Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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Non-Archimedean Geometry and Applications
No full textThe workshop focused on recent developments in non-Archimedean analytic geometry with various applications to other fields. The topics of the talks included applications to complex geometry, mirror symmetry, p-adic Hodge theory, tropical geometry, resolution of singularities, p-adic dynamical systems and diophantine geometry
Groups with Spanier-Whitehead Duality
No full textWe introduce the notion of Spanier-Whitehead -duality for a discrete group , defined as duality in the KK-category between two -algebras which are naturally attached to the group, namely the reduced group -algebra and the crossed product for the group action on the universal example for proper actions. We compare this notion to the Baum-Connes conjecture by constructing duality classes based on two methods: the standard "gamma element" technique, and the more recent approach via cycles with property gamma. As a result of our
analysis, we prove Spanier-Whitehead duality for a large class of groups, including Bieberbach's space groups, groups acting on trees, and lattices in Lorentz groups
Mini-Workshop: Algebraic Tools for Solving the Yang–Baxter Equation
No full textThe workshop was focused on three facets of the interplay between set-theoretic solutions to the Yang--Baxter equation and classical algebraic structures (groups, monoids, algebras, lattices, racks etc.): structures used to construct new solutions; structures as invariants of solutions; and YBE as a source of structures with interesting properties
Weighted Surface Algebras: General Version
No full textWe introduce general weighted surface algebras of triangulated surfaces with arbitrarily oriented triangles and describe their basic properties. In particular, we prove that all these algebras, except the singular disc, triangle, tetrahedral and spherical algebras, are symmetric tame periodic algebras of period 4
Mixed-integer Nonlinear Optimization: a hatchery for modern mathematics
No full textThe second MFO Oberwolfach Workshop on Mixed-Integer Nonlinear Programming (MINLP) took place between 2nd and 8th June 2019. MINLP refers to one of the hardest Mathematical Programming (MP) problem classes, involving both nonlinear functions as well as continuous and integer decision variables. MP is a formal language for describing optimization problems, and is traditionally part of Operations Research (OR), which is itself at the intersection of mathematics, computer science, engineering and econometrics. The scientific program has covered the three announced areas (hierarchies of approximation, mixed-integer nonlinear optimal control, and dealing with uncertainties) with a variety of tutorials, talks, short research announcements, and a special "open problems'' session
Touching the transcendentals: tractional motion from the bir th of calculus to future perspectives
No full textWhen the rigorous foundation of calculus was developed,
it marked an epochal change in the approach
of mathematicians to geometry. Tools from geometry
had been one of the foundations of mathematics
until the 17th century but today, mainstream conception
relegates geometry to be merely a tool of visualization.
In this snapshot, however, we consider
geometric and constructive components of calculus.
We reinterpret “tractional motion”, a late 17th century
method to draw transcendental curves, in order
to reintroduce “ideal machines” in math foundation
for a constructive approach to calculus that avoids
the concept of infinity
Uncertainty Quantification
No full textUncertainty quantification (UQ) is concerned with including and characterising uncertainties in mathematical models.
Major steps comprise proper description of system uncertainties, analysis and efficient quantification of uncertainties in predictions and design problems, and statistical inference on uncertain parameters starting from available measurements.
Research in UQ addresses fundamental mathematical and statistical challenges, but has also wide applicability in areas such as engineering, environmental, physical and biological applications.
This workshop focussed on mathematical challenges at the interface of applied mathematics, probability and statistics, numerical analysis, scientific computing and application domains.
The workshop served to bring together experts from those disciplines in order to enhance their interaction, to exchange ideas and to develop new, powerful methods for UQ
Mini-Workshop: Mathematics of Crystallisation
No full textCrystallisation, by which we mean the formation of solids
precipitating from a solution, is the central theme of the present
mini-workshop. Participants discussed different approaches towards a
rigorous mathematical understanding of crystallisation as well as
detecting, modelling and establishing properties of crystalline and
quasicrystalline structures
Configuration spaces and braid groups
No full textIn this snapshot we introduce configuration spaces
and explain how a mathematician studies their ‘shape’.
This will lead us to consider paths of configurations
and braid groups, and to explore how algebraic properties
of these groups determine features of the spaces
Mini-Workshop: Seshadri Constants
No full textSeshadri constants were defined by Demailly around 30 years ago using the ampleness criterion of Seshadri. Demailly was interested in studying problems related to separation of jets of line bundles on projective varieties, specifically in the context of the well-known Fujita Conjecture. However, Seshadri constants turned out to be objects of fundamental importance in the study of positivity of linear series and many other areas. Consequently, in the past three decades, they have become a central object of study in numerous directions in algebraic geometry and commutative algebra. In this mini-workshop, we studied some of the most interesting current research problems concerning Seshadri constants. We expect that this exploration will help focus research on some of the most important questions in this area in the years to come