Oberwolfach Publications (Mathematisches Forschungsinst. Oberwolfach)
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2063 research outputs found
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MATRIX-MFO Tandem Workshop/Small Collaboration: Rough Wave Equations (hybrid meeting)
No full textThe consideration of wave propagation in inhomogeneous media or the modelling of nonlinear waves often requires the study of wave equations with low regularity data and/or coefficients. Several Australian-European collaborations have recently led to deeper analytical understanding of rough wave equations.
This tandem workshop provided a platform for such collaborations and brought together early career researchers and leading experts in harmonic analysis, microlocal analysis and spectral theory. The workshop focused on collaboration and technical knowledge exchange on topics such as local smoothing, spectral multipliers, restriction estimates, Hardy spaces for Fourier integral operators, and nonlinear partial differential equations
Mini-Workshop: (Anosov) (hybrid meeting)
No full textThree different active fields are subsumed under the keyword Anosov theory: Spectral theory of Anosov flows, dynamical rigidity of Anosov actions, and Anosov representations. In all three fields there have been dynamic developments and substantial breakthroughs in recent years.
The mini-workshop brought together researchers from the three different communities and sparked a joint discussion of current ideas, common interests, and open problems
Homogeneous Structures: Model Theory meets Universal Algebra (online meeting)
No full textThe workshop "Homogeneous Structures: Model Theory meets Universal
Algebra'' was centred around transferring recently obtained advances
in universal algebra from the finite to the infinite. As it turns out,
the notion of homogeneity together with other model-theoretic concepts
like -categoricity and the Ramsey property play an
indispensable role in this endeavour
Singularities (hybrid meeting)
No full textSingularity theory concerns local and global structure of singularities of (algebraic) varieties and maps. As such, it combines tools from algebraic geometry, complex analysis, topology, algebra and combinatorics
The Elser Nuclei Sum Revisited
No full textFix a finite undirected graph and a vertex of . Let be the set of edges of . We call a subset of if each edge of has at least one endpoint that can be connected to by an -path (i.e., a path using edges from only). In 1984, Elser showed that the sum of over all pandemic subsets of is if . We give a simple proof of this result via a sign-reversing involution, and discuss variants, generalizations and a refinement using discrete Morse theory
Small Collaboration: Modeling Phenomena from Nature by Hyperbolic Partial Differential Equations (hybrid meeting)
No full textNonlinear hyperbolic partial differential equations constitute a plethora of models from physics, biology, engineering, etc. In this workshop we cover the range from modeling, mathematical questions of well-posedness, numerical discretization and numerical simulations to compare with the phenomenon from nature that was modeled in the first place. Both kinetic and fluid models were discussed
The Enigma behind the Good–Turing formula
No full textFinding the total number of species in a population
based on a finite sample is a difficult but practically
important problem. In this snapshot, we will attempt
to shed light on how during World War II, two
cryptanalysts, Irving J. Good and Alan M. Turing,
discovered one of the most widely applied formulas in
statistics. The formula estimates the probability of
missing some of the species in a sample drawn from
a heterogeneous population. We will provide some
intuition behind the formula, show its wide range of
applications, and give a few technical details
Applications of Optimal Transportation in the Natural Sciences (online meeting)
No full textConcepts and methods from the mathematical theory of optimal transportation
have reached significant importance in various fields of the natural sciences.
The view on classical problems from a "transport perspective''
has lead to the development of powerful problem-adapted mathematical tools,
and sometimes to a novel geometric understanding of the matter.
The natural sciences, in turn, are
the most important source of ideas for the further development of the optimal transport theory,
and are a driving force for the design of efficient and reliable numerical methods
to approximate Wasserstein distances and the like.
The presentations and discussions in this workshop have been centered around
recent analytical results and numerical methods in the field of optimal transportation
that have been motivated by specific applications in statistical physics, quantum mechanics, and chemistry
Fundamental Theorem of Projective Geometry over Semirings
No full textWe state the fundamental theorem of projective geometry for semimodules over semirings, which is facilitated by recent work in the study of bases in semimodules defined over semirings. In the process we explore in detail the linear algebra setup over semirings. We also provide more explicit results to understand the implications of our main theorem on maps between tropical lines in the tropical plane. Along with this we also look at geometrical connections to the rich theory of tropical geometry
Invitation to quiver representation and Catalan combinatorics
No full textRepresentation theory is an area of mathematics that
deals with abstract algebraic structures and has numerous
applications across disciplines. In this snapshot,
we will talk about the representation theory of
a class of objects called quivers and relate them to
the fantastic combinatorics of the Catalan numbers