Related papers: Fixed point adjunctions for equivariant module spe…
Let $X$ and $\mathfrak{a}$ be an affine scheme and (respectively) a finite-dimensional associative algebra over an algebraically-closed field $\Bbbk$, both equipped with actions by a linearly-reductive linear algebraic group $G$. We…
We construct the global phase portraits of inflationary dynamics in teleparallel gravity models with a scalar field nonminimally coupled to torsion scalar. The adopted set of variables can clearly distinguish between different asymptotic…
(This is an updated version; following an idea of Voevodsky, we have strengthened our results so all of them apply to one form of motivic homotopy theory). We give two general constructions for the passage from unstable to stable homotopy…
This article presents, in an illustrative fashion, a first step towards an extension of the spectral theory of constant length substitutions. Our starting point is the general observation that the symbolic picture (as defined by the…
Given a global equivariant ultracommutative ring spectrum $E$ and inclusion $H\hookrightarrow G$ of finite groups, one may apply geometric fixed points to the norm $N_H^G E_H \to E_G$ to obtain what we call a \emph{geometric norm} $\Phi^H E…
We develop a constructive model of homotopy type theory in a Quillen model category that classically presents the usual homotopy theory of spaces. Our model is based on presheaves over the cartesian cube category, a well-behaved…
We establish isomorphism ranges for the comparison maps between algebraic and topological K-groups, extending classical Quillen-Lichtenbaum conjecture to separated complex schemes of finite type after refinement. Additionally, we…
We consider bifurcation of critical points from a trivial branch for families of functionals that are invariant under the orthogonal action of a compact Lie group. Based on a recent construction of an equivariant spectral flow by the…
Quantum gravity computations suggest the existence of an ultraviolet and an infrared fixed point where quantum scale invariance emerges as an exact symmetry. We discuss a particular variable gravity model for the crossover between these…
I generalize the inflationary flow equations of Hoffman and Turner to arbitrary order in slow roll. This makes it possible to study the predictions of slow roll inflation in the full observable parameter space of tensor/scalar ratio $r$,…
Inspired by the amplitude bootstrap program, the spirit of this work is to constrain the space of consistent inflationary correlation functions - specifically, the bispectrum of curvature perturbations - using fundamental principles such as…
For a field $k$ of characteristic $0$, we compare $k$-linear chain complexes, semisimplicial vector spaces, augmented semisimplicial vector spaces, semicubical vector spaces, and arboreal vector spaces through small differential categorical…
Multifield models of inflation with nonminimal couplings are in excellent agreement with the recent results from {\it Planck}. Across a broad range of couplings and initial conditions, such models evolve along an effectively single-field…
We show that certain tilting results for quivers are formal consequences of stability, and as such are part of a formal calculus available in any abstract stable homotopy theory. Thus these results are for example valid over arbitrary…
The aim of this paper is to present a very simple original, purely formal, proof of Quillen's adjunction theorem for derived functors, and of some more recent variations and generalizations of this theorem. This is obtained by proving an…
We present an overview of inflationary models derived from string theory focusing mostly on closed string moduli as inflatons. After a detailed discussion of the eta-problem and different approaches to address it, we describe possible ways…
We study the representation theory of Dynkin quivers of type A in abstract stable homotopy theories, including those associated to fields, rings, schemes, differential-graded algebras, and ring spectra. Reflection functors, (partial)…
We extend the equivariant holomorphic Morse inequalities of circle actions to cases with torus and non-Abelian group actions on holomorphic vector bundles over Kahler manifolds and show the necessity of the Kahler condition. For torus…
We explain the motivation and main idea of our work in reference arXiv:0907.2476 [hep-th]. We present a simple model of multifield Dirac-Born-Infeld inflation whose bispectrum exhibits a linear combination of the equilateral and local…
We generalise the Atiyah-Segal-Singer fixed point theorem to noncompact manifolds. Using $KK$-theory, we extend the equivariant index to the noncompact setting, and obtain a fixed point formula for it. The fixed point formula is the…