2011
2011
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Second Main Theorems and Unicity of Meromorphic Mappings with Moving Hypersurfaces
[OWP201138] (Mathematisches Forschungsinstitut Oberwolfach, 2011)In this article, we establish some new second main theorems for meromorphic mappings of $\mathbf{C}^m$ into $\mathbf{P}^n(\mathbf{C})$ and moving hypersurfaces with truncated counting functions. As an application, we prove ... 
The Cleavage Operad and String Topology of Higher Dimension
[OWP201137] (Mathematisches Forschungsinstitut Oberwolfach, 2011) 
The TGraph of a Multigraded Hilbert Scheme
[OWP201134] (Mathematisches Forschungsinstitut Oberwolfach, 2011)The $T$graph of a multigraded Hilbert scheme records the zero and onedimensional orbits of the $T=(K^*)^n$ action on the Hilbert scheme induced from the $T$action on $\mathbb{A}^n$. It has vertices the $T$fixed points, ... 
Analytic Varieties with Finite Volume Amoebas are Algebraic
[OWP201133] (Mathematisches Forschungsinstitut Oberwolfach, 2011)In this paper, we study the amoeba volume of a given $k$dimensional generic analytic variety $V$ of the complex algebraic torus $(C^*)^n$. When $n>=2k$, we show that $V$ is algebraic if and only if the volume of its amoeba ... 
Products of pairs of Dehn twists and maximal real Lefschetz fibrations
[OWP201132] (Mathematisches Forschungsinstitut Oberwolfach, 2011)We address the problem of existence and uniqueness of a factorization of a given element of the modular group into a product of two Dehn twists. As a geometric application, we conclude that any maximal real elliptic ... 
Positive recurrence of piecewise OrnteinUhlenbeck processes and common quadratic Lyapunov functions
[OWP201126] (Mathematisches Forschungsinstitut Oberwolfach, 2011)We study the positive recurrence of piecewise OrnsteinUhlenbeck (OU) diffusion processes, which arise from manyserver queueing systems with phasetype service requirements. These diffusion processes exhibit different ... 
Upper bounds for the number of solutions to quartic thue equations
[OWP201121] (Mathematisches Forschungsinstitut Oberwolfach, 2011)We will give upper bounds for the number of integral solutions to quartic Thue equations. Our main tool here is a logarithmic curve $\phi(x,y)$ that allows us to use the theory of linear forms in logarithms. This manuscript ... 
New representations of matroids and generalizations
[OWP201118] (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 ... 
Monoid valuations and value ordered supervaluations
[OWP201117] (Mathematisches Forschungsinstitut Oberwolfach, 2011)We complement two papers on supertropical valuation theory ([IKR1], [IKR2]) by providing natural examples of mvaluations (= monoid valuations), after that of supervaluations and transmissions between them. The supervaluations ... 
Classification of totally real elliptic Lefschetz fibrations via necklace diagrams
[OWP201113] (Mathematisches Forschungsinstitut Oberwolfach, 2011)We show that totally real elliptic Lefschetz brations that admit a real section are classified by their "real loci" which is nothing but an $S^1$valued Morse function on the real part of the total space. We assign to ... 
Dominance and Transmissions in Supertropical Valuation Theory
[OWP201107] (Mathematisches Forschungsinstitut Oberwolfach, 2011)This paper is a sequel of [IKR1], where we defined supervaluations on a commutative ring $R$ and studied a dominance relation $\Phi >= v$ between supervaluations $\varphi$ and $\upsilon$ on $R$, aiming at an enrichment of ... 
Some Combinatorial Identities Related to Commuting Varieties and Hilbert Schemes
[OWP201102] (Mathematisches Forschungsinstitut Oberwolfach, 2011)In this article we explore some of the combinatorial consequences of recent results relating the isospectral commuting variety and the Hilbert scheme of points in the plane. 
Legendrian Knots in Lens Spaces
[OWP201101] (Mathematisches Forschungsinstitut Oberwolfach, 2011)In this note, we first classify all topological torus knots lying on the Heegaard torus in Lens spaces, and then we classify Legendrian representatives of torus knots. We show that all Legendrian torus knots in universally ... 
Quotients of Index Two and General Quotients in a Space of Orderings
[OWP201136] (Mathematisches Forschungsinstitut Oberwolfach, 20110530)In this paper we investigate quotient structures and quotient spaces of a space of orderings arising from subgroups of index two. We provide necessary and sufficient conditions for a quotient structure to be a quotient ... 
On Canonical Forms for Twoperson Zerosum Limit Average Payoff Stochastic Games
[OWP201135] (Mathematisches Forschungsinstitut Oberwolfach, 20110529)We consider twoperson zerosum mean payoff undiscounted stochastic games. We give a sufficient condition for the existence of a saddle point in uniformly optimal stationary strategies. Namely, we obtain sufficient ... 
The Weyl group of the Curtz algebra
[OWP201131] (Mathematisches Forschungsinstitut Oberwolfach, 20110528)The Weyl group of the Cuntz algebra $\mathcal{O}_n$ is investigated. This is (isomorphic to) the group of polynomial automorphisms $\lambda_u$ of $\mathcal{O}_n$, namely those induced by unitaries u that can be written ... 
Algebraic geometric comparison of probability distributions
[OWP201130] (Mathematisches Forschungsinstitut Oberwolfach, 20110527)We propose a novel algebraic framework for treating probability distributions represented by their cumulants such as the mean and covariance matrix. As an example, we consider the unsupervised learning problem of finding ... 
Steinberg groups for Jordan pairs
[OWP201129] (Mathematisches Forschungsinstitut Oberwolfach, 20110526)We introduce categories of groups with commutator relations with respect to root groups and Weyl elements, permuting the root groups. This allows us to view the classical Steinberg groups, for example the Steinberg group ... 
Infeasibility certificates for linear matrix inequalities
[OWP201128] (Mathematisches Forschungsinstitut Oberwolfach, 20110525)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 ... 
Selfadjoint differentialalgebraic equations
[OWP201127] (Mathematisches Forschungsinstitut Oberwolfach, 20110524)Motivated from linearquadratic optimal control problems for differentialalgebraic equations (DAEs), we study the functional analytic properties of the operator associated with the necessary optimality boundary value ...