A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Quantum duality map extended to general marked surfaces and its compatibility with skein algebras proven.
We define a canonical map from a certain space of laminations on a punctured surface into the quantized algebra of functions on a cluster variety. We show that this map satisfies a number of special properties conjectured by Fock and Goncharov. Our construction is based on the "quantum trace" map introduced by Bonahon …
Quantum trace maps for surfaces are shown to be compatible under triangulations.
Finiteness predicts dualities in quantum gravity.
Unified study of homological representations of mapping class groups.
The relationship between expectation and price is commonly established with two principles: no-arbitrage, which asserts that both maps are positive; and equivalence, which asserts that the maps share the same null events. Constructed from the Arrow-Debreu securities, classical and quantum models of economics are then d…
We study generalized electric/magnetic duality in Abelian gauge theory by combining techniques from locally covariant quantum field theory and Cheeger-Simons differential cohomology on the category of globally hyperbolic Lorentzian manifolds. Our approach generalizes previous treatments using the Hamiltonian formalism …
New structure for quantum algebra representations.
Quantum invariants derived from link holonomy.
Recently we introduced T-duality in the study of topological insulators, and used it to show that T-duality trivialises the bulk-boundary correspondence in 2 dimensions. In this paper, we partially generalise these results to higher dimensions and briefly discuss the 4D quantum Hall effect.
New proof of SL(n) skein algebra for twice punctured sphere, showing it's a polynomial algebra.
Recently we introduced T-duality in the study of topological insulators. In this paper, we study the bulk-boundary correspondence for three phenomena in condensed matter physics, namely, the quantum Hall effect, the Chern insulator, and time reversal invariant topological insulators. In all of these cases, we show that…
Preprint proves quantum coideal Schur-Weyl duality and generalizes Jones-Wenzl projectors.
Unified geometric approach to quantum indeterminacy.
Introduces Legendre bundle for dually flat manifolds and quantum field theories.
We define and study the category of symmetric -webs. This category is a combinatorial description of the category of all finite dimensional quantum -modules. Explicitly, we show that (the additive closure of) the symmetric -spider is (braided monoidally) equivalent to …
We exhibit a Poisson module restoring a twisted Poincare duality between Poisson homology and cohomology for the polynomial algebra R=C[X_1,...,X_n] endowed with Poisson bracket arising from a uniparametrised quantum affine space. This Poisson module is obtained as the semiclassical limit of the dualising bimodule for …
Dirichlet-Neumann duality for Riemannian submersions
Study framizations of algebras using Schur--Weyl duality and tied braids.
New algebraic setup defines quantum link invariants.
We construct link invariants using the subfactor planar algebras, and use these to prove new identities relating certain specializations of colored Jones polynomials to specializations of other quantum knot polynomials. These identities can also be explained by coincidences between small modular categories inv…
We study the geometry of complexified moduli spaces of special Lagrangian submanifolds in the complement of an anticanonical divisor in a compact Kahler manifold. In particular, we explore the connections between T-duality and mirror symmetry in concrete examples, and show how quantum corrections arise in this context.
We elaborate a detailed study of certain aspects of (a version of) the AdS/CFT correspondence, conjectured by Maldacena and Witten, between quantum field theories in a gravitational background given by an asymptotically anti-de Sitter (AAdS) spacetime, and conformally covariant quantum field theories in the latter's co…
This paper explains the conjectured algebraic duality between genus zero Gromov-Witten theory and genus zero "Closed String topology". This duality in another perspective is discussed on page 87 of the book "Frobenius manifold, quantum cohomology, and moduli spaces" (by Yuri Manin). This paper also discusses Fulton Mac…
Maps self-duality in little disks operad to framed manifolds.
In these lectures we present a general introduction to topological quantum field theories. These theories are discussed in the framework of the Mathai-Quillen formalism and in the context of twisted N=2 supersymmetric theories. We discuss in detail the recent developments in Donaldson-Witten theory obtained from the ap…
New duality found between harmonic maps and self-dual solutions.
We construct new examples of torsional heterotic backgrounds using duality with orientifold flux compactifications. We explain how duality provides a perturbative solution to the type I/heterotic string Bianchi identity. The choice of connection used in the Bianchi identity plays an important role in the construction. …
Dualities in physics help in machine learning tasks.
Handlebody groups are virtual duality groups in positive genus.
The paper shows compatibility between two quantum maps for surfaces and 3-manifolds.
We describe how generalized complex geometry, which interpolates between complex and symplectic geometry, is compatible with T-duality, a relation between quantum field theories discovered by physicists. T-duality relates topologically distinct torus bundles, and prescribes a method for transporting geometrical structu…
Quantum machine learning models can approximate any continuous function.
Quantum trace map defined for 3-manifolds with torus boundaries.
This work forms a foundational study of factorization homology, or topological chiral homology, at the generality of stratified spaces with tangential structures. Examples of such factorization homology theories include intersection homology, compactly supported stratified mapping spaces, and Hochschild homology with c…
Explains a property of algebras related to quantum field theories.
New algebras and maps defined in knot Floer homology for trivalent vertices.
We establish a long exact sequence for Legendrian submanifolds L in P x R, where P is an exact symplectic manifold, which admit a Hamiltonian isotopy that displaces the projection of L off of itself. In this sequence, the singular homology H_* maps to linearized contact cohomology CH^* which maps to linearized contact …
New basis and Schur-Weyl duality for loop Hecke algebra defined.
Researchers resolve a SYZ conjecture for A_n singularities using quantum-corrected T-duality.
The paper extends T-duality and Jacobi forms to Witten gerbe modules.
Study topological quantum mechanics on orbifolds with geometric interpretation.
The goal of this paper is to exhibit a deep relation between the partition function of the Ising model on a planar trivalent graph and the generating series of the spin network evaluations on the same graph. We provide respectively a fermionic and a bosonic Gaussian integral formulation for each of these functions and …
We explain how, starting with a stack of D4-branes ending on an NS5-brane in type IIA string theory, one can, via T-duality and the topological-holomorphic nature of the relevant worldvolume theories, relate (i) the lattice models realized by Costello's 4d Chern-Simons theory, (ii) links in 3d analytically-continued Ch…
Restricts quantum representations of mapping class groups to integral coefficients.
3D quantum trace map connects 3-manifold quantizations.
Quantum Frobenius map for skein modules constructed and described.
We study quantum moment maps of -invariant star products, which are a quantum analogue of the moment map for classical Hamiltonian systems. Introducing an integral representation, we show that any quantum moment map for a -invariant star product is differentiable. This property gives us a new method for the class…