Related papers: A note on Green functors with inflation
Let R be a commutative Noetherian ring, I and J ideals of R and M a finitely generated R-module. Let F be a covariant R-linear functor from the category of finitely generated R-modules to itself. We first show that if F is coherent, then…
We study a class of generalized inflation models in which the inflaton is coupled to the Ricci scalar by a general $f(\phi, R)$ term. The scalar power spectrum, the spectral index, the running of the spectral index, the tensor mode spectrum…
We study collections of additive categories $\mathcal{M}(G)$, indexed by finite groups $G$ and related by induction and restriction in a way that categorifies usual Mackey functors. We call them `Mackey 2-functors'. We provide a large…
The so called induction functors appear in several areas of Algebra in different forms. Interesting examples are the induction functors in the Theory of Affine Algebraic groups. In this note we investigate the so called Hopf pairings…
In this paper, we explore functional identities with central values in gr-prime rings involving pairs of homogeneous derivations. We establish commutativity conditions that extend classical results from prime rings to the graded setting. In…
We state a conjecture which gives a combinatorial parametrization of the irreducible tempered representations with real central character of a graded Hecke algebra with unequal labels, associated to a root sytem of type B or C. This…
If a coupling between the inflaton and the Gauss-Bonnet term is introduced, many models of inflation that were ruled out by the most recent Planck data can be made viable again. The predictions for the scalar spectral index and…
In this Colloqium Lecture (by one of the authors (D.S)) a thorough presentation of the authors' research on the subjects, stated in the title, is given. By quite laborious mathematics it is explained how one can handle systems in which each…
A model of inflation realization driven by fermions with curvature-dependent mass is studied. Such a term is derived from the Covariant Canonical Gauge Theory of gravity (CCGG) incorporating Dirac fermions. We obtain an initial de Sitter…
We characterize group representations that factor through monomial representations, respectively, block-triangular representations with monomial diagonal blocks, by arithmetic properties. Similar results are obtained for semigroup…
We investigate the inflationary attractors in models of inflation inspired from general conformal transformation of general scalar-tensor theories to the Einstein frame. The coefficient of the conformal transformation in our study depends…
We consider the Gauss-Bonnet term coupled to the inflaton in the Palatini formulation of gravity. Unlike in the metric formulation, the Gauss-Bonnet term is not always a total derivative. We solve for the connection and insert it into the…
As a first step towards inflation in genuinely F-theoretic setups, we propose a scenario where the inflaton is the relative position of two 7-branes on holomorphic 4-cycles. Non-supersymmetric gauge flux induces an attractive inter-brane…
We study the dynamics of axion-like fields in F-theory and suggest that they can serve as inflatons in models of natural inflation. The axions arise from harmonic three-forms on the F-theory compactification space and parameterize a complex…
We find conditions such that cup products induce isomorphisms in low degrees for extensions between stable polynomial representations of the general linear group. We apply this result to prove generalizations and variants of the Steinberg…
Let FI denote the category whose objects are the sets $[n] = \{1,\ldots, n\}$, and whose morphisms are injections. We study functors from the category FI into the category of sets. We write $\mathfrak{S}_n$ for the symmetric group on $[n]$.…
In this paper, we prove an averaged version of an algebraicity conjecture in \cite{GKZ87} concerning the values of higher Green's function at CM points. Furthermore, we give the factorization of the ideal generated by such algebraic value…
We extend the effective field theory of inflation to a general Lagrangian constructed from Arnowitt-Deser-Misner variables that encompasses the most general interactions with up to second derivatives of the scalar field whose background…
Sp\"ath showed that the Alperin-McKay conjecture in the representation theory of finite groups holds if the so-called inductive Alperin-McKay condition holds for all finite simple groups. In a previous article, we showed that the…
String theory models of axion monodromy inflation exhibit scalar potentials which are quadratic for small values of the inflaton field and evolve to a more complicated function for large field values. Oftentimes the large field behaviour is…