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On the autonomous metric on groups of Hamiltonian diffeomorphisms of closed hyperbolic surfaces
[OWP201318] (Mathematisches Forschungsinstitut Oberwolfach, 20130723)Let $\Sigma_g$ be a closed hyperbolic surface of genus $g$ and let Ham($\Sigma_ g$) be the group of Hamiltonian diffeomorphisms of $\Sigma_g$. The most natural word metric on this group is the autonomous metric. It has ... 
On the autonomous metric on the group of areapreserving diffeomorphisms of the 2disc
[OWP201216] (Mathematisches Forschungsinstitut Oberwolfach, 2012)Let $D^2$ be the open unit disc in the Euclidean plane and let $G := Diff(D^2; area)$ be the group of smooth compactly supported areapreserving diffeomorphisms of $D^2$. For every natural number $k$ we construct an injective ... 
On the complement of the dense orbit for a quiver of type A
[OWP201011] (Mathematisches Forschungsinstitut Oberwolfach, 2010)Let $\mathbb{A}_t$ be the directed quiver of type $A$ with $t$ vertices. For each dimension vector $d$ there is a dense orbit in the corresponding representation space. The principal aim of this note is to use just rank ... 
On the Complement of the Richardson Orbit
[OWP201009] (Mathematisches Forschungsinstitut Oberwolfach, 20100313)We consider parabolic subgroups of a general algebraic group over an algebraically closed field $k$ whose Levi part has exactly $t$ factors. By a classical theorem of Richardson, the nilradical of a parabolic subgroup $P$ ... 
On the Computational Content of the Theory of Borel Equivalence Relations
[OWP202106] (Mathematisches Forschungsinstitut Oberwolfach, 20210317)This preprint offers computational insights into the theory of Borel equivalence relations. Specifically, we classify equivalence relations on the Cantor space up to computable reductions, i.e., reductions induced by Turing ... 
On the containment problem
[SNAP2016003EN] (Mathematisches Forschungsinstitut Oberwolfach, 2016)Mathematicians routinely speak two languages: the language of geometry and the language of algebra. When translating between these languages, curves and lines become sets of polynomials called “ideals”. Often there are ... 
On the Derived Category of Grassmannians in Arbitrary Characteristic
[OWP201324] (Mathematisches Forschungsinstitut Oberwolfach, 20131209)In this paper we consider Grassmannians in arbitrary characteristic. Generalizing Kapranov's wellknown characteristiczero results we construct dual exceptional collections on them (which are however not strong) as well ... 
On the Directionally Newtonnondegenerate Singularities of Complex Hypersurfaces
[OWP200816] (Mathematisches Forschungsinstitut Oberwolfach, 2008)We introduce a minimal generalization of Newtonnondegenerate singularities of hypersurfaces. Roughly speaking, an isolated hypersurface singularity is called directionally Newtonnondegenerate if the local embedded ... 
On the distribution of a second class particle in the asymmetric simple exclusion process
[OWP200922] (Mathematisches Forschungsinstitut Oberwolfach, 20090315)We give an exact expression for the distribution of the position $X(t)$ of a single second class particle in the asymmetric simple exclusion process (ASEP) where initially the second class particle is located at the origin ... 
On the Enumeration of Finite $L$Algebras
[OWP202211] (Mathematisches Forschungsinstitut Oberwolfach, 20220629)We use Constraint Satisfaction Methods to construct and enumerate finite Lalgebras up to isomorphism. These objects were recently introduced by Rump and appear in Garside theory, algebraic logic, and the study of the ... 
On the Gauss Algebra of Toric Algebras
[OWP201807] (Mathematisches Forschungsinstitut Oberwolfach, 20180425)Let $A$ be a $K$subalgebra of the polynomial ring $S=K[x_1,\ldots,x_d]$ of dimension $d$, generated by finitely many monomials of degree $r$. Then the Gauss algebra $\mathbb{G}(A)$ of $A$ is generated by monomials of ... 
On the geometry of regular maps from a quasiprojective surface to a curve
[OWP201303] (Mathematisches Forschungsinstitut Oberwolfach, 20130314)We explore consequences of the triviality of the monodromy group, using the condition of purity of the mixed Hodge structure on the cohomology of the surface X. 
On the geometry of the space of fibrations
[OWP200915] (Mathematisches Forschungsinstitut Oberwolfach, 20090309)We study geometrical aspects of the space of fibrations between two given manifolds $M$ and $B$, from the point of view of Fréchet geometry. As a first result, we show that any connected component of this space is the ... 
On the Invariants of the Cohomology of Complements of Coxeter Arrangements
[OWP201821] (Mathematisches Forschungsinstitut Oberwolfach, 20181022)We refine Brieskorn's study of the cohomology of the complement of the reflection arrangement of a finite Coxeter group W. As a result we complete the verification of a conjecture by Felder and Veselov that gives an explicit ... 
On the L2 Markov Inequality with Laguerre Weight
[OWP201615] (Mathematisches Forschungsinstitut Oberwolfach, 20160817) 
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. ... 
On the Markov inequality in the $L_2$norm with the Gegenbauer weight
[OWP201705] (Mathematisches Forschungsinstitut Oberwolfach, 20170222)Let $w_{\lambda}(t) := (1t^2)^{\lambda1/2}$, where ${\lambda} > \frac{1}{2}$, be the Gegenbauer weight function, let $\\cdot\_{w_{\lambda}}$ be the associated $L_2$norm, $$ f\_{w_{\lambda}} = \left\{\int_{1}^1 ... 
On the nonanalyticity locus of an arcanalytic function
[OWP200903] (Mathematisches Forschungsinstitut Oberwolfach, 20090221)A function is called arcanalytic if it is real analytic on each real analytic arc. In real analytic geometry there are many examples of arcanalytic functions that are not real analytic. Arc analytic functions appear ... 
On the prediction of stationary functional time series
[OWP201406] (Mathematisches Forschungsinstitut Oberwolfach, 20140425)This paper addresses the prediction of stationary functional time series. Existing contributions to this problem have largely focused on the special case of firstorder functional autoregressive processes because of their ... 
On the δ=const Collisions of Singularities of Complex Plane Curves
[OWP200815] (Mathematisches Forschungsinstitut Oberwolfach, 2008)We study a specific class of deformations of curve singularities: the case when the singular point splits to several ones, such that the total $\delta$ invariant is preserved. These are also known as equinormalizable or ...