Related papers: The topological period-index problem over 6-comple…
For any flag simplicial complex $K$, we describe the multigraded Poincare series, the minimal number of relations and the degrees of these relations in the Pontryagin algebra of the corresponding moment-angle complex $Z_K$. We compute the…
We introduce \emph{local Urysohn width}, a complexity measure for classification problems on metric spaces. Unlike VC dimension, fat-shattering dimension, and Rademacher complexity, which characterize the richness of hypothesis…
It was well known that there are $e$-particles and $m$-strings in the 3-dimensional (spatial dimension) toric code model, which realizes the 3-dimensional $\mathbb{Z}_2$ topological order. Recent mathematical result, however, shows that…
Given integers $a_1,a_2,a_3$, there is a complex rank $3$ topological bundle on $\mathbb CP^5$ with $i$-th Chern class equal to $a_i$ if and only if $a_1,a_2,a_3$ satisfy the Schwarzenberger condition. Provided that the Schwarzenberger…
The paper deals with planar polynomial vector fields. We aim to estimate the number of orbital topological equivalence classes for the fields of degree n. An evident obstacle for this is the second part of Hilbert's 16th problem. To…
We establish an index theorem for Toeplitz operators on odd dimensional spin manifolds with boundary. It may be thought of as an odd dimensional analogue of the Atiyah-Patodi-Singer index theorem for Dirac operators on manifolds with…
We study the topologically twisted index of $\mathcal{N}=6$ supersymmetric Chern-Simons matter theory with $U(N)_k \times U(N)_{-k}$ gauge group in the 't Hooft limit, that is, for $N, k \, \to \infty$ with $\lambda=N/k$ fixed. In the…
The study of topological band structures have sparked prominent research interest the past decade, culminating in the recent formulation of rather prolific classification schemes that encapsulate a large fraction of phases and features.…
Let $M$ be a hyperkahler manifold, $\Gamma$ its mapping class group, and $Teich$ the Teichmuller space of complex structures of hyperkahler type. After we glue together birationally equivalent points, we obtain the so-called birational…
Let $f : X \to S$ be a family of smooth projective algebraic varieties over a smooth connected base $S$, with everything defined over $\overline{\mathbb{Q}}$. Denote by $\mathbb{V} = R^{2i} f_{*} \mathbb{Z}(i)$ the associated integral…
We obtain new invariants of topological link concordance and homology cobordism of 3-manifolds from Hirzebruch-type intersection form defects of towers of iterated p-covers. Our invariants can extract geometric information from an arbitrary…
We propose a generalization of the topological vertex, which we call the "non-commutative topological vertex". This gives open BPS invariants for a toric Calabi-Yau manifold without compact 4-cycles, where we have D0/D2/D6-branes wrapping…
Periodic Hamiltonians on a three-dimensional (3-D) lattice with a spectral gap not only on the bulk but also on two edges at the common Fermi level are considered. By using K-theory applied for the quarter-plane Toeplitz extension, two…
In this paper we advance the theory of O'Neil's period-index obstruction map and derive consequences for the arithmetic of genus one curves over global fields. Our first result implies that for every pair of positive integers (P,I) with P…
We find the sharp bounds on $h^0(F)$ for one-dimensional semistable sheaves $F$ on a projective variety $X$ by using the spectrum of semistable sheaves. The result generalizes the Clifford theorem. When $X$ is the projective plane…
Although topological band theory has been used to discover and classify a wide array of novel topological phases in insulating and semi-metal systems, it is not well-suited to identifying topological phenomena in metallic or gapless…
In this paper, we will consider the period index problems of elliptic curves and introduce a value called generic index which is closed related to the essential dimension of Picard stacks. In particular, we will use examples to see that…
We examine the noncommutative index theory associated to the dynamics of a Delone set and the corresponding transversal groupoid. Our main motivation comes from the application to topological phases of aperiodic lattices and materials, and…
We propose a three-dimensional field theory construction that realizes the vertex algebras associated with the intermediate Lie algebras and the related $C_2$-cofinite minimal $W$-algebras of the Deligne-Cvitanovi\'c (DC) series as boundary…
We study a class of quantum integrable systems derived from dimer graphs and also described by local toric Calabi-Yau geometries with higher genus mirror curves, generalizing some previous works on genus one mirror curves. We compute the…