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.
Constructs combinatorial 2D topological field theories from cyclic A-infinity algebras.
Estimates quantum cohomology complexity for Fano varieties and homogeneous spaces.
Cone structures in quantum field theory linked to information geometry.
The paper develops a theory linking Hamiltonian and quasi-Hamiltonian manifolds.
New geometric perspective for optimal learning on hexagonal structures.
To formulate the universal constraints of quantum statistics data of generic long-range entangled quantum systems, we introduce the geometric-topology surgery theory on spacetime manifolds where quantum systems reside, cutting and gluing the associated quantum amplitudes, specifically in 2+1 and 3+1 spacetime dimension…
We derive the general state sum construction for 2D topological quantum field theories (TQFTs) with source defects on oriented curves, extending the state-sum construction from special symmetric Frobenius algebra for 2-D TQFTs without defects (cf. Lauda \& Pfeiffer \cite{LP}). From the extended Pachner moves (Crane \& …
The abstract discusses connecting quantum mechanics and algebraic index theories.
The study classifies Kähler-Frobenius manifolds and their properties.
Summing over 3-manifolds using TQFT partition functions.
We give a construction of the abelian Chern-Simons gauge theory from the point of view of a 2+1 dimensional topological quantum field theory. The definition of the quantum theory relies on geometric quantization ideas which have been previously explored in connection to the nonabelian Chern-Simons theory [JW,ADW]. We f…
Using probabilistic methods, we first define Liouville quantum field theory on Riemann surfaces of genus and show that it is a conformal field theory. We use the partition function of Liouville quantum field theory to give a mathematical sense to Polyakov's partition function of noncritical bosonic s…
We construct a simple finite-dimensional topological quantum field theory for compact 3-manifolds with triangulated boundary.
The paper explores mapping class groups and their quantum field theory representations.
Link homology theories connect to 4-manifold invariants and TQFTs.
We prove that the associativity equations of two-dimensional topological quantum field theories are very natural reductions of the fundamental nonlinear equations of the theory of submanifolds in pseudo-Euclidean spaces and give a natural class of potential flat torsionless submanifolds. We show that all potential flat…
We investigate link homology theories for stable equivalence classes of link diagrams on orientable surfaces. We apply (1+1)-dimensional unoriented topological quantum field theories to Bar-Natan's geometric formalism to define new theories for stable equivalence classes.
Tropical geometry aids in computing topological quantum field theories.
In this article we prove that any unitary, axiomatic topological quantum field theory in four-dimensions can not detect changes in the smooth structure of M, a simply connected, closed (compact without boundary), oriented smooth manifold. However, as Donaldson-Witten theory (a topological quantum field theory but not a…
The theory of quantum computation can be constructed from the abstract study of anyonic systems. In mathematical terms, these are unitary topological modular functors. They underlie the Jones polynomial and arise in Witten-Chern-Simons theory. The braiding and fusion of anyonic excitations in quantum Hall electron liqu…
We present some ideas for a possible Noncommutative Floer Homology. The geometric motivation comes from an attempt to build a theory which applies to practically every 3-manifold (closed, oriented and connected) and not only to homology 3-spheres. There is also a physical motivation: one would like to construct a nonco…
This thesis is concerned with the application of operadic methods, particularly modular operads, to questions arising in the study of moduli spaces of surfaces as well as applications to the study of homotopy algebras and new constructions of 'quantum invariants' of manifolds inspired by ideas originating from physics.…
A quantum field theory for Spin(7)-instantons derived from moduli spaces.
We establish a relation between the trace evaluation in SO(3) topological quantum field theory and evaluations of a topological Tutte polynomial. As an application, a generalization of the Tutte golden identity is proved for graphs on the torus.
We define some new invariants for 3-manifolds using the space of taut codim-1 foliations along with various techniques from noncommutative geometry. These invariants originate from our attempt to generalise Topological Quantum Field Theories in the Noncommutative geometry / topology realm.
Open 2D TFTs extend to closed theories with circle value as Hochschild homology.
Lectures detail field theory dynamics and exact WKB analysis.
New framework for quantum invariants of 3-manifolds using homology.
Canonical quantization of abelian BF-type topological field theory coupled to extended sources on generic d-dimensional manifolds and with curved line bundles is studied. Sheaf cohomology is used to construct the appropriate topological extension of the action and the topological flux quantization conditions, in terms …
Constructs 3D topological field theories from a specific quantum group, linking to physics invariants.
The paper extends topological field theory to noncompact surfaces using symmetric powers.
Mednykh proved that for any finite group G and any orientable surface S, there is a formula for #Hom(pi_1(S), G) in terms of the Euler characteristic of S and the dimensions of the irreducible representations of G. A similar formula in the nonorientable case was proved by Frobenius and Schur. Both of these proofs use c…
Graph potentials link to topological QFTs, with computational methods.
Homotopy Quantum Field Theories (HQFTs) generalize more familiar Topological Quantum Field Theories (TQFTs). In generalization of the surgery construction of 3-dimensional TQFTs from modular categories, we use surgery to derive 3-dimensional HQFTs from G-modular categories.
This paper studies both the conductance and charge transport on 2D orbifolds in a strong magnetic field. We consider a family of Landau Hamiltonians on a complex, compact 2D orbifold that are parametrised by the Jacobian torus of . We calculate the degree of the associated stable holomorphic spectral orbi…
The paper explores how the unit inclusion affects topological quantum field theories in non-semisimple categories.
Researchers create projective representations of Hecke groups using TQFT.
Summarizes quantum field theories with discrete symmetry, classifying representations and anomalies.
Paper connects 3D gravity averages to 2D CFT correlators.
We review "quantum" invariants of closed oriented 3-dimensional manifolds arising from operator algebras.
Program connects quantum computing and topological field theories.
New K-theory approach classifies anyonic topological phases in 2D semimetals.
We extend the topological field theory (``itsy bitsy topological field theory"') of our previous work from mod-2 to twisted coefficients. This topological field theory is derived from sutured Floer homology but described purely in terms of surfaces with signed points on their boundary (occupied surfaces) and curves on …
We use the conformal invariance and the holographic correspondence to fully specify the dependence of entanglement entropy on the extrinsic geometry of the 2d surface that separates two subsystems of quantum strongly coupled SU(N) superconformal gauge theory. We extend this result and calculate en…
We use topological quantum field theory to derive an invariant of a three-manifold with boundary. We then show how to use this invariant as an obstruction to embedding one three-manifold in another.
Defines a map connecting 3d-index and skein module.
Arithmetic Dijkgraaf-Witten theory constructs analogues in Chern-Simons TQFT.
We construct an elementary, combinatorial kind of topological quantum field theory, based on curves, surfaces, and orientations. The construction derives from contact invariants in sutured Floer homology and is essentially an elaboration of a TQFT defined by Honda--Kazez--Matic. This topological field theory stores inf…