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1422b  Okounkov Bodies and Applications
[OWR201427] (2014)  (25 May  31 May 2014)The theory of Newton–Okounkov bodies, also called Okounkov bodies, is a relatively new connection between algebraic geometry and convex geometry. It generalizes the wellknown and extremely rich correspondence between ... 
On a Cheeger Type Inequality in Cayley Graphs of Finite Groups
[OWP201920] (Mathematisches Forschungsinstitut Oberwolfach, 20190722)  (7 July  7 October 2017)Let $G$ be a finite group. It was remarked by BreuillardGreenGuralnickTao that if the Cayley graph $C(G,S)$ is an expander graph and is nonbipartite then the spectrum of the adjacency operator $T$ is bounded away from ... 
On a Conjecture of Khoroshkin and Tolstoy
[OWP202214] (Mathematisches Forschungsinstitut Oberwolfach, 20220802)We prove a nogo theorem on the factorization of the lower triangular part in the Gaussian decomposition of the Yangian's universal $R$matrix, yielding a negative answer to a conjecture of Khoroshkin and Tolstoy from ... 
On a Group Functor Describing Invariants of Algebraic Surfaces
[OWP201908] (Mathematisches Forschungsinstitut Oberwolfach, 20190301)Liedtke (2008) has introduced group functors $K$ and $\tilde K$, which are used in the context of describing certain invariants for complex algebraic surfaces. He proved that these functors are connected to the theory of ... 
On an Effective Variation of Kronecker’s Approximation Theorem Avoiding Algebraic Sets
[OWP201728] (Mathematisches Forschungsinstitut Oberwolfach, 20171019)Let $\Lambda \subset \mathbb R^n$ be an algebraic lattice, coming from a projective module over the ring of integers of a number field $K$. Let $\mathcal Z \subset \mathbb R^n$ be the zero locus of a finite collection of ... 
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 ... 
On CoMinimal Pairs in Abelian Groups
[OWP201919] (Mathematisches Forschungsinstitut Oberwolfach, 20190709)A pair of nonempty subsets $(W,W')$ in an abelian group $G$ is a complement pair if $W+W'=G$. $W'$ is said to be minimal to $W$ if $W+(W'\setminus \{w'\}) \neq G, \forall \,w'\in W'$. In general, given an arbitrary subset ... 
On commuting varieties of nilradicals of Borel subalgebras of reductive Lie algebras
[OWP201214] (Mathematisches Forschungsinstitut Oberwolfach, 20121204)Let $G$ be a connected reductive algebraic group defined over an algebraically closed field $\mathbb{k}$ of characteristic zero. We consider the commuting variety $\mathcal{C}(\mathfrak{u})$ of the nilradical $\mathfrak{u}$ ... 
On Concentrators and Related Approximation Constants
[OWP201314] (Mathematisches Forschungsinstitut Oberwolfach, 20130610)Pippenger ([Pip77]) showed the existence of (6m, 4m, 3m, 6)concentrator for each positive integer m using a probabilistic method. We generalize his approach and prove existence of (6m, 4m, 3m, 5.05)concentrator (which ... 
On conjugacy of MASAs and the outer automorphism group of the Cuntz algebra
[OWP201321] (Mathematisches Forschungsinstitut Oberwolfach, 20131029)We investigate the structure of the outer automorphism group of the Cuntz algebra and the closely related problem of conjugacy of MASAa in $\mathcal{O}_n$. In particular, we exhibit an uncountable family of MASAs, conjugate ... 
On densities of lattice arrangements intersecting every idimensional affine subspace
[OWP201608] (Mathematisches Forschungsinstitut Oberwolfach, 20160510)In 1978, Makai Jr. established a remarkable connection between the volumeproduct of a convex body, its maximal lattice packing density and the minimal density of a lattice arrangement of its polar body intersecting every ... 
On Generalizations of KacMoody Groups
[OWP201006] (Mathematisches Forschungsinstitut Oberwolfach, 20100310)In [7] we define a CurtisTits group as a certain generalization of a KacMoody group. We distinguish between orientable and nonorientable CurtisTits groups and identify all orientable CurtisTits groups as KacMoody ... 
On Local Combinatorial Formulas for Chern Classes of Triangulated Circle Bundle
[OWP201616] (Mathematisches Forschungsinstitut Oberwolfach, 20160817)Principal circle bundle over a PL polyhedron can be triangulated and thus obtains combinatorics. The triangulation is assembled from triangulated circle bundles over simplices. To every triangulated circle bundle over a ... 
On Logic, Choices and Games
[SNAP2019009EN] (Mathematisches Forschungsinstitut Oberwolfach, 20190904)Can we always mathematically formalise our taste and preferences? We discuss how this has been done historically in the field of game theory, and how recent ideas from logic and computer science have brought an interesting ... 
On periodic solutions and global dynamics in a periodic differential delay equation
[OWP201408] (Mathematisches Forschungsinstitut Oberwolfach, 20140513)Several aspects of global dynamics and the existence of periodic solutions are studied for the scalar differential delay equation $x'(t) = a(t)f(x([tK]))$, where $f(x)$ is a continuous negative feedback function, $x \cdot ... 
On radial basis functions
[SNAP2019002EN] (Mathematisches Forschungsinstitut Oberwolfach, 20190313)Many sciences and other areas of research and applications from engineering to economics require the approximation of functions that depend on many variables. This can be for a variety of reasons. Sometimes we have a ... 
On Reflection Subgroups of Finite Coxeter Groups
[OWP201106] (Mathematisches Forschungsinstitut Oberwolfach, 2011059)Let $W$ be a finite Coxeter group. We classify the reflection subgroups of $W$ up to conjugacy and give necessary and sufficient conditions for the map that assigns to a reflection subgroup $R$ of $W$ the conjugacy class ... 
On Residuals of Finite Groups
[OWP201917] (Mathematisches Forschungsinstitut Oberwolfach, 20190528)A theorem of Dolfi, Herzog, Kaplan, and Lev [DHKL07, Thm. C] asserts that in a finite group with trivial Fitting subgroup, the size of the soluble residual of the group is bounded from below by a certain power of the group ... 
On Selfinjective Artin Algebras Having Generalized Standard Quasitubes
[OWP201018] (Mathematisches Forschungsinstitut Oberwolfach, 20100318)We give a complete description of the Morita equivalence classes of all connected selfinjective artin algebras for which the AuslanderReiten quiver admits a family of quasitubes having common composition factors, closed ... 
On Siegel modular forms of level p and their properties mod p
[OWP200923] (Mathematisches Forschungsinstitut Oberwolfach, 20090316)Using theta series we construct Siegel modular forms of level p which behave well modulo $p$ in all cusps. This construction allows us to show (under a mild condition) that all Siegel modular forms of level p and weight 2 ...