Related papers: Frobenius morphisms and stability conditions

We analyze in detail the case of a marginally stable D-Brane on a collapsed del Pezzo surface in a Calabi-Yau threefold using the derived category of quiver representations and the idea of aligned gradings. We show how the derived category…

We explain how structures analogous to those appearing in the theory of stability conditions on abelian and triangulated categories arise in geometric invariant theory. This leads to an axiomatic notion of a central charge on a scheme with…

We consider the $s$-fractional Klein-Gordon equation with space-dependent damping on $\mathbb{R}^d$. Recent studies reveal that the so-called geometric control conditions (GCC) are closely related to semigroup estimates of the equation.…

We establish Kirchberg's Local Lifting Property and Lubotzky--Shalom's Property FD for classes of finitely generated groups of central importance in geometric and combinatorial group theory: $3$-manifold groups, limit groups, and certain…

Let $G$ be a connected reductive algebraic group defined over the finite field $\F_q$, where $q$ is a power of a good prime for $G$, and let $F$ denote the corresponding Frobenius endomorphism, so that $G^F$ is a finite reductive group. Let…

We study some aspects of dynamical compactification scenario where stabilisation of extra dimensions occurs due to presence the Gauss-Bonnet term and non-zero spatial curvature. In the framework of the model under consideration there exists…

For a finite group $G$, the so-called $G$-Mackey functors form an abelian category $M(G)$ that has many applications in the study of $G$-equivariant stable homotopy. One would expect that the derived category $D(M(G))$ would be similarly…

We consider a class of relative $n$-Calabi--Yau dg-algebras, referred to as relative Ginzburg algebras, associated with marked surfaces equipped with a decomposition into $n$-gons ($n$-angulation). We relate their derived categories to the…

We show that an orthogonal basis for a finite-dimensional Hilbert space can be equivalently characterised as a commutative dagger-Frobenius monoid in the category FdHilb, which has finite-dimensional Hilbert spaces as objects and continuous…

A recent experimental realization of quantum degenerate gas of $^{40}$K$^{87}$Rb molecules opens up prospects of exploring strong dipolar Fermi gases and many-body phenomena arising in that regime. Here we derive a mean-field variational…

Let $X$ be a very general Gushel-Mukai (GM) variety of dimension $n\geq 4$, and let $Y$ be a smooth hyperplane section. There are natural pull-back and push-forward functors between the semi-orthogonal components (known as the Kuznetsov…

For a finite extension $F$ of $\mathbb{Q}_p$ and $n \geq 1$, let $D$ be the division algebra over $F$ of invariant $1/n$ and let $G^0$ be the subgroup of $\text{GL}_n(F)$ of elements with norm $1$ determinant. We show that the action of…

We prove a homological stabilization theorem for Hurwitz spaces: moduli spaces of branched covers of the complex projective line. This has the following arithmetic consequence: let l>2 be prime and A a finite abelian l-group. Then there…

We prove the existence of Bridgeland stability conditions on the Kuznetsov components of Gushel-Mukai varieties, and describe the structure of moduli spaces of Bridgeland semistable objects in these categories in the even-dimensional case.…

We compute the minimal model for Ginzburg algebras associated to acyclic quivers $Q$. In particular, we prove that there is a natural grading on the Ginzburg algebra making it formal and quasi-isomorphic to the preprojective algebra in…

We define new invariants of 3d Calabi-Yau categories endowed with a stability structure. Intuitively, they count the number of semistable objects with fixed class in the K-theory of the category ("number of BPS states with given charge" in…

We study moduli stabilisation in four-dimensional $N=1$ supergravity theories which originate from compactifications of the heterotic string on certain manifolds with $SU(3)$ structure. These theories have a non-trivial superpotential…

Consider the general linear group $G=GL_{n}(K)$ defined over an infinite field $K$ of positive characteristic $p$. We denote by $\Delta(\lambda)$ the Weyl module of $G$ which corresponds to a partition $\lambda$. Let $\lambda, \mu $ be…

In this paper we study the interplay between Lagrangian cobordisms and stability conditions. We show that any stability condition on the derived Fukaya category $D\mathcal{F}uk(M)$ of a symplectic manifold $(M,\omega)$ induces a stability…

We prove that, when $n$ goes to infinity, the expression, with respect to the dual Kazhdan-Lusztig basis, of the product $\hat{\underline{H}}_x\underline{H}_y$ of elements of the dual and the usual Kazhdan-Lusztig bases in the Hecke algebra…