2022
2022
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Deciding Non-Freeness of Rational Möbius Groups
[OWP-2022-07] (Mathematisches Forschungsinstitut Oberwolfach, 2022-03-22)We explore a new computational approach to a classical problem: certifying non-freeness of (2-generator, parabolic) Möbius subgroups of SL(2, $\mathbb{Q}$). The main tools used are algorithms for Zariski dense groups and ... -
Characterization of Tropical Planar Curves up to Genus Six
[OWP-2022-06] (Mathematisches Forschungsinstitut Oberwolfach, 2022-03-16)We provide new forbidden criterion for realizability of smooth tropical plane curves. This in turn provides us a complete classification of smooth tropical plane curves up to genus six. -
Local and Global Canonical Forms for Differential-Algebraic Equations with Symmetries
[OWP-2022-05] (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 ... -
Aeppli-Bott-Chern-Massey Products, Bigraded Notions of Formality, and Non-Zero Degree Maps
[OWP-2022-04] (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 ... -
Some Homological Properties of Borel Type Ideals
[OWP-2022-03] (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 ... -
Trivial Source Character Tables of SL2(q)
[OWP-2022-02] (Mathematisches Forschungsinstitut Oberwolfach, 2022-01-28)We compute the trivial source character tables (also called species tables of the trivial source ring) of the infinite family of finite groups SL(2,q) over a large enough field of positive characteristic $\ell$ via ... -
Applications of Nijenhuis Geometry III: Frobenius Pencils and Compatible Non-Homogeneous Poisson Structures
[OWP-2022-01] (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 ...