相关论文: Exact WKB analysis and cluster algebras

We consider (iced) quiver with potential $(\bar{Q}(D), F(D), \bar{W}(D))$ associated to a Postnilov Diagram $D$ and prove the mutation of the quiver with potential $(\bare{Q}(D), F(D), \bar{W}(D))$ is compatible with the geometric exchange…

The Stokes formalism of polarization physics has astounding structural parallels with the formalism used for relativity theory in Minkowski spacetime. The structure and symmetry properties of the Mueller matrices are the same as those for…

Mutation of compact silting objects is a fundamental operation in the representation theory of finite-dimensional algebras due to its connections to cluster theory and to the lattice of torsion pairs in module or derived categories. In this…

We construct a cubic field theory which provides all genus amplitudes of the topological A-model for all non-compact Calabi-Yau toric threefolds. The topology of a given Feynman diagram encodes the topology of a fixed Calabi-Yau, with…

Using Bloch-Ogus theorem and Chern character from K-theory to cyclic homology, we answer a question of Green and Griffiths on extending Bloch formula. Moreover, we construct a map from local Hilbert functor to local cohomology. With…

In this paper we study some new theories of characteristic homology classes for singular complex algebraic varieties. First we introduce a natural transformation T_{y}: K_{0}(var/X) -> H_{*}(X,Q)[y] commuting with proper pushdown, which…

A coordinate-free definition for Wick-type symbols is given for symplectic manifolds by means of the Fedosov procedure. The main ingredient of this approach is a bilinear symmetric form defined on the complexified tangent bundle of the…

I conjecture that index formulas for $K$-theory classes on the moduli of holomorphic $G$-bundles over a compact Riemann surface $\Sigma$ are controlled, in a precise way, by Frobenius algebra deformations of the Verlinde algebra of $G$. The…

Grothendieck-Verdier categories (also known as $\ast$-autonomous categories) generalize rigid monoidal categories, with notable representation-theoretic examples including categories of bimodules, modules over Hopf algebroids, and modules…

In 2007, Alekseev-Meinrenken proved that there exists a Ginzburg-Weinstein diffeomorphism from the dual Lie algebra ${\rm u}(n)^*$ to the dual Poisson Lie group $U(n)^*$ compatible with the Gelfand-Zeitlin integrable systems. In this paper,…

Deformation K-theory associates to each discrete group G a spectrum built from spaces of finite dimensional unitary representations of G. In all known examples, this spectrum is 2-periodic above the rational cohomological dimension of G…

Cluster algebras, introduced by Fomin and Zelevinsky through the process of quiver mutation, have become central objects in modern algebra and geometry, linking combinatorial constructions with diverse mathematical domains such as…

In topology, a torus remains invariant under certain non-trivial transformations known as modular transformations. In the context of topologically ordered quantum states of matter, these transformations encode the braiding statistics and…

We offer a pedestrian level review of the wall-crossing invariants. The story begins from the scattering theory in quantum mechanics where the spectrum reshuffling can be related to permutations of S-matrices. In non-trivial situations,…

A universal geometric cluster algebra over an exchange matrix B is a universal object in the category of geometric cluster algebras over B related by coefficient specializations. (Following an earlier paper on universal geometric cluster…

The exact 2-point function of certain physically motivated operators in SYK-like spin glass models is computed, bypassing the Schwinger-Dyson equations. The models possess an IR low energy conformal window, but our results are exact at all…

Separable Bregman divergences induce Riemannian metric spaces that are isometric to the Euclidean space after monotone embeddings. We investigate fixed rate quantization and its codebook Voronoi diagrams, and report on experimental…

We propose a geometric interpretation for the Stokes phenomenon in de Sitter spacetime that particles are produced in even dimensions but not in odd dimensions. The scattering amplitude for a quantum field between the in-vacuum and the…

We formulate two-dimensional $N=(2,2)$ supersymmetric conformal field theories in terms of unitary full vertex operator superalgebras and develop their cohomology theory. Cohomology rings, Hodge numbers, and the Witten index of a unitary…

Let $\Delta+V$ be the discrete Schr\"odinger operator, where $\Delta$ is the discrete Laplacian on $\mathbb{Z}^d$ and potential $V:\mathbb{Z}^d\to \mathbb{C}$ is $\Gamma$-periodic with $\Gamma=q_1\mathbb{Z}\oplus q_2…