Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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GAP Functionality for Zariski Dense Groups
No full textoai:publications.mfo.de:mfo/1321Research in Pairs 2017In this document we describe the functionality of GAP [4] routines for Zariski dense or arithmetic groups that are developed in [1, 2, 3]. The research underlying the software was supported through the programme "Research in Pairs", at the Mathematisches Forschungsinstitut Oberwolfach, and part of the software was written during a stay in June 2017. The hospitality we received has been greatly appreciated. Our research was also supported by a Marie Sklodowska-Curie Individual Fellowship grant under Horizon 2020 (EU Framework Programme for Research and Innovation), and a Simons Foundation Collaboration Grant Nr. 244502. All support is acknowledged with gratitude
Some Results on Reducibility of Parabolic Induction for Classical Groups
No full textResearch in Pairs 2016Given a (complex, smooth) irreducible representation of the general
linear group over a non-archimedean local field and an irreducible
supercuspidal representation of a classical group, we show that the
(normalized) parabolic induction is reducible if there
exists in the supercuspidal support of such that
is reducible. In special cases we also give irreducibility
criteria for when the above condition is not satisfied
Material Theories
No full textMaterial theories is a series of workshops concerned with a broad range of topics related to the mechanics and mathematics of materials. As such, this edition brought together researchers from diverse fields converging toward the interaction between mathematics, mechanics, and material science
An Extension Problem and Trace Hardy Inequality for the Sublaplacian on H-Type Groups
No full textMSC: 35R03; 22E25; 22E46; 35C15; 35J25Research in Pairs 2017In this paper we study the extension problem for the sublaplacian on a H-type group and use the solutions to prove trace Hardy and Hardy inequalities for fractional powers of the sublaplacian
Mini-Workshop: Lattice Polytopes: Methods, Advances, Applications
No full textLattice polytopes arise naturally in many different branches of pure and applied mathematics such as number theory, commutative algebra, combinatorics, toric geometry, optimization, and mirror symmetry. The miniworkshop on “Lattice polytopes: methods, advances, applications” focused on two current hot topics: the classification of lattice polytopes with few lattice points and unimodality questions for Ehrhart polynomials. The workshop consisted of morning talks on recent breakthroughs and new methods, and afternoon discussion groups where participants from a variety of different backgrounds explored further applications, identified open questions and future research directions, discussed specific examples and conjectures, and collaboratively tackled open research problems
Automorphic Forms and Arithmetic
No full textThe workshop brought together leading experts and young researchers at the interface of automorphic forms and analytic number theory to disseminate, discuss and develop important recent methods and results. A particular focus was on higher rank groups, as well as their arithmetic applications. This includes, for instance, the study of various aspects of -functions, the fine distribution properties of their Fourier coefficients and Hecke eigenvalues, the mass distribution of automorphic forms on general symmetric spaces, and applications of results of algebraic geometry to automorphic forms
Mini-Workshop: Reflectionless Operators: The Deift and Simon Conjectures
No full textReflectionless operators in one dimension are particularly amenable to inverse scattering and are intimately related to integrable systems like KdV and Toda. Recent work has indicated a strong (but not equivalent) relationship between reflectionless operators and almost periodic potentials with absolutely continuous spectrum. This makes the realm of reflectionless operators a natural place to begin addressing Deift’s conjecture on integrable flows with almost periodic initial conditions and Simon’s conjecture on gems of spectral theory establishing correspondences between certain coefficient and spectral properties
Spectral Structures and Topological Methods in Mathematical Quasicrystals
No full textThe mathematical theory of aperiodic order grew out of various predecessors in discrete geometry, harmonic analysis and mathematical physics, and developed rapidly after the discovery of real world quasicrystals in 1982 by Shechtman. Many mathematical disciplines have contributed to the development of this field. In this meeting, the goal was to bring leading researchers from several of them together to exchange the state of affairs, with special focus on spectral aspects, dynamics and topology
Dynamische Systeme
No full textThis workshop continued the biannual series at Oberwolfach on Dynamical Systems that started as the “Moser–Zehnder meeting” in 1981. The main themes of the workshop are the new results and developments in the area of dynamical systems, in particular in Hamiltonian systems and symplectic geometry. This year special emphasis where laid on symplectic methods with applications to dynamics. The workshop was dedicated to the memory of John Mather, Jean-Christophe Yoccoz and Krzysztof Wysocki
Classical Algebraic Geometry
No full textProgress in algebraic geometry often comes through the introduction of new tools and ideas to tackle the classical problems the development of the field. Examples include new invariants that capture some aspect of geometry in a novel way, such as the derived category, and the extension of the class of geometric objects considered to allow constructions not previously possible, such as the transition from varieties to schemes or from schemes to stacks. Many famous old problems and outstanding conjectures have been resolved in this way over the last 50 years. While the new theories are sometimes studied for their own sake, they are in the end best understood in the context of the classical questions they illuminate. The goal of the workshop was to study new developments in algebraic geometry, with a view toward their application to the classical problems