodromy Groups
No full textWe present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results are obtained by extending our previous algorithms for Zariski dense groups, based on the strong approximation and congruence subgroup properties
Group-Graded Rings Satisfying the Strong Rank Condition
No full textA ring satisfies the (SRC) if, for every natural number , the free -submodules of all have rank . Let be a group and a ring strongly graded by such that the base ring is a domain. Using an argument originated by Laurent Bartholdi for studying cellular automata, we prove that satisfies SRC if and only if
satisfies SRC and is amenable. The special case of this result for group rings allows us to prove a characterization of amenability involving the group von Neumann algebra that was conjectured by Wolfgang Lück. In addition, we include two applications to the study of group rings and their modules
The First Hochschild Cohomology as a Lie Algebra
No full textIn this paper we study sufficient conditions for the solvability of the first Hochschild cohomology of a finite dimensional algebra as a Lie algebra in terms of its Ext-quiver in arbitrary characteristic. In particular, we show that if the quiver has no parallel arrows and no loops then the first Hochschild cohomology is solvable. For quivers containing loops, we determine easily verifiable sufficient conditions for the solvability of the first Hochschild cohomology. We apply these criteria to show the solvabilty of the first Hochschild cohomology space for large families of algebras, namely, several families of self-injective tame algebras including all tame blocks of finite groups and some wild algebras including quantum complete intersections
Mathematical Foundations of Isogeometric Analysis
No full textIsogeometric analysis is a recent technology for numerical simulation, unifying computer aided design and finite element analysis. It offers a true design-through-analysis pipeline by employing the same representation models for both creating geometries and approximating the solution of partial differential equations defined on those geometries. This combined concept leads to improved convergence and smoothness properties of the solutions and dramatically faster overall simulations.
Even though substantial progress has been made in the isogeometric context over the last few years, there are several profound theoretical issues that are not yet well understood and that
are currently investigated by researchers in numerical analysis, approximation theory, and applied geometry.
The workshop reported the substantial progress, both from the theoretical and applicative point of view, which has been made in the isogeometric context over the last three years. It offered a meeting point for leading scientists from isogeometric analysis and the mentioned mathematically relevant fields, and provided a rich and open ground of discussion within a diversified audience, profiting of different backgrounds and various perspectives
Mathematical Methods in Quantum Molecular Dynamics
No full textThe workshop on "Mathematical Methods in Quantum Molecular Dynamics" has brought together chemists, mathematicians, and physicists developing new mathematical methods for studying the motion of atoms in molecules and in reacting chemical systems.
Thereby, the main focus was on dynamical properties of quantum molecular systems in many dimensions.
The development of mathematical methods for quantum molecular systems is an intrinsically interdisciplinary field of research, whose progress can be improved by opening additional channels of communication between the different disciplines.
The workshop has contributed to advance the exchange of ideas related to development of new methods as well as the creation of personal links between mathematicians and theorists in chemistry and physics
On Logic, Choices and Games
No full textCan we always mathematically formalise our taste
and preferences? We discuss how this has been done
historically in the field of game theory, and how recent
ideas from logic and computer science have brought
an interesting twist to this beautiful theory
Snake graphs, perfect matchings and continued fractions
No full textA continued fraction is a way of representing a real
number by a sequence of integers. We present a new
way to think about these continued fractions using
snake graphs, which are sequences of squares in the
plane. You start with one square, add another to
the right or to the top, then another to the right or
the top of the previous one, and so on. Each continued
fraction corresponds to a snake graph and vice
versa, via “perfect matchings” of the snake graph. We
explain what this means and why a mathematician
would call this a combinatorial realization of continued
fractions
Time Discretization Schemes for Hyperbolic Systems on Networks by ε-Expansion
No full textWe consider partial differential equations on networks with a small parameter , which are hyperbolic for and parabolic for . With a combination of an -expansion and Runge-Kutta schemes for constrained systems of parabolic type, we derive a new class of time discretization schemes for hyperbolic systems on networks, which are constrained due to interconnection conditions. For the analysis we consider the coupled system equations as partial differential-algebraic equations based on the variational formulation of the problem. We discuss well-posedness of the resulting systems and estimate the error caused by the -expansion