Auflistung nach Erscheinungsdatum
Anzeige der Dokumente 1621-1640 von 1987
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Weighted Surface Algebras: General Version
[OWP-2019-07] (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-28)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, ... -
On a Group Functor Describing Invariants of Algebraic Surfaces
[OWP-2019-08] (Mathematisches Forschungsinstitut Oberwolfach, 2019-03-01)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 radial basis functions
[SNAP-2019-002-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-03-13)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 ... -
The First Hochschild Cohomology as a Lie Algebra
[OWP-2019-09] (Mathematisches Forschungsinstitut Oberwolfach, 2019-04-16)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 Ext-quiver in arbitrary characteristic. In particular, ... -
On the Lie Algebra Structure of $HH^1(A)$ of a Finite-Dimensional Algebra A
[OWP-2019-10] (Mathematisches Forschungsinstitut Oberwolfach, 2019-04-17)Let $A$ be a split finite-dimensional associative unital algebra over a field. The first main result of this note shows that if the Ext-quiver of $A$ is a simple directed graph, then $HH^1(A)$ is a solvable Lie algebra. ... -
Diophantine equations and why they are hard
[SNAP-2019-003-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-04-24)Diophantine equations are polynomial equations whose solutions are required to be integer numbers. They have captured the attention of mathematicians during millennia and are at the center of much of contemporary research. ... -
Positive Scalar Curvature and Applications
[SNAP-2019-004-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-04-25)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 why ... -
Algebra, matrices, and computers
[SNAP-2019-005-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-03)What part does algebra play in representing the real world abstractly? How can algebra be used to solve hard mathematical problems with the aid of modern computing technology? We provide answers to these questions that ... -
Minimal Codimension One Foliation of a Symmetric Space by Damek-Ricci Spaces
[OWP-2019-11] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-07)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 $A$ ... -
The Fourier Transform on Harmonic Manifolds of Purely Exponential Volume Growth
[OWP-2019-12] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-08)Let $X$ be a complete, simply connected harmonic manifold of purely exponential volume growth. This class contains all non-flat harmonic manifolds of non-positive curvature and, in particular all known examples of harmonic ... -
The Becker-Gottlieb Transfer: a Geometric Description
[OWP-2019-13] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-14)In this note, we examine geometric aspects of the Becker-Gottlieb transfer in terms of the Umkehr and index maps, and rework some classic index theorems, using the cohomological formulae of the Becker-Gottlieb transfer. ... -
Chirality of Real Non-Singular Cubic Fourfolds and Their Pure Deformation Classification
[OWP-2019-14] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-15)In our previous works we have classified real non-singular cubic hypersurfaces in the 5-dimensional projective space up to equivalence that includes both real projective transformations and continuous variations of ... -
Experimenting with Symplectic Hypergeometric Monodromy Groups
[OWP-2019-15] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-22)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 ... -
Congruences Associated with Families of Nilpotent Subgroups and a Theorem of Hirsch
[OWP-2019-16] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-27)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 ... -
On Residuals of Finite Groups
[OWP-2019-17] (Mathematisches Forschungsinstitut Oberwolfach, 2019-05-28)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 ... -
Counting self-avoiding walks on the hexagonal lattice
[SNAP-2019-006-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-06-04)In how many ways can you go for a walk along a lattice grid in such a way that you never meet your own trail? In this snapshot, we describe some combinatorial and statistical aspects of these so-called self-avoiding ... -
A Quantitative Analysis of the “Lion-Man” Game
[OWP-2019-18] (Mathematisches Forschungsinstitut Oberwolfach, 2019-07-08)In this paper we analyze, based on an interplay between ideas and techniques from logic and geometric analysis, a pursuit-evasion game. More precisely, we focus on a discrete lion and man game with an $\varepsilon$-capture ... -
On Co-Minimal Pairs in Abelian Groups
[OWP-2019-19] (Mathematisches Forschungsinstitut Oberwolfach, 2019-07-09)A pair of non-empty 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 ... -
Random permutations
[SNAP-2019-007-EN] (Mathematisches Forschungsinstitut Oberwolfach, 2019-07-12)100 people leave their hats at the door at a party and pick up a completely random hat when they leave. How likely is it that at least one of them will get back their own hat? If the hats carry name tags, how difficult ... -
On a Cheeger Type Inequality in Cayley Graphs of Finite Groups
[OWP-2019-20] (Mathematisches Forschungsinstitut Oberwolfach, 2019-07-22) - (7 July - 7 October 2017)Let $G$ be a finite group. It was remarked by Breuillard-Green-Guralnick-Tao that if the Cayley graph $C(G,S)$ is an expander graph and is non-bipartite then the spectrum of the adjacency operator $T$ is bounded away from ...