Recent Submissions

• 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 ...
• 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 ...
• 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 ...
• 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 ...
• 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. ...
• 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 ...
• 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 $A$ ...
• 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. ...
• 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 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 ...
• 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, ...
• Group Algebras of Compact Groups. A New Way of Producing Group Hopf Algebras over Real and Complex Fields: Weakly Complete Topological Vector Spaces ﻿

[OWP-2019-06] (Mathematisches Forschungsinstitut Oberwolfach, 2019-02-27)
• Cataland: Why the Fuß? ﻿

[OWP-2019-01] (Mathematisches Forschungsinstitut Oberwolfach, 2019-01-21)
The three main objects in noncrossing Catalan combinatorics associated to a finite Coxeter system are noncrossing partitions, clusters, and sortable elements. The first two of these have known Fuß-Catalan generalizations. ...