Related papers: The Adams spectral sequence for 3-local $\mathrm{t…
This paper is a continuation of the version I of the same title, which intends to clarify and expand the results in the last chapter of `the green book' by the second author. In particular, we give the stable homotopy groups of $p$-local…
Tapping mode atomic force microscopy is a standard technique for inspection and analysis at the nanometer scale. The understanding of the non-linear dynamics of the system due to the tip sample interaction is an important prerequisite for a…
Localized at almost all primes, we describe the structure of differentials in several important spectral sequences that compute the cohomology of classifying spaces of topological Kac-Moody groups. In particular, we show that for all but a…
We develop a localisation theory for certain categories, yielding a 3-arrow calculus: Every morphism in the localisation is represented by a diagram of length 3, and two such diagrams represent the same morphism if and only if they can be…
We analyze the functorial and multiplicative properties of the Thom spectrum functor in the setting of symmetric spectra, and we establish the relevant homotopy invariance.
We establish abstract Adams isomorphisms in an arbitrary equivariantly presentable equivariantly semiadditive global category. This encompasses the well-known Adams isomorphism in equivariant stable homotopy theory, and applies more…
We introduce a formalism to produce several families of spectral sequences involving the derived functors of the limit and colimit functors over a finite partially ordered set. The first type of spectral sequences involves the left derived…
The aim of this short note is to provide a very simple proof for obtaining the fundamental two-term transformation for the series ${}_3F_2(1)$ due to Thomae.
This very speculative sketch suggests that a theory of fundamental groupoids for tensor triangulated categories could be used to describe the ring of integers as the singular fiber in a family of ring-spectra parametrized by a structure…
We present an algorithm enabling computation of the anisotropic redshift-space galaxy 3-point correlation function (3PCF) scaling as $N^2$, with $N$ the number of galaxies. Our previous work showed how to compute the isotropic 3PCF with…
We make some computations in stable motivic homotopy theory over Spec \mathbb{C}, completed at 2. Using homotopy fixed points and the algebraic K-theory spectrum, we construct a motivic analogue of the real K-theory spectrum KO. We also…
We study the cost of multiplication modulo triangular families of polynomials. Following previous work by Li, Moreno Maza and Schost, we propose an algorithm that relies on homotopy and fast evaluation-interpolation techniques. We obtain a…
We introduce the category Pstem[n] of n-stems, with a functor P[n] from spaces to Pstem[n]. This can be thought of as the n-th order homotopy groups of a space. We show how to associate to each simplicial n-stem Q an (n+1)-truncated…
In this paper we lay the foundations of an $\infty$-categorical theory of Stokes data.
We review the state-of-the-art knowledge of IR singularities in multileg QCD amplitudes, identifying the key reasons for the remarkable simplicity of the soft anomalous dimension. We then present a novel strategy to compute this quantity…
The aim of this paper is to explain how, through the work of a number of people, some algebraic structures related to groupoids have yielded algebraic descriptions of homotopy n-types. Further, these descriptions are explicit, and in some…
We employ the Goodwillie spectral sequence for the iterated loop space functor in order to provide realizability conditions on certain unstable modules over the Steenrod algebra at an odd prime.
A separable, proper morphism of varieties with geometrically connected fibers induces a homotopy exact sequence relating the \'etale fundamental groups of source, target and fiber. Extending work of dos Santos, we prove the existence of an…
We consider the time-harmonic electromagnetic transmission problem for the unit sphere. Appealing to a vector spherical harmonics analysis, we prove the first stability result of the local multiple trace formulation (MTF) for…
This paper aims at bridging existing theories in numerical and analytical homogenization. For this purpose the multiscale method of M{\aa}lqvist and Peterseim [Math. Comp. 2014], which is based on orthogonal subspace decomposition, is…