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Crystal energy functions via the charge in types A and C
[OWP-2011-25] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-23)
The Ram-Yip formula for Macdonald polynomials (at t=0) provides a statistic which we call charge. In types A and C it can be defined on tensor products of Kashiwara-Nakashima single column crystals. In this ...
Monoid valuations and value ordered supervaluations
[OWP-2011-17] (Mathematisches Forschungsinstitut Oberwolfach, 2011)
We complement two papers on supertropical valuation theory ([IKR1], [IKR2]) by providing natural examples of m-valuations (= monoid valuations), after that of supervaluations and transmissions between them. The supervaluations ...
The Cleavage Operad and String Topology of Higher Dimension
[OWP-2011-37] (Mathematisches Forschungsinstitut Oberwolfach, 2011)
Localized Endomorphisms of Graph Algebras
[OWP-2011-04] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-7)
Endomorphisms of graph C∗-algebras are investigated. A combinatorial approach to analysis of permutative endomorphisms is developed. Then invertibility criteria for localized endomorphisms are given. Furthermore, ...
Self-adjoint differential-algebraic equations
[OWP-2011-27] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-24)
Motivated from linear-quadratic optimal control problems for differential-algebraic equations (DAEs), we study the functional analytic properties of the operator associated with the necessary optimality boundary value ...
Second Main Theorems and Unicity of Meromorphic Mappings with Moving Hypersurfaces
[OWP-2011-38] (Mathematisches Forschungsinstitut Oberwolfach, 2011)
In this article, we establish some new second main theorems for meromorphic mappings of Cm into Pn(C) and moving hypersurfaces with truncated counting functions. As an application, we prove ...
Infeasibility certificates for linear matrix inequalities
[OWP-2011-28] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-25)
Farkas' lemma is a fundamental result from linear programming providing linear certi cates for infeasibility of systems of linear inequalities. In semidefinite programming, such linear certificates only exist for strongly ...
Cluster structures on simple complex lie groups and the Belavin-Drinfeld classification
[OWP-2011-10] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-12)
We study natural cluster structures in the rings of regular functions on simple complex Lie groups and Poisson-Lie structutures compatible with these cluster structures. According to our main conjecture, each class in the ...
New representations of matroids and generalizations
[OWP-2011-18] (Mathematisches Forschungsinstitut Oberwolfach, 2011)
We extend the notion of matroid representations by matrices over fields by considering new representations of matroids by matrices over finite semirings, more precisely over the boolean and the superboolean semirings. This ...
Formal adjoints of linear DAE operators and their role in optimal control
[OWP-2011-15] (Mathematisches Forschungsinstitut Oberwolfach, 2011-05-16)
For regular strangeness-free linear differential-algebraic equations (DAEs) the definition of an adjoint DAE is straightforward. This definition can be formally extended to general linear DAEs. In this paper, we analyze ...