Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Mini-Workshop: Positivity in Higher-dimensional Geometry: Higher-codimensional Cycles and Newton-Okounkov Bodies
No full textThere are several flavors of positivity in Algebraic Geometry. They range from conditions that determine vanishing of cohomology, to intersection theoretic properties, and to convex geometry. They offer excellent invariants that have been shown to govern the classification and the parameterization programs in Algebraic Geometry, and are finer than the classical topological ones. This mini-workshop aims to facilitate research collaboration in the area, strengthening the relationship between various positivity notions, beyond the now classical case of divisors/line bundles
Overlap Synchronisation in Multipartite Random Energy Models
No full textResearch in Pairs 2016In a multipartite random energy model, made of coupled GREMs, we determine the joint law of the overlaps in terms of the ones of the single GREMs. This provides the simplest example of the so-called synchronisation of the overlaps
O-Minimality and its Applications to Number Theory and Analysis
No full textThe workshop brought together researchers in the areas of o-minimal structures, analysis and number theory. The latest developments in o-minimality and their applications to number theory and analysis were presented in a series of talks; one focus, in particular, was on the Pila–Wilkie Theorem and its impact on diophantine problems
Real Analysis, Harmonic Analysis, and Applications
No full textThe workshop focused on important developments within the last few years in real and harmonic analysis, including polynomial partitioning and decoupling as well as significant concurrent progress in the application of these for example to number theory and partial differential equations
Space-time Methods for Time-dependent Partial Differential Equations
No full textModern discretizations of time-dependent PDEs consider the full problem in the space-time cylinder and aim to overcome limitations of classical approaches such as the method of lines (first discretize in space and then solve the resulting ODE) and the Rothe method (first discretize in time and then solve the PDE). A main advantage of a holistic space-time method is the direct access to space-time adaptivity and to the backward problem (required for the dual problem in optimization or error control). Moreover, this allows for parallel solution strategies simultaneously in time and space.
Several space-time concepts where proposed (different conforming and nonconforming space-time finite elements, the parareal method, wavefront relaxation etc.) but this topic has become a rapidly growing field in numerical analysis and scientific computing. In this workshop the focus is the development of adaptive and flexible space-time discretization methods for solving parabolic and hyperbolic space-time partial differential equations
Discrete Geometry
No full textA number of important recent developments in various branches of discrete geometry were presented at the workshop. The presentations illustrated both the diversity of the area and its strong connections to other fields of mathematics such as topology, combinatorics or algebraic geometry. The open questions abound and many of the results presented were obtained by young researchers, confirming the great vitality of discrete geometry
Experimenting with Zariski Dense Subgroups
No full textResearch in Pairs 2017We give a method to describe all congruence images of a finitely generated Zariski dense group . The method is applied to obtain efficient algorithms for solving this problem in odd prime degree ; if then we compute all congruence images only modulo primes. We propose a separate method that works for all as long as contains a known transvection. The algorithms have been implemented in , enabling computer experiments with important classes of linear groups that have recently emerged
Network Models: Structure and Function
No full textThe focus of the meeting was on the mathematical analysis of complex networks, both on how networks emerge through microscopic interaction rules as well as on dynamic processes and optimization problems on networks, including random walks, interacting particle systems and search algorithms. Topics that were addressed included: percolation on graphs and critical regimes for the emergence of a giant component; graph limits and graphons; epidemics, propagation and competition; trees and forests; dynamic random graphs; local versus global algorithms; statistical learning on networks
News on quadratic polynomials
No full textMany problems in mathematics have remained unsolved because of missing links between mathematical disciplines, such as algebra, geometry, analysis, or number theory. Here we introduce a recently discovered result concerning quadratic polynomials, which uses a bridge between algebra and analysis. We study the iterations of quadratic polynomials, obtained by computing the value of a polynomial for a given number and feeding the outcome into the exact same polynomial again. These iterations of polynomials have interesting applications, such as in fractal theory
Closed geodesics on surfaces and Riemannian manifolds
No full textGeodesics are special paths in surfaces and so-called
Riemannian manifolds which connect close points
in the shortest way. Closed geodesics are geodesics
which go back to where they started. In this snapshot
we talk about these special paths, and the efforts to
find closed geodesics