Related papers: Quantum BCOV theory on Calabi-Yau manifolds and th…
We first develop theories of differential rings of quasi-Siegel modular and quasi-Siegel Jacobi forms for genus two. Then we apply them to the Eynard-Orantin topological recursion of certain local Calabi-Yau threefolds equipped with branes,…
We study stratification, that is the classification of localizing tensor ideal subcategories by geometric means, in the context of Kasparov's equivariant KK-theory of C*-algebras. We introduce a straightforward countable analog of the…
We construct cubic scalar field theory on $\lambda$-Minkowski space by combining the Batalin-Vilkovisky formalism with harmonic analysis, and produce two inequivalent noncommutative quantum field theories. The braided theory is based on a…
Dubrovin has shown that the spectrum of the quantization (with respect to the first Poisson structure) of the dispersionless Korteweg-de Vries (KdV) hierarchy is given by shifted symmetric functions; the latter are related by the…
We study a mirror interpretation of the relation between the exact partition functions of N=(2,2) gauged linear sigma-models (GLSM) on the 2d sphere and Kahler potentials on the moduli spaces of the CY manifolds proposed by Jockers et al.…
We prove a structural result in mirror symmetry for projective Calabi--Yau (CY) manifolds. Let $X$ be a connected symplectic CY manifold, whose Fukaya category $\mathcal{F}(X)$ is defined over some suitable Novikov field $\mathbb{K}$; its…
Topological strings on toric Calabi--Yau threefolds can be defined non-perturbatively in terms of a free Fermi gas of N particles. Using this approach, we propose a definition of quantum mirror curves as quantum distributions on phase…
In this series of papers we aim to provide a mathematically comprehensive framework to the Hamiltonian pictures of quantum field theory in curved spacetimes. Our final goal is to study the kinematics and the dynamics of the theory from the…
The classical Beauville-Bogomolov Decomposition Theorem asserts that any compact K\"ahler manifold with numerically trivial canonical bundle admits an \'etale cover that decomposes into a product of a torus, and irreducible,…
We derive an integral expression for the leading-order type I-I-I three-point functions in the $\mathfrak{su}(2) $-sector of $\mathcal{N}=4$ super Yang-Mills theory, for which no determinant formula is known. To this end, we first map the…
Mirror symmetry gives predictions for the genus zero Gromov-Witten invariants of a closed Calabi--Yau variety in terms of period integrals on a mirror family of Calabi-Yau varieties. We deduce an analogous mirror theorem for the open…
Starting from a Whitney decomposition of a symmetric cone $\Omega$, analog to the dyadic partition $[2^j, 2^{j+1})$ of the positive real line, in this paper we develop an adapted Littlewood-Paley theory for functions with spectrum in…
The goal of this note is to give a brief overview of the BV-BFV formalism developed by the first two authors and Reshetikhin in [arXiv:1201.0290], [arXiv:1507.01221] in order to perform perturbative quantisation of Lagrangian field theories…
In this paper, we propose an ansatz for defining Gopakumar-Vafa invariants of Calabi-Yau threefolds, using perverse sheaves of vanishing cycles. Our proposal is a modification of a recent approach of Kiem-Li, which is itself based on…
We define and study refined Gopakumar-Vafa invariants of contractible curves in complex algebraic 3-folds, alongside the cohomological Donaldson--Thomas theory of finite-dimensional Jacobi algebras. These Gopakumar-Vafa invariants can be…
We conjecture that appropriate K-theoretic Gromov-Witten invariants of complex flag manifolds G/B are governed by finite-difference versions of Toda systems constructed in terms of the Langlands-dual quantized universal enveloping algebras…
Quantitative (or controlled) $K$-theory for $C^*$-algebras was used by Guoliang Yu in his work on the Novikov conjecture, and later developed more formally by Yu together with Herv\'e Oyono-Oyono. In this paper, we extend their work by…
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…
We illustrate the use of the theory of $qq$-characters by deriving the BPZ and KZ-type equations for the partition functions of certain surface defects in quiver ${\mathcal N}=2$ theories. We generate a surface defect in the linear quiver…
For local Calabi-Yau manifolds which are total spaces of vector bundle over balloon manifolds, we propose a formal definition of reduced Genus one Gromov-Witten invariants, by assigning contributions from the refined decorated rooted trees.…