• Flag-Accurate Arrangements 

      [OWP-2023-01] Mücksch, Paul; Röhrle, Gerhard; Tran, Tan Nhat (Mathematisches Forschungsinstitut Oberwolfach, 2023-02-13)
      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 ...
    • Real Enumerative Invariants Relative to the Anti-Canonical Divisor and their Refinement 

      [OWP-2023-02] Itenberg, Ilia; Shustin, Eugenii (Mathematisches Forschungsinstitut Oberwolfach, 2023-03-24)
      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 ...
    • Computer Algebra with GAP 

      [OWP-2023-03] Piterman, Kevin I.; Vendramin, Leandro (Mathematisches Forschungsinstitut Oberwolfach, 2023-04-13)
      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 ...
    • Edifices: Building-like Spaces Associated to Linear Algebraic Groups; In memory of Jacques Tits 

      [OWP-2023-04] Bate, Michael; Martin, Benjamin; Röhrle, Gerhard (Mathematisches Forschungsinstitut Oberwolfach, 2023-06-19)
      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 ...
    • Hypergroups and Twin Buildings, I 

      [OWP-2023-10] French, Christopher; Zieschang, Paul-Hermann (Mathematisches Forschungsinstitut Oberwolfach, 2023-06-19)
      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 ...
    • Automatic Differentiation for ML-Familiy Languages: Correctness via Logical Relations 

      [OWP-2023-07] Lucatelli Nunes, Fernando; Vákár, Matthijs (Mathematisches Forschungsinstitut Oberwolfach, 2023-06-19)
    • Semantic Factorization and Descent 

      [OWP-2023-05] Lucatelli Nunes, Fernando (Mathematisches Forschungsinstitut Oberwolfach, 2023-06-19)
      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 ...
    • Logical Relations for Partial Features and Automatic Differentiation Correctness 

      [OWP-2023-09] Lucatelli Nunes, Fernando; Vákár, Matthijs (Mathematisches Forschungsinstitut Oberwolfach, 2023-06-19)
      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 

      [OWP-2023-08] Clementino, Maria Manuel; Lucatelli Nunes, Fernando (Mathematisches Forschungsinstitut Oberwolfach, 2023-06-19)
      Let $\mathsf{Ord} $ be the category of (pre)ordered sets. Unlike $\mathsf{Ord}/X$, whose behaviour is well-known, not much can be found in the literature about the lax comma 2-category $\mathsf{Ord} //X$. In this paper ...
    • Cauchy Completeness, Lax Epimorphisms and Effective Descent for Split Fibrations 

      [OWP-2023-06] Lucatelli Nunes, Fernando; Prezado, Rui; Sousa, Lurdes (Mathematisches Forschungsinstitut Oberwolfach, 2023-06-19)
      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 $F \colon \mathcal{A} \to \mathcal{B}$ ...
    • Rank Deviations for Overpartitions 

      [OWP-2023-11] Lovejoy, Jeremy; Osburn, Robert (Mathematisches Forschungsinstitut Oberwolfach, 2023-07-12)
      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 ...
    • The Simplicial Complex of Brauer Pairs of a Finite Reductive Group 

      [OWP-2023-12] Rossi, Damiano (Mathematisches Forschungsinstitut Oberwolfach, 2023-07-17)
      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 ...
    • The Brown Complex in Non-Defining Characteristic and Applications 

      [OWP-2023-14] Rossi, Damiano (Mathematisches Forschungsinstitut Oberwolfach, 2023-07-25)
      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 ...
    • Multi-Dimensional Summation-by-Parts Operators for General Function Spaces: Theory and Construction 

      [OWP-2023-13] Glaubitz, Jan; Klein, Simon-Christian; Nordström, Jan; Öffner, Philipp (Mathematisches Forschungsinstitut Oberwolfach, 2023-07-25)
      Summation-by-parts (SBP) operators allow us to systematically develop energy-stable and high-order accurate numerical methods for time-dependent differential equations. Until recently, the main idea behind existing SBP ...
    • The Character Triple Conjecture for Maximal Defect Characters and the Prime 2 

      [OWP-2023-15] Rossi, Damiano (Mathematisches Forschungsinstitut Oberwolfach, 2023-08-22)
      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 so-called ...
    • Bochner-Riesz Means at the Critical Index: Weighted and Sparse Bounds 

      [OWP-2023-16] Beltran, David; Roos, Joris; Seeger, Andreas (Mathematisches Forschungsinstitut Oberwolfach, 2023-11-27)
      We consider Bochner-Riesz means on weighted $L^p$ spaces, at the critical index $\lambda(p)=d(\frac 1p-\frac 12)-\frac 12$. For every $A_1$-weight we obtain an extension of Vargas' weak type $(1,1)$ inequality in some range ...
    • Ground State of Bose Gases Interacting through Singular Potentials 

      [OWP-2023-18] Boßmann, Lea; Leopold, Nikolai; Petrat, Sören; Rademacher, Simone (Mathematisches Forschungsinstitut Oberwolfach, 2023-11-27)
      We consider a system of $N$ bosons on the three-dimensional unit torus. The particles interact through repulsive pair interactions of the form $N^{3β-1} v (N^βx)$ for $β\in (0,1)$. We prove the next order correction to ...
    • A Note on Endpoint Bochner-Riesz Estimates 

      [OWP-2023-17] Beltran, David; Roos, Joris; Seeger, Andreas (Mathematisches Forschungsinstitut Oberwolfach, 2023-11-27)
      We revisit an $\varepsilon$-removal argument of Tao to obtain sharp $L^p \to L^r(L^p)$ estimates for sums of Bochner-Riesz bumps which are conditional on non-endpoint bounds for single scale bumps. These can be used to ...