Related papers: Global spectra, polytopes and stacky invariants

There exist exactly 166 4-dimensional reflexive polytopes such that the corresponding 4-dimensional Gorenstein toric Fano varieties have at worst terminal singularities in codimension 3 and their anticanonical divisor is divisible by 2. For…

With an explicit, algebraic indexing $(2,1)$-category, we develop an efficient homotopy theory of cyclonic objects: circle-equivariant objects relative to the family of finite subgroups. We construct an $\infty$-category of cyclotomic…

We obtain combinatorial model categories of parametrised spectra, together with systems of base change Quillen adjunctions associated to maps of parameter spaces. We work with simplicial objects and use Hovey's sequential and symmetric…

For a fixed quadratic polynomial $\mathfrak{p}$ in $n$ non-commuting variables, and $n$ independent $N\times N$ complex Ginibre matrices $X_1^N,\dots, X_n^N$, we establish the convergence of the empirical spectral distribution of $P^N…

We provide a multiplicative classification of polynomial endofunctors on spectra in terms of their Mackey functors of cross--effects. More precisely, we prove that various categories of multivariable excisive functors from spectra to…

We study the spectral polynomial of the Treibich-Verdier potential. Such spectral polynomial, which is a generalization of the classical Lame polynomial, plays fundamental roles in both the finite-gap theory and the ODE theory of Heun's…

We introduce the notion of tame $\rho$-quaternionic manifold that permits the construction of a finite family of $\rho$-connections, significant for the geometry involved. This provides, for example, the following: (1) a new simple global…

We prove a general representation stability result for polynomial coefficient systems which lets us prove representation stability and secondary homological stability for many families of groups with polynomial coefficients. This gives two…

In the (covariant) topos approach to quantum theory by Heunen, Landsman and Spitters, one associates to each unital C*-algebra, A, a topos T(A) of sheaves on a locale and a commutative C*-algebra, a, within that topos. The Gelfand spectrum…

We consider a global, nonlinear version of the Whitney extension problem for manifold-valued smooth functions on closed domains $C$, with non-smooth boundary, in possibly non-compact manifolds. Assuming $C$ is a submanifold with corners, or…

Symmetric Grothendieck polynomials are inhomogeneous versions of Schur polynomials that arise in combinatorial $K$-theory. A polynomial has saturated Newton polytope (SNP) if every lattice point in the polytope is an exponent vector. We…

We prove a thick subcategory theorem for the category of $d$-excisive functors from finite spectra to spectra. This generalizes the Hopkins-Smith thick subcategory theorem (the $d=1$ case) and the $C_2$-equivariant thick subcategory theorem…

We calculate the Picard group of generic (very general) spectral varieties living in the total space of a very ample line bundle over an algebraically closed field $k$ of odd characteristics or characteristic 0. We follow the strategy of…

We introduce a theory of stratifications of noncommutative stacks (i.e. presentable stable $\infty$-categories), and we prove a reconstruction theorem that expresses them in terms of their strata and gluing data. This reconstruction theorem…

This paper announces results on the behavior of some important algebraic and topological invariants --- Euler characteristic, arithmetic genus, and their intersection homology analogues; the signature, etc. --- and their associated…

We give a new fast method for evaluating sprectral approximations of nonlinear polynomial functionals. We prove that the new algorithm is convergent if the functions considered are smooth enough, under a general assumption on the spectral…

We prove that open Gromov-Witten invariants for semi-Fano toric manifolds of the form $X=\mathbb{P}(K_Y\oplus\mathcal{O}_Y)$, where $Y$ is a toric Fano manifold, are equal to certain 1-pointed closed Gromov-Witten invariants of $X$. As…

Strassen's asymptotic spectrum offers a framework for analyzing the complexity of tensors. It has found applications in diverse areas, from computer science to additive combinatorics and quantum information. A long-standing open problem,…

We make progress in understanding the geometry associated to the Generalized Toric Polygons (GTPs) encoding the Physics of 5d Superconformal Field Theories (SCFTs), by exploiting the connection between Hanany-Witten transitions and the…

We propose conjectural semiorthogonal decompositions for Fano schemes of linear subspaces on intersections of two quadrics, in terms of symmetric powers of the associated hyperelliptic (resp. stacky) curve. When the intersection is…