2019
2019
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A Cheeger Type Inequality in Finite Cayley Sum Graphs
[OWP201921] (Mathematisches Forschungsinstitut Oberwolfach, 20190731)  (5 May  27 July 2019)Let $G$ be a finite group and $S$ be a symmetric generating set of $G$ with $S = d$. We show that if the undirected Cayley sum graph $C_{\Sigma}(G,S)$ is an expander graph and is nonbipartite, then the spectrum of its ... 
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 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 ... 
A Quantitative Analysis of the “LionMan” Game
[OWP201918] (Mathematisches Forschungsinstitut Oberwolfach, 20190708)In this paper we analyze, based on an interplay between ideas and techniques from logic and geometric analysis, a pursuitevasion game. More precisely, we focus on a discrete lion and man game with an $\varepsilon$capture ... 
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 ... 
Congruences Associated with Families of Nilpotent Subgroups and a Theorem of Hirsch
[OWP201916] (Mathematisches Forschungsinstitut Oberwolfach, 20190527)Our main result associates a family of congruences with each suitable system of nilpotent subgroups of a finite group. Using this result, we complete and correct the proof of a theorem of Hirsch concerning the class number ... 
Experimenting with Symplectic Hypergeometric Monodromy Groups
[OWP201915] (Mathematisches Forschungsinstitut Oberwolfach, 20190522)We present new computational results for symplectic monodromy groups of hypergeometric differential equations. In particular, we compute the arithmetic closure of each group, sometimes justifying arithmeticity. The results ... 
Chirality of Real NonSingular Cubic Fourfolds and Their Pure Deformation Classification
[OWP201914] (Mathematisches Forschungsinstitut Oberwolfach, 20190515)In our previous works we have classified real nonsingular cubic hypersurfaces in the 5dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of ... 
The BeckerGottlieb Transfer: a Geometric Description
[OWP201913] (Mathematisches Forschungsinstitut Oberwolfach, 20190514)In this note, we examine geometric aspects of the BeckerGottlieb transfer in terms of the Umkehr and index maps, and rework some classic index theorems, using the cohomological formulae of the BeckerGottlieb transfer. ... 
The Fourier Transform on Harmonic Manifolds of Purely Exponential Volume Growth
[OWP201912] (Mathematisches Forschungsinstitut Oberwolfach, 20190508)Let $X$ be a complete, simply connected harmonic manifold of purely exponential volume growth. This class contains all nonflat harmonic manifolds of nonpositive curvature and, in particular all known examples of harmonic ... 
Minimal Codimension One Foliation of a Symmetric Space by DamekRicci Spaces
[OWP201911] (Mathematisches Forschungsinstitut Oberwolfach, 20190507)In this article we consider solvable hypersurfaces of the form $N \exp(\mathbb{R} H)$ with induced metrics in the symmetric space $M = SL(3,\mathbb{C})/SU(3)$, where $H$ a suitable unit length vector in the subgroup $A$ ... 
On the Lie Algebra Structure of $HH^1(A)$ of a FiniteDimensional Algebra A
[OWP201910] (Mathematisches Forschungsinstitut Oberwolfach, 20190417)Let $A$ be a split finitedimensional associative unital algebra over a field. The first main result of this note shows that if the Extquiver of $A$ is a simple directed graph, then $HH^1(A)$ is a solvable Lie algebra. ... 
The First Hochschild Cohomology as a Lie Algebra
[OWP201909] (Mathematisches Forschungsinstitut Oberwolfach, 20190416)In this paper we study sufficient conditions for the solvability of the first Hochschild cohomology of a finite dimensional algebra as a Lie algebra in terms of its Extquiver in arbitrary characteristic. In particular, ... 
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 ... 
Weighted Surface Algebras: General Version
[OWP201907] (Mathematisches Forschungsinstitut Oberwolfach, 20190228)We introduce general weighted surface algebras of triangulated surfaces with arbitrarily oriented triangles and describe their basic properties. In particular, we prove that all these algebras, except the singular disc, ... 
Group Algebras of Compact Groups. A New Way of Producing Group Hopf Algebras over Real and Complex Fields: Weakly Complete Topological Vector Spaces
[OWP201906] (Mathematisches Forschungsinstitut Oberwolfach, 20190227)Weakly complete real or complex associative algebras $A$ are necessarily projective limits of finite dimensional algebras. Their group of units $A^{1}$ is a proLie group with the associated topological Lie algebra $A_{\rm ... 
Hölder Continuity of the Spectra for Aperiodic Hamiltonians
[OWP201905] (Mathematisches Forschungsinstitut Oberwolfach, 20190226)We study the spectral location of a strongly pattern equivariant Hamiltonians arising through configurations on a colored lattice. Roughly speaking, two configurations are "close to each other" if, up to a translation, ... 
Applications of BV Type Spaces
[OWP201904] (Mathematisches Forschungsinstitut Oberwolfach, 20190213) 
Time Discretization Schemes for Hyperbolic Systems on Networks by εExpansion
[OWP201903] (Mathematisches Forschungsinstitut Oberwolfach, 20190212)We consider partial differential equations on networks with a small parameter $\epsilon$, which are hyperbolic for $\epsilon>0$ and parabolic for $\epsilon=0$. With a combination of an $\epsilon$expansion and RungeKutta ... 
A Function Algebra Providing New Mergelyan Type Theorems in Several Complex Variables
[OWP201902] (Mathematisches Forschungsinstitut Oberwolfach, 20190211)For compact sets $K\subset \mathbb C^{d}$, we introduce a subalgebra $A_{D}(K)$ of $A(K)$, which allows us to obtain Mergelyan type theorems for products of planar compact sets as well as for graphs of functions.