Related papers: Formality of the chain operad of framed little dis…
We study some formality criteria for differential graded algebras over differential graded operads. This unifies and generalizes other known approaches like the ones by Manetti and Kaledin. In particular, we construct general operadic…
The antifield formalism is extended so as to incorporate the rigid symmetries of a given theory. To that end, it is necessary to introduce global ghosts not only for the given rigid symmetries, but also for all the higher order conservation…
The traditional Riemann Mapping Theorem can be proved with circle packing techniques. We prove the Combinatorial Riemann Mapping Theorem for tilings of bounded size using circle packings.
Motivated by (perturbative) quantum observables in Lorentzian signature we define a new operad: the operad of causally disjoint disks. In order to describe this operad we use the orthogonal categories of Benini, Schenkel, and Woike and the…
We extend the formalism of "log spaces" of arXiv:1507.06752 to topoi equipped with a sheaf of monoids, and discuss Deligne--Faltings structures and root stacks in this context.
Given a strongly stationary Markov chain and a finite set of stopping rules, we prove the existence of a polynomial algorithm which projects the Markov chain onto a minimal Markov chain without redundant information. Markov complexity is…
It is feasible to obtain any basic rule of the already known Quantum Mechanics applying the Hamilton-Jacobi formalism to an interacting system of 2 fermionic degrees of freedom. The interaction between those fermionic variables unveils also…
Using configuration space level Pontryagin--Thom constructions, we construct a simple Koszul self duality map for the little disks operad $\Sigma^\infty_+ E_n$. For a framed $n$-manifold $M$, we show that a compatible self duality map…
We provide the detailed proof of a strengthened version of the M. Artin Approximation Theorem.
We introduce an operad of formal fractions, abstracted from the Mould operads and containing both the Dendriform and the Tridendriform operads. We consider the smallest set-operad contained in this operad and containing four specific…
We develop a self-dual, bivariant extension of the concept of an operadic category, its associated operads and their algebras. Our new theory covers, besides all classical subjects, also generalized traces and bivariant versions of…
In [KW14], the new concept of Feynman categories was introduced to simplify the discussion of operad--like objects. In this present paper, we demonstrate the usefulness of this approach, by introducing the concept of decorated Feynman…
An extension of dimensional regularization to the case of compact dimensions is presented. The procedure preserves the Kaluza-Klein tower structure, but has a regulator specific to the compact dimension. Possible 5 and 4 dimensional…
Given a non-invertible dynamical system with a transfer operator, we show there is a minimal cover with a transfer operator that preserves continuous functions. We also introduce an essential cover with even stronger continuity properties.…
We study a geometric notion related to formality for Bott-Chern cohomology on complex manifolds.
Extending an earlier result for real matrices we show that multiple eigenvalues of a complex matrix lie in a reduced Gershgorin disk. One consequence is a slightly better estimate in the real case. Another one is a geometric application.…
Following [14] and [12], we formalize the notion of an oscillatory integral interpreted as a functional on the amplitudes supported near a fixed critical point $x_0$ of the phase function with zero critical value. We relate to an…
We give a combinatorial definition of the second parameter describing Sturmian words, that we call formal intercept, as an infinite Ostrowski expansion. We recall the well-known properties of Sturmian words, study factors graphs and…
This paper discusses the question of how to recognize whether an operad is E_n (ie. equivalent to the little n-cubes operad). A construction is given which produces many new examples of E_n operads. This construction is developed in the…
In an earlier paper we introduced a notion of Markov automaton, together with parallel operations which permit the compositional description of Markov processes. We illustrated by showing how to describe a system of n dining philosophers,…