Related papers: Decomposing the Univalence Axiom
The famous G\"odel incompleteness theorem says that for every sufficiently rich formal theory (containing formal arithmetic in some natural sense) there exist true unprovable statements. Such statements would be natural candidates for being…
The famous G\"odel incompleteness theorem states that for every consistent sufficiently rich formal theory T there exist true statements that are unprovable in T. Such statements would be natural candidates for being added as axioms, but…
We introduce a simple extension of the $\lambda$-calculus with pairs---called the distributive $\lambda$-calculus---obtained by adding a computational interpretation of the valid distributivity isomorphism $A \Rightarrow (B\wedge C)\ \…
We provide a reduction in the classification problem for non-compact, homogeneous, Einstein manifolds. Using this work, we verify the (Generalized) Alekseevskii Conjecture for a large class of homogeneous spaces.
First three sections of this overview paper cover classical topics of deformation theory of associative algebras and necessary background material. We then analyze algebraic structures of the Hochschild cohomology and describe the relation…
Coquand's cubical set model for homotopy type theory provides the basis for a computational interpretation of the univalence axiom and some higher inductive types, as implemented in the cubical proof assistant. This paper contributes to the…
In this paper we discuss gauging one-form symmetries in two-dimensional theories. The existence of a global one-form symmetry in two dimensions typically signals a violation of cluster decomposition -- an issue resolved by the observation…
Ulm's Theorem presents invariants that classify countable abelian torsion groups up to isomorphism. Barwise and Eklof extended this result to the classification of arbitrary abelian torsion groups up to $L_{\infty \omega}$-equivalence. In…
We consider an abstract space of measurable linear cocycles and we assume the availability in this space of some appropriate uniform large deviation type estimates. Under these hypotheses we establish the continuity of the Oseledets…
An arbitrary-depth reduction theorem for the `convolution' multiple L-values of Euler-Zagier type is proven by an analytic method. To this end, generalized polylogarithms associated to Dirichlet characters are defined. The proof uses the…
We consider the category of Deligne 1-motives over a perfect field k of exponential characteristic p and its derived category for a suitable exact structure after inverting p. As a first result, we provide a fully faithful embedding into an…
We define a computational type theory combining the contentful equality structure of cartesian cubical type theory with internal parametricity primitives. The combined theory supports both univalence and its relational equivalent, which we…
In this note, we give a short proof of the Torelli theorem for cubic fourfolds that relies on the global Torelli theorem for irreducible holomorphic symplectic varieties proved by Verbitsky.
Current quantum theories of an elementary free particle assume unitary space inversion and anti-unitary time reversal operators. In so doing robust classes of possible theories are discarded. The present work shows that consistent theories…
We explore systems of polynomial equations where we seek complex solutions with absolute value 1. Geometrically, this amounts to understanding intersections of algebraic varieties with tori -- Cartesian powers of the unit circle. We study…
We present a framework to decompose real multivariate polynomials while preserving invariance and positivity. This framework has been recently introduced for tensor decompositions, in particular for quantum many-body systems. Here we…
We present a system of axioms motivated by a topological intuition: The set of subsets of any set is a topology on that set. On the one hand, this system is a common weakening of Zermelo-Fraenkel set theory ZF, the positive set theory GPK…
We propose a simple abstract version of Calderon--Zygmund theory, which is applicable to spaces with exponential volume growth, and then show that amenable Lie groups can be treated within this framework.
We show canonicity and normalization for dependent type theory with a cumulative sequence of universes and a type of Boolean. The argument follows the usual notion of reducibility, going back to Godel's Dialectica interpretation and the…
The existence of a homogeneous decomposition for continuous and epi-translation invariant valuations on super-coercive functions is established. Continuous and epi-translation invariant valuations that are epi-homogeneous of degree $n$ are…