相关论文: Elliptic Genus Derivation of 4d Holomorphic Blocks

The notion of the genus of a quadratic form is generalized to vertex operator algebras. We define it as the modular braided tensor category associated to a suitable vertex operator algebra together with the central charge. Statements…

The singularity structure of the Coulomb and Higgs branches of good $3d$ $\mathcal{N}=4$ circular quiver gauge theories (CQGTs) with unitary gauge groups is studied. The central method employed is the Kraft--Procesi transition. CQGTs are…

We describe the birational correspondences, induced by the Fourier-Mukai functor, between moduli spaces of semistable sheaves on elliptic surfaces with sections, using the notion of $P$-stability in the derived category. We give explicit…

Nekrasov's gauge origami theory provides a (complex) 4-dimensional generalization of the ADHM quiver and its moduli spaces of representations. We describe the origami moduli space as the zero locus of an isotropic section of a quadratic…

For a proper scheme X with a fixed 1-perfect obstruction theory, we define virtual versions of holomorphic Euler characteristic, chi y-genus, and elliptic genus; they are deformation invariant, and extend the usual definition in the smooth…

In this talk I study the topology of mathematically idealised center vortices, defined in a gauge invariant way as closed (infinitely thin) flux surfaces (in D=4 dimensions) which contribute the $n^{th}$ power of a non-trivial center…

We completely determine the moduli space M_{N,k} of k-vortices in U(N) gauge theory with N Higgs fields in the fundamental representation. Its open subset for separated vortices is found as the symmetric product (C x CP^{N-1})^k / S_k.…

The object of this article is to construct certain classes of arithmetically significant, holomorphic Siegel cusp forms F of genus 2, which are neither of Saito-Kurokawa type, in which case the degree 4 spinor L-function L(s, F) is…

We present a self-contained analysis of theories of discrete 2D gravity coupled to matter, using geometric methods to derive equations for generating functions in terms of free (noncommuting) variables. For the class of discrete gravity…

For physicists: For supersymmetric quantum mechanics, there are cases when a mod-2 Witten index can be defined, even when a more ordinary $\mathbb{Z}$-valued Witten index vanishes. Similarly, for 2d supersymmetric quantum field theories,…

This work deals with the topological classification of germs of singular foliations on $(\mathbb C^{2},0)$. Working in a suitable class of foliations we fix the topological invariants given by the separatrix set, the Camacho-Sad indices and…

A modular category is a braided category with some additional algebraic features. The interest of this concept is that it provides a Topological Quantum Field Theory in dimension 3. The Verlinde formulas associated with a modular category…

Using the invariant form of the equation of geodesic deviation, which describes relative motion of free test particles, we investigate a general family of D-dimensional Kundt spacetimes. We demonstrate that local influence of the…

We investigate invertible projective representations and their 2-categorical analogues using the language of TQFTs with defects. The main result is a freeness property for invertible projective representatios. While trivial in the…

In this article we perform an extensive study of the spaces of automorphic forms for GL(2) of weight two and level N, for N an ideal in the ring of integers of the quartic CM field generated by the twelfth roots of unity. This study is…

We use finite group topological lattice gauge theory, also known as the quantum double model, as a lens to explore a notion of topological order enriched by a non-invertible symmetry. For invertible symmetry enriched topological order,…

We study 2d $\mathcal{N}=(0,2)$ and $\mathcal{N}=(0,4)$ theories derived from compactifying class $\mathcal{S}$ theories on $S^2$ with a topological twist. We present concise expressions for the elliptic genera of both classes of theories,…

In the paper we study two types of relations: a one is between the elliptic genus of Calabi-Yau manifolds and Jacobi modular forms, another one is between the second quantized elliptic genus, Siegel modular forms and Lorentzian Kac-Moody…

Let $\mathcal N$ be the moduli space of sextics with 3 (3,4)-cusps. The quotient moduli space ${\mathcal N}/G$ is one-dimensional and consists of two components, ${\mathcal N}_{torus}/G$ and ${\mathcal N}_{gen}/G$. By quadratic…

The 102581 flat toric elliptic fibrations over P^2 are identified among the Calabi-Yau hypersurfaces that arise from the 473800776 reflexive 4-dimensional polytopes. In order to analyze their elliptic fibration structure, we describe the…