arXiv research

This paper constructs cohomological Hall algebras for 3-Calabi-Yau categories.

The BPS decomposition theorem splits cohomology of symmetric stacks into invariant parts.

In this paper, we study both the continuous model and the discrete model of the Quantum Hall Effect (QHE) on the hyperbolic plane. The Hall conductivity is identified as a geometric invariant associated to an imprimitivity algebra of observables. We define a twisted analogue of the Kasparov map, which enables us to use…

Constructs cohomology decompositions for symmetric stacks.

Given a finitely-generated group G, and a finite group Γ, Philip Hall defined δ_Γto be the number of factor groups of G that are isomorphic to Γ. We show how to compute the Hall invariants by cohomological and combinatorial methods, when G is finitely-presented, and Γbelongs to a certain class of metabelian groups. Key…

Geometrically proves Zabrodin-Wiegmann conjecture for integer QH states.

We study both the continuous model and the discrete model of the integer quantum Hall effect on the hyperbolic plane in the presence of disorder, extending the results of an earlier paper [CHMM]. Here we model impurities, that is we consider the effect of a random or almost periodic potential as opposed to just periodi…

The elliptic Hall algebra governs torus link homology.

Town hall discusses AI's impact on statistics, culture, and training.

A celebrated theorem of Marshall Hall Jr. implies that finitely generated free groups are subgroup separable and that all of their finitely generated subgroups are retracts of finite-index subgroups. We use topological techniques inspired by the work of Stallings to prove that all limit groups share these two propertie…

The trace of the affine Hecke category is compared with the elliptic Hall algebra.

Bayesian inference calibrates Hall thruster model uncertainty at varying pressures.

Ends and cohomology theory for noncompact spaces.

In the paper we consider the following conjecture: if a finite group $G$ possesses a solvable $π$-Hall subgroup $H$, then there exist elements $x,y,z,t\in G$ such that the identity $H\cap H^x\cap H^y\cap H^z\cap H^t=O_π(G)$ holds. The minimal counter example is shown to be an almost simple group of Lie type.

In this paper, we study a refined L2 version of the semiclassical approximation of projectively invariant elliptic operators with invariant Morse type potentials on covering spaces of compact manifolds. We work on the level of spectral projections (and not just their traces) and obtain an information about classes of t…

Paper analyzes origami slope gaps and their distribution, finding a unique pattern.

This paper is the continuation of Part I, expanding previous results of math.DG/9803051. This paper uses techniques in noncommutative geometry as developed by Alain Connes in order to study the twisted higher index theory of elliptic operators on orbifold covering spaces of compact good orbifolds, which are invariant u…

Extends Borsuk-Ulam theorem with applications in sphere coverings and colorings.

Study on Lin-Lu-Yau curvature and diameter of amply regular graphs.

Proves a pentagon relation in skein theory.

A new geometric framework resolves singularities in anomalous transport.

Analyzes geometric structures on profinite diffeological spaces.

We study the generating functional, the adiabatic curvature and the adiabatic phase for the integer quantum Hall effect (QHE) on a compact Riemann surface. For the generating functional we derive its asymptotic expansion for the large flux of the magnetic field, i.e., for the large degree $k$ of the positive Hermitian …

Given a family of (almost) disjoint strictly convex subsets of a complete negatively curved Riemannian manifold M, such as balls, horoballs, tubular neighborhoods of totally geodesic submanifolds, etc, the aim of this paper is to construct geodesic rays or lines in M which have exactly once an exactly prescribed (big e…

Symmetric function $L_{M,N}$ lifts torus link homology.

We further develop the asymptotic analytic approach to the study of scattering diagrams. We do so by analyzing the asymptotic behavior of Maurer-Cartan elements of a differential graded Lie algebra constructed from a (not-necessarily tropical) monoid-graded Lie algebra. In this framework, we give alternative differenti…

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.

In this paper, we prove a formula for the 2-head of the colored Jones polynomial for an infinite family of pretzel knots. Following Hall, the proof utilizes skein-theoretic techniques and a careful examination of higher order stability properties for coefficients of the colored Jones polynomial.

The study finds quasi-Einstein metrics on sphere bundles.

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…

We suggest to use the Hall-Littlewood version of Rosso-Jones formula to define the germs of $p$-adic HOMFLY-PT polynomials for torus knots $[m,n]$, which possess at least the $[m,n] \longleftrightarrow [n,m]$ topological invariance. This calls for generalizations to other knot families and is a challenge for several br…

In an earlier paper [Acta Mathematica, v. 176, 1996, 145-169, alg-geom/9505024 ] the present authors and Dennis Sullivan constructed the universal direct system of the classical Teichmüller spaces of Riemann surfaces of varying genus. The direct limit, which we called the universal commensurability Teichmüller space, $…

We study the open string integrality invariants (LMOV invariants) for toric Calabi-Yau 3-folds with Aganagic-Vafa brane (AV-brane). In this paper, we focus on the case of the resolved conifold with one out AV-brane in any integer framing $τ$, which is the large $N$ duality of the Chern-Simons theory for a framed unknot…

The twisted Connes-Moscovici higher index theorem is generalized to the case of good orbifolds. The higher index is shown to be a rational number, and in fact non-integer in specific examples of 2-orbifolds. This results in a non-commutative geometry model that predicts the occurrence of fractional quantum numbers in t…

In arXiv:1106.4305 extended superpolynomials were introduced for the torus links T[m,mk+r], which are functions on the entire space of time variables and, at expense of reducing the topological invariance, possess additional algebraic properties, resembling those of the matrix model partition functions and the KP/Toda …

Introduces linear K-systems for Hamiltonian Floer theory.

The paper considers the block sampling method for long-range dependent processes. Our theory generalizes earlier ones by Hall, Jing and Lahiri (1998) on functionals of Gaussian processes and Nordman and Lahiri (2005) on linear processes. In particular, we allow nonlinear transforms of linear processes. Under suitable c…

Paper studies homology and cohomology of Temperley-Lieb algebra TL_n(a).

Paper explores how knowledge distillation transfers inductive biases between models.

Interpolated-MLPs control inductive bias for better performance in low-compute tasks.

New method quantifies inductive bias for machine learning tasks.

The main result of this article is a refinement of the well-known subgroup separability results of Hall and Scott for free and surface groups. We show that for any finitely generated subgroup, there is a finite dimensional representation of the free or surface group that separates the subgroup in the induced Zariski to…

We extend the coherent state transform (CST) of Hall to the context of the moduli spaces of semistable holomorphic vector bundles with fixed determinant over elliptic curves. We show that by applying the CST to appropriate distributions, we obtain the space of level k, rank n and genus one non-abelian theta functions w…

One-layer transformers can't solve induction heads task efficiently.

OTI extends OTP for inductive semi-supervised learning.

Study magnetic geodesics on Kähler potentials using variational methods.

We present Tanaka's prolongation procedure for filtered structures on manifolds discovered in [Tanaka N., J. Math. Kyoto. Univ. 10 (1970), 1-82] in a spirit of Singer-Sternberg's description of the prolongation of usual G-structures [Singer I.M., Sternberg S., J. Analyse Math. 15 (1965), 1-114; Sternberg S., Prentice-H…

Strong inductive biases prevent harmless interpolation in overparameterized models.