Mathematics

In the generality of a rigidly-compactly generated tensor triangulated category, we introduce semi-Bousfield classes in terms of the vanishing of the tensor product in positive degrees with respect to a fixed reasonable $t$-structure. We…

In this paper, we answer negatively to a question posed in the context of the 2025 Oberwolfach Mini-Workshop ``The Yang-Baxter Equation and Representations of Braid Groups'' regarding the existence of split extensions classifiers in the…

The term Gibbons conjecture is widely used in connection with symmetry results for the Allen-Cahn equation. However, its origin is less transparent than its frequent citation suggests. In this note, we revisit its emergence, tracing it to a…

We prove that smooth quartic threefolds are symplectically irrational, i.e., cannot be related to projective space by a series of symplectic blow-ups, blow-downs, and deformations. This implies that they are algebraically irrational,…

This paper develops new aspects of the interplay between shifted symplectic geometry and classical Poisson geometry, focusing on lagrangian morphisms into 2-shifted symplectic groups. We establish a Lie-type correspondence between such…

We show that prequantization bundles have explicit Legendrian barriers, whose removal obstruct the embedding of long cylinders over Legendrian submanifolds.

Let $L$ be a closed Lagrangian submanifold of a symplectic manifold $(X,\omega)$. Cieliebak and Mohnke define the symplectic area of $L$ as the minimal positive symplectic area of a smooth $2$-disk in $X$ with boundary on $L$. An extremal…

For K\"ahler K3 surfaces we consider Kulikov models of type III tamed by a symplectic form. Our main result shows that the generic smooth fiber admits an almost toric fibration over the intersection complex, which inherits a natural nodal…

This article is a generalization of a result in Quillen's note ``Module theory over non-unital rings'' giving a one-to-one correspondence between bilocalization of abelian categories of modules and idempotent ideals of the base ring.…

K. S. S. Nambooripad introduced an interesting class of categories known as normal categories, which are categories with subobjects, morphisms admitting factorization and having sufficiently many cones. These normal categories plays…

We explore Seshadri constants associated to weighted blow-ups of complex projective varieties and demonstrate how to use this notion to construct symplectic embeddings of ellipsoids. We illustrate the utility of this point of view by…

In one of his posthumous papers, conserved in G\"ottingen, Riemann considers the derivatives of $\log\zeta(s)$ at the point $1/2$, giving explicit values for them. Around 2010 we shared Riemann's value of the second derivative with some…

We establish the equivalence between models of enhanced $2$-sketches and algebras over monads, including the (co)lax morphisms. More precisely, for any enhanced limit $2$-sketch $\mathbb{T}$ with tight cones, the enhanced $2$-category…

We extend a property of Mazzola's theory of cadential sets in relation to the modulation between minor and major tonalities from triadic to tetradic harmony, using the PLRQ group of Cannas et al. (2017) as the analogue of the classical PLR…

In this paper, we explore the connections between Christiaan Huygens and Niels Henrik Abel through the tautochrone problem. The problem -- determining the curve along which a particle descends under gravity in the same time, regardless of…

We study the symplectic semi-characteristic of a closed 4n-dimensional symplectic manifold. First, using the even-degree part of the primitive cohomology, we define the symplectic semi-characteristic. Second, using a vector field with…

We investigate a new notion of regularity for tensor triangulated categories, called residual regularity. We show that residual regularity descends and ascends via finite separable extensions and we classify all finite groups whose derived…

We construct open Gromov-Witten invariants in genus zero for arbitrary closed symplectic manifolds and embedded relatively spin Lagrangians, which are weakly unobstructed by a bounding cochain. This uses the foundational work of…

Drawing on well-known results from the theory of canonical extensions and the theory of categories enriched over a quantale, we define canonical extensions of quantale-enriched categories and establish their basic properties.

Lezama \cite{LezamaLatorre2017} introduced the notion of semi-graded ring with the aim of generalizing $\mathbb{Z}$-graded rings and several families of noncommutative rings of polynomial type non-$\mathbb{N}$-graded such as the skew…