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Photonic Crystals: Mathematical Analysis and Numerical Approximation
[OWS42] (Birkhäuser Basel, 2011)This volume collects a series of lectures which provide an introduction to the mathematical background needed for the modeling and simulation of light, in particular in periodic media, and for its applications in optical ... 
Plethysms, replicated Schur functions and series, with applications to vertex operators
[OWP201012] (Mathematisches Forschungsinstitut Oberwolfach, 20100314)Specializations of Schur functions are exploited to define and evaluate the Schur functions $s_\lambda [\alpha X]$ and plethysms $s_\lambda [\alpha s_\nu(X))]$ for any $\alpha$integer, real or complex. Plethysms are then ... 
Plethystic Vertex Operators and BosonFermion Correspondences
[OWP201611] (Mathematisches Forschungsinstitut Oberwolfach, 20160617)We study the algebraic properties of plethystic vertex operators, introduced in J. Phys. A: Math. Theor. 43 405202 (2010), underlying the structure of symmetric functions associated with certain generalized universal ... 
Pointwise hyperbolicity implies uniform hyperbolicity
[OWP200906] (Mathematisches Forschungsinstitut Oberwolfach, 20090223)We provide a general mechanism for obtaining uniform information from pointwise data. A sample result is that if a diffeomorphism of a compact Riemannian manifold has pointwise expanding and contracting continuous invariant ... 
Polyhedra and commensurability
[SNAP2016009EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)This snapshot introduces the notion of commensurability of polyhedra. At its bottom, this concept can be developed from constructions with paper, scissors, and glue. Starting with an elementary example, we formalize it ... 
Polynomiality, wall crossings and tropical geometry of rational double hurwitz cycles
[OWP201213] (Mathematisches Forschungsinstitut Oberwolfach, 20121204)We study rational double Hurwitz cycles, i.e. loci of marked rational stable curves admitting a map to the projective line with assigned ramification profiles over two fixed branch points. Generalizing the phenomenon ... 
Polytopes  combinatorics and computation
[OWS29] (Birkhäuser Basel, 2000)Questions that arose from linear programming and combinatorial optimization have been a driving force for modern polytope theory, such as the diameter questions motivated by the desire to understand the complexity of the ... 
Positional Games
[OWS44] (Birkhäuser Basel, 2014)This text is based on a lecture course given by the authors in the framework of Oberwolfach Seminars at the Mathematisches Forschungsinstitut Oberwolfach in May, 2013. It is intended to serve as a thorough introduction to ... 
Positive Margins and Primary Decomposition
[OWP201206] (Mathematisches Forschungsinstitut Oberwolfach, 2012)We study random walks on contingency tables with fixed marginals, corresponding to a (loglinear) hierarchical model. If the set of allowed moves is not a Markov basis, then there exist tables with the same marginals that ... 
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 ... 
Positive Scalar Curvature and Applications
[SNAP2019004EN] (Mathematisches Forschungsinstitut Oberwolfach, 20190425)We introduce the idea of curvature, including how it developed historically, and focus on the scalar curvature of a manifold. A major current research topic involves understanding positive scalar curvature. We discuss ... 
Positivity of the Tsystem cluster algebra
[OWP200921] (Mathematisches Forschungsinstitut Oberwolfach, 20090314)We give the path model solution for the cluster algebra variables of the $A_r$ Tsystem with generic boundary conditions. The solutions are partition functions of (strongly) nonintersecting paths on weighted graphs. The ... 
A potential reduction algorithm for twoperson zerosum mean payoff stochastic games
[OWP201519] (Mathematisches Forschungsinstitut Oberwolfach, 2015)We suggest a new algorithm for twoperson zerosum undiscounted stochastic games focusing on stationary strategies. Given a positive real $\epsilon$, let us call a stochastic game $\epsilon$ergodic, if its values from any ... 
Preconditioning of Block Tridiagonal Matrices
[OWP200805] (Mathematisches Forschungsinstitut Oberwolfach, 20080309)Preconditioning methods via approximate block factorization for block tridiagonal matrices are studied. Bounds for the resulting condition numbers are given, and two methods for the recursive construction of the approximate ... 
Prediction and Quantification of Individual Athletic Performance
[OWP201511] (Mathematisches Forschungsinstitut Oberwolfach, 20150827)We present a novel, quantitative view on the human athletic performance of individuals. We obtain a predictor for athletic running performances, a parsimonious model, and a training state summary consisting of three numbers, ... 
Prime tuples in function fields
[SNAP2016010EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)How many prime numbers are there? How are they distributed among other numbers? These are questions that have intrigued mathematicians since ancient times. However, many questions in this area have remained unsolved, and ... 
Das Problem der Kugelpackung
[SNAP2016004DE] (Mathematisches Forschungsinstitut Oberwolfach, 2016)Wie würdest du Tennisbälle oder Orangen stapeln? Oder allgemeiner formuliert: Wie dicht lassen sich identische 3dimensionale Objekte überschneidungsfrei anordnen? Das Problem, welches auch Anwendungen in der digitalen ... 
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 ... 
Profinite groups
[SNAP2016014EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)Profinite objects are mathematical constructions used to collect, in a uniform manner, facts about infinitely many finite objects. We shall review recent progress in the theory of profinite groups, due to Nikolov and Segal, ... 
Prony’s method: an old trick for new problems
[SNAP2018004EN] (Mathematisches Forschungsinstitut Oberwolfach, 20180306)In 1795, French mathematician Gaspard de Prony invented an ingenious trick to solve a recovery problem, aiming at reconstructing functions from their values at given points, which arose from a specific application in ...