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 ...

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 ...

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 ...

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 ...

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 $F \colon \mathcal{A} \to \mathcal{B}$ ...

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 ...

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 ...

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 ...

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 ...