• 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 ...
    • 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 ...
    • 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 ...
    • 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 ...
    • 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 ...
    • 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 ...
    • 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 ...
    • 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 ...