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On a Conjecture of Khoroshkin and Tolstoy

[OWP-2022-14] Appel, Andrea; Gautam, Sachin; Wendlandt, Curtis (Mathematisches Forschungsinstitut Oberwolfach, 2022-08-02)

We prove a no-go 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 ...

Aeppli-Bott-Chern-Massey Products, Bigraded Notions of Formality, and Non-Zero Degree Maps

[OWP-2022-04] Milivojević, Aleksandar; Stelzig, Jonas (Mathematisches Forschungsinstitut Oberwolfach, 2022-02-15)

We introduce and study notions of bigraded formality for the algebra of forms on a complex manifold, along with their relation to higher Aeppli-Bott-Chern-Massey products which extend, in an augmented setting, the case of ...

Applications of Nijenhuis Geometry III: Frobenius Pencils and Compatible Non-Homogeneous Poisson Structures

[OWP-2022-01] Bolsinov, Alexey V.; Konyaev, Andrey Yu.; Matveev, Vladimir S. (Mathematisches Forschungsinstitut Oberwolfach, 2022-01-20)

We consider multicomponent local Poisson structures of the form

$\mathcal P_3 + \mathcal P_1$ , under the assumption that the third order term

$\mathcal P_3$ is Darboux-Poisson and non-degenerate, and study the Poisson ...

Embedding Spaces of Split Links

[OWP-2022-13] Boyd, Rachael; Bregman, Corey (Mathematisches Forschungsinstitut Oberwolfach, 2022-08-01)

We study the homotopy type of the space

$\mathcal{E}(L)$ of unparametrised embeddings of a split link

$L=L_1\sqcup \ldots \sqcup L_n$ in

$\mathbb{R}^3$ . Inspired by work of Brendle and Hatcher, we introduce a semi-simplicial ...

Local and Global Canonical Forms for Differential-Algebraic Equations with Symmetries

[OWP-2022-05] Kunkel, Peter; Mehrmann, Volker (Mathematisches Forschungsinstitut Oberwolfach, 2022-02-21)

Linear time-varying differential-algebraic equations with symmetries are studied. The structures that we address are self-adjoint and skew-adjoint systems. Local and global canonical forms under congruence are presented ...

Shock-avoiding Slicing Conditions: Tests and Calibrations

[OWP-2022-12] Baumgarte, Thomas W.; Hilditch, David (Mathematisches Forschungsinstitut Oberwolfach, 2022-07-19)

While the 1+log slicing condition has been extremely successful in numerous numerical relativity simulations, it is also known to develop "gauge-shocks" in some examples. Alternative "shockavoiding" slicing conditions ...

Birational Rowmotion on a Rectangle over a Noncommutative Ring

[OWP-2022-17] Grinberg, Darij; Roby, Tom (Mathematisches Forschungsinstitut Oberwolfach, 2022-09-20)

We extend the periodicity of birational rowmotion for rectangular posets to the case when the base field is replaced by a noncommutative ring (under appropriate conditions). This resolves a conjecture from 2014. The proof ...

Some Homological Properties of Borel Type Ideals

[OWP-2022-03] Herzog, Jürgen; Moradi, Somayeh; Rahimbeigi, Masoomeh; Zhu, Guangjun (Mathematisches Forschungsinstitut Oberwolfach, 2022-02-01)

We study ideals of Borel type, including

$k$ -Borel ideals and

$t$ -spread Veronese ideals. We determine their free resolutions and their homological shift ideals. The multiplicity and the analytic spread of equigenerated ...

Discretization of Inherent ODEs and the Geometric Integration of DAEs with Symmetries

[OWP-2022-10] Kunkel, Peter; Mehrmann, Volker (Mathematisches Forschungsinstitut Oberwolfach, 2022-06-08)

Discretization methods for differential-algebraic equations (DAEs) are considered that are based on the integration of an associated inherent ordinary differential equation (ODE). This allows to make use of any discretization ...

On the Enumeration of Finite $L$ -Algebras

[OWP-2022-11] Dietzel, Carsten; Menchón, Paula; Vendramin, Leandro (Mathematisches Forschungsinstitut Oberwolfach, 2022-06-29)

We use Constraint Satisfaction Methods to construct and enumerate finite L-algebras up to isomorphism. These objects were recently introduced by Rump and appear in Garside theory, algebraic logic, and the study of the ...