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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 ...

Automatic Differentiation for ML-Familiy Languages: Correctness via Logical Relations

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

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 ...

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 ...

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 ...

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 ...

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 ...