Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Fokus-Erkennung bei Epilepsiepatienten mithilfe moderner Verfahren der Zeitreihenanalyse
No full textViele epileptische Anfälle entstehen in einer begrenzten Region im Gehirn, dem sogenannten Anfallsursprung. Eine chirurgische Entfernung dieser Region kann in vielen Fällen zu Anfallsfreiheit führen. Aus diesem Grund ist die Frage nach der Lokalisation des Anfallsursprungs aus EEG-Aufzeichnungen wichtig. Wir beschreiben hier ein Verfahren zur Lokalisation des Anfallsursprungs mittels Zeitreihenanalyse, das auf der Schätzung von Spektren im EEG beruht
Swarming robots
No full textWhen lots of robots come together to form shapes, spread in an area, or move in one direction, their motion has to be planned carefully. We discuss how mathematicians devise strategies to help swarms of robots behave like an experienced, coordinated team
Mini-Workshop: Applied Koopmanism
No full textKoopman and Perron–Frobenius operators are linear operators that encapsulate dynamics of nonlinear dynamical systems without loss of information. This is accomplished by embedding the dynamics into a larger infinite-dimensional space where the focus of study is shifted from trajectory curves to measurement functions evaluated along trajectories and densities of trajectories evolving in time. Operator-theoretic approach to dynamics shares many features with an optimization technique: the Lasserre moment–sums-of-squares (SOS) hierarchies, which was developed for numerically solving non-convex optimization problems with semialgebraic data. This technique embeds the optimization problem into a larger primal semidefinite programming (SDP) problem consisting of measure optimization over the set of globally optimal solutions, where measures are manipulated through their truncated moment sequences. The dual SDP problem uses SOS representations to certify bounds on the global optimum. This workshop highlighted the common threads between the operator-theoretic dynamical systems and moment–SOS hierarchies in optimization and explored the future directions where the synergy of the two techniques could yield results in fluid dynamics, control theory, optimization, and spectral theory
Prime tuples in function fields
No full textHow many prime numbers are there? How are they distributed among other numbers? These are questions that have intrigued mathematicians since ancient times. However, many questions in this area have remained unsolved, and seemingly unsolvable in the forseeable future. In this snapshot, we will discuss one such problem, the Twin Prime Conjecture, and a quantitative version of it known as the Hardy–Littlewood Conjecture. We will also see that these and other questions about prime numbers can be extended to questions about function fields, and discuss recent progress which has been made to answer them in this context
Mini-Workshop: New Interactions between Homotopical Algebra and Quantum Field Theory
No full textRecent developments in quantum field theory strongly call for techniques from homotopical algebra to develop the mathematical foundations of quantum gauge theories. This mini-workshop brought together experts working at the interface between topological field theory, quantum field theory and homotopical algebra with the goal of triggering major advances towards understanding quantum gauge theory. This was achieved via a fruitful exchange of ideas and technologies across different research communities and encouraging a comparison between recent approaches to homotopical quantum field theory
Topological Recursion and TQFTs
No full textThe topological recursion is an ubiquitous structure in enumerative geometry of surfaces and topological quantum field theories. Since its invention in the context of matrix models, it has been found or conjectured to compute intersection numbers in the moduli space of curves, topological string amplitudes, asymptotics of knot invariants, and more generally semiclassical expansion in topological quantum field theories. This workshop brought together mathematicians and theoretical physicists with various background to understand better the underlying geometry, learn about recent advances (notably on quantisation of spectral curves, topological strings and quantum gauge theories, and geometry of moduli spaces) and discuss the hot topics in the area
Real group orbits on flag ind-varieties of SL (∞, C)
No full textOWLF 2015We consider the complex ind-group and its real forms , , , . Our main object of study are the -orbits on an ind-variety for an arbitrary splitting parabolic ind-subgroup , under the assumption that the subgroups and are aligned in a natural way. We prove that the intersection of any -orbit on with a finite-dimensional flag variety from a given exhaustion of via for , is a single ()-orbit. We also characterize all ind-varieties on which there are finitely many -orbits, and provide criteria for the existence of open and close -orbits on in the case of infinitely many -orbits
Calculus of Variations
No full textThe Calculus of Variations is subject with a long and distinguished history, a great deal of diverse current activity, and close connections to other fields such as geometry and mathematical physics. The July 2016 workshop on the Calculus of Variations presented research that resolved long-standing conjectures, shed new light on classical results, pointed toward new research directions, and displayed progress on a range of aspects, classical and otherwise, of the Calculus of Variations
Computational Group Theory
No full textThis was the seventh workshop on Computational Group Theory. It showed that Computational Group Theory has significantly expanded its range of activities. For example, symbolic computations with groups and their representations and computations with infinite groups play a major role nowadays. The talks also presented connections and applications to cryptography, number theory and the algorithmic theory of algebras
Mini-Workshop: Max Dehn: his Life, Work, and Influence
No full textThis mini-workshop is part of a long-term project that aims to produce a book documenting Max Dehn’s singular life and career. The meeting brought together scholars with various kinds of expertise, several of whom gave talks on topics for this book. During the week a number of new ideas were discussed and a plan developed for organizing the work. A proposal for the volume is now in preparation and will be submitted to one or more publishers during the summer of 2017