arXiv research

Develops deformed algebras and groups from formal series over groupoids, with applications to cobordism.

Study on pure virtual braids, their formality, and related ranks.

The paper explores various braid-like groups and their properties.

New field invariant refines real spectrum and relates to absolute Galois group.

Solves Cauchy problem for a KP hierarchy on non-formal operators and relates to diffeomorphisms.

Establishes Poincaré's lemma for formal manifolds.

Proves well-posedness of KP hierarchy using Frölicher Lie groups and formal pseudo-differential operators.

Explores local structure of morphisms and formal submanifolds in formal manifolds theory.

Foundations laid for formal manifolds in differential geometry.

Study of groups for virtual trefoil and Kishino knots.

We develop here a concept of deformed algebras through three examples and an application. Deformed algebras are obtained from a fixed algebra by deformation along a family of indexes, through formal series. We show how the example of deformed algebra used in \cite{Ma2013} is only an example among others, and how they o…

This paper presents algebraic structures of Lie-Butcher series.

Researchers use orbital integrals to recover group theoretic information from $K$-theory classes.

Our aim is to prove that two formal power series of importance to quantum topology are Gevrey. These series are the Kashaev invariant of a knot (reformulated by Huynh and the second author) and the Gromov norm of the LMO of an integral homology 3-sphere. It follows that the power series associated to a simple Lie algeb…

We consider analytic curves $\nabla^t$ of symplectic connections of Ricci type on the torus $T^{2n}$ with $\nabla^0$ the standard connection. We show, by a recursion argument, that if $\nabla^t$ is a formal curve of such connections then there exists a formal curve of symplectomorphisms $ψ_t$ such that $ψ_t\cdot\nabla^…

In this paper, we consider formal series associated with events, profiles derived from events, and statistical models that make predictions about events. We prove theorems about realizations for these formal series using the language and tools of Hopf algebras.

The 3D Index is extended to meromorphic functions on triangulated 3-manifolds.

Explicit Taylor series for the volume of tubes in Lie groups

In this paper, we consider the formal power series whose n-th coefficient is the number of copies of a given finite graph in the ball of radius n centred at the identity element in the Cayley graph of a finitely generated group and call it the growth function. Epstein, Iano-Fletcher and Uri Zwick proved that the growth…

Power series invariant of hyperbolic 3-manifolds matches knot invariants.

The authors define a polytope invariant for certain groups, including 3-manifold and free-by-cyclic groups.

The loop invariants of Dimofte-Garoufalidis is a formal power series with arithmetically interesting coefficients that conjecturally appears in the asymptotics of the Kashaev invariant of a knot to all orders in $1/N$. We develop methods implemented in SnapPy that compute the first 6 coefficients of the formal power se…

Global methods outperform local in forecasting groups of time series, even in heterogeneous datasets.

Mathematical treatment of path integrals in quantum field theory.

The paper is concerned with the Kontsevich-Zagier formal power series $f(q)=\sum_{n=0}^\infty (1-q)... (1-q^n)$ and its analytic properties. To begin with, we give an explicit formula for the Borel transform of the associated formal power series $F(x)=e^{-1/(24x)}f(e^{-1/x})$ from which its analytic continuation, i…

A new robust time series distance metric for k-NN classification.

Paper develops a weighted linearization approach for vector fields.

Method finds all cross caps formally isometric to a given one.

Researchers construct a series from knot data to match Kashaev invariant coefficients.

Constructs complexes of differential operators on homogeneous spaces.

Classifies cobounded hyperbolic actions of metabelian groups.

Defines formal vertex laws related to Lie conformal algebras.

Study of nonlinear PDEs using derived geometry and BV formalism.

The paper describes algebraic operations on surface fundamental groups.

Proves resurgence properties for Habiro elements from radial limits of theta series.

This paper extends Lie algebra contractions to infinite-dimensional spaces for better understanding of group limits.

We recall the construction of non-formal deformation quantization of the Poincare Group ISO(1,1) on its coadjoint orbit and exhibit the associated non-formal star-exponentials.

The abstract discusses convergent realizations of Lie subalgebras in control theory.

Study series invariants of plumbed 3-manifolds using root lattices.

Formalizes synthetic differential geometry in Lean.

The paper examines formality properties of finitely generated groups and Lie algebras.

In this paper, we start from an extension of the notion of holonomy on diffeological bundles, reformulate the notion of regular Lie group or Frölicher Lie groups, state an Ambrose-Singer theorem that enlarges the one stated in \cite{Ma2}, and conclude with a differential geometric treatment of KP hierarchy. The example…

Survey on finite dimensional Lie groups over real numbers.

The paper explores connections between braids, links, and cobordisms using algebraic methods.

Abstract: Proves Tutte's sequence connection to complex space forms.

Report on formalizing differential geometry in Lean.

Paper classifies solutions to oriented associativity equations on flat F-manifolds.

Framework infers coordination strategies from movement data.