2023
2023
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The Character Triple Conjecture for Maximal Defect Characters and the Prime 2
[OWP202315] (Mathematisches Forschungsinstitut Oberwolfach, 20230822)We prove that Späth’s Character Triple Conjecture holds for every finite group with respect to maximal defect characters at the prime 2. This is done by reducing the maximal defect case of the conjecture to the socalled ... 
The Brown Complex in NonDefining Characteristic and Applications
[OWP202314] (Mathematisches Forschungsinstitut Oberwolfach, 20230725)We study the Brown complex associated to the poset of $\ell$subgroups in the case of a finite reductive group defined over a field $\mathbb{F}_q$ of characteristic prime to $\ell$. First, under suitable hypotheses, we ... 
MultiDimensional SummationbyParts Operators for General Function Spaces: Theory and Construction
[OWP202313] (Mathematisches Forschungsinstitut Oberwolfach, 20230725)Summationbyparts (SBP) operators allow us to systematically develop energystable and highorder accurate numerical methods for timedependent differential equations. Until recently, the main idea behind existing SBP ... 
The Simplicial Complex of Brauer Pairs of a Finite Reductive Group
[OWP202312] (Mathematisches Forschungsinstitut Oberwolfach, 20230717)In this paper we study the simplicial complex induced by the poset of Brauer pairs ordered by inclusion for the family of finite reductive groups. In the defining characteristic case the homotopy type of this simplicial ... 
Rank Deviations for Overpartitions
[OWP202311] (Mathematisches Forschungsinstitut Oberwolfach, 20230712)We prove general fomulas for the deviations of two overpartition ranks from the average, namely \begin{equation*} \overline{D}(a, M) := \sum_{n \geq 0} \Bigl( \overline{N}(a, M, n)  \frac{\overline{p}(n)}{M} \Bigr) q^n ... 
Hypergroups and Twin Buildings, I
[OWP202310] (Mathematisches Forschungsinstitut Oberwolfach, 20230619)We discuss a conjecture on thick twin buildings the verification of which is needed in order to show that thick twin buildings are mathematically equivalent to regular actions of certain twin Coxeter hypergroups. (A ... 
Logical Relations for Partial Features and Automatic Differentiation Correctness
[OWP202309] (Mathematisches Forschungsinstitut Oberwolfach, 20230619)We present a simple technique for semantic, open logical relations arguments about languages with recursive types, which, as we show, follows from a principled foundation in categorical semantics. We demonstrate how it can ... 
Lax Comma Categories of Ordered Sets
[OWP202308] (Mathematisches Forschungsinstitut Oberwolfach, 20230619)Let $\mathsf{Ord} $ be the category of (pre)ordered sets. Unlike $\mathsf{Ord}/X$, whose behaviour is wellknown, not much can be found in the literature about the lax comma 2category $\mathsf{Ord} //X$. In this paper ... 
Automatic Differentiation for MLFamiliy Languages: Correctness via Logical Relations
[OWP202307] (Mathematisches Forschungsinstitut Oberwolfach, 20230619) 
Cauchy Completeness, Lax Epimorphisms and Effective Descent for Split Fibrations
[OWP202306] (Mathematisches Forschungsinstitut Oberwolfach, 20230619)For any suitable base category $\mathcal{V} $, we find that $\mathcal{V} $fully faithful lax epimorphisms in $\mathcal{V} $$\mathsf{Cat} $ are precisely those $\mathcal{V}$functors $F \colon \mathcal{A} \to \mathcal{B}$ ... 
Semantic Factorization and Descent
[OWP202305] (Mathematisches Forschungsinstitut Oberwolfach, 20230619)Let $\mathbb{A}$ be a $2$category with suitable opcomma objects and pushouts. We give a direct proof that, provided that the codensity monad of a morphism $p$ exists and is preserved by a suitable morphism, the factorization ... 
Edifices: Buildinglike Spaces Associated to Linear Algebraic Groups; In memory of Jacques Tits
[OWP202304] (Mathematisches Forschungsinstitut Oberwolfach, 20230619)Given a semisimple linear algebraic $k$group $G$, one has a spherical building $Δ_G$, and one can interpret the geometric realisation $Δ_G(\mathbb R)$ of $Δ_G$ in terms of cocharacters of $G$. The aim of this paper is to ... 
Computer Algebra with GAP
[OWP202303] (Mathematisches Forschungsinstitut Oberwolfach, 20230413)This monograph includes the following topics: a basic introduction to the language, basic arithmetic, permutations, matrices, polynomial rings, finite fields, finite and finitely presented groups, small groups, group ... 
Real Enumerative Invariants Relative to the AntiCanonical Divisor and their Refinement
[OWP202302] (Mathematisches Forschungsinstitut Oberwolfach, 20230324)We introduce new invariants of the projective plane (and, more generally, of certain toric surfaces) that arise from the appropriate enumeration of real elliptic curves. These invariants admit a refinement (according to ... 
FlagAccurate Arrangements
[OWP202301] (Mathematisches Forschungsinstitut Oberwolfach, 20230213)In [MR21], the first two authors introduced the notion of an accurate arrangement, a particular notion of freeness. In this paper, we consider a special subclass, where the property of accuracy stems from a flag of flats ...