Related papers: Iterability for (transfinite) stacks
We give a complete and self-contained exposition of the $J$-tame inflation lemma: Given any tame almost complex structure $J$ on a symplectic $4$-manifold $(M,\omega)$, and given any compact, embedded, $J$-holomorphic submanifold $Z$, it is…
Let $\mu$ be the geometric realization on $[0,1]$ of a Gibbs measure on $\Sigma=\{0,1\}^{\mathbb{N}}$ associated with a H\"older potential. The thermodynamic and multifractal properties of $\mu$ are well known to be linked via the…
We study partition properties for uncountable regular cardinals that arise by restricting partition properties defining large cardinal notions to classes of simply definable colourings. We show that both large cardinal assumptions and…
A pseudo-Nambu-Goldstone boson, with a potential of the form $V(\phi) = \Lambda^4[1 \pm \cos(\phi/f)], naturally gives rise to inflation if $f \sim M_{Pl}$ and $\Lambda \sim M_{GUT}$. We show how this can arise in technicolor-like and…
We consider a 4+N dimensional Einstein gravity coupled to a non-linear sigma model. This theory admits a solution in which the N extra dimensions contract exponentially while the ordinary space expand exponentially. Physically, the…
For each natural number $n$, let $C^{(n)}$ be the closed and unbounded proper class of ordinals $\alpha$ such that $V_\alpha$ is a $\Sigma_n$ elementary substructure of $V$. We say that $\kappa$ is a \emph{$C^{(n)}$-cardinal} if it is the…
A multiplicative cascade can be thought of as a randomization of a measure on the boundary of a tree, constructed from an iid collection of random variables attached to the tree vertices. Given an initial measure with certain regularity…
We examine normal form solutions of decision trees under typical choice functions induced by lower previsions. For large trees, finding such solutions is hard as very many strategies must be considered. In an earlier paper, we extended…
Let $R$ be a formal power series ring over a field, with maximal ideal $\mathfrak m$, and let $I$ be an ideal of $R$ such that $R/I$ is Artinian. We study the iterated socles of $I$, that is the ideals which are defined as the largest ideal…
When M is a finitely generated graded module over a standard graded algebra S and I is an ideal of S, it is known from work of Cutkosky, Herzog, Kodiyalam, R\"omer, Trung and Wang that the Castelnuovo-Mumford regularity of I^mM has the form…
We investigate forcing properties of perfect tree forcings defined by Prikry to answer a question of Solovay in the late 1960's regarding first failures of distributivity. Given a strictly increasing sequence of regular cardinals $\langle…
The standard algorithm for higher-order contract checking can lead to unbounded space consumption and can destroy tail recursion, altering a program's asymptotic space complexity. While space efficiency for gradual types---contracts…
We formalize an existing computability-theoretic method of presenting first-order structures whose domains have the cardinality of the continuum. Work using these methods until now has emphasized their topological properties. We shift the…
In the ``natural inflation'' model, the inflaton potential is periodic. We show that Planck scale physics may induce corrections to the inflaton potential, which is also periodic with a greater frequency. Such high frequency corrections…
We consider uniform random permutations drawn from a family enumerated through generating trees. We develop a new general technique to establish a central limit theorem for the number of consecutive occurrences of a fixed pattern in such…
We study models M of set theory that are "condensable", in the sense that there is an "ordinal" v of M such that the rank initial segment of M determined by v is both isomorphic to M, and also an elementary submodel of M for infinitary…
For an inaccessible cardinal $\kappa$, the super tree property (ITP) at $\kappa$ holds if and only if $\kappa$ is supercomact. However, just like the tree property, it can hold at successor cardinals. We show that ITP holds at the successor…
An alternative refined de Sitter conjecture giving rise to a natural combination of the first and second derivatives of the scalar potential was proposed recently by David Andriot and Christoph Roupec (Fortsch. Phys. 67 (2019) no.1-2,…
We present a simple mechanism for obtaining large-field inflation, and hence a gravitational wave signature, from string theory compactified on twisted tori. For Nil manifolds, we obtain a leading inflationary potential proportional to…
A novel framework is proposed for embedding the natural inflation into the type IIA superstrings compactified on a Calabi-Yau (CY) three-fold. Inflaton is identified with axion of the Universal Hypermultiplet (UH). The other UH scalars…