Related papers: Substitudes, Bousfield localization, higher braide…
In this paper we study perturbations of constant cocycles for actions of higher rank semi-simple algebraic groups and their lattices. Roughly speaking, for ergodic actions, Zimmer's cocycle superrigidity theorems implies that the perturbed…
We provide, among other things: (i) a Bousfield--Kan formula for colimits in $\infty$-categories (generalizing the 1-categorical formula for a colimit as a coequalizer of maps between coproducts); (ii) $\infty$-categorical generalizations…
We study stabilization of moduli in the type--IIB superstring theory on the six-dimensional toroidal orientifold $\T^6/\Omega\cdot(-1)^{F_L}\cdot\Z_2$. We consider background space-filling D9-branes wrapped on the orientifold along with…
This paper is part of a series of three articles with the objective of investigating a stratified version of the homotopy hypothesis in terms of semi-model structures that interact well with classical examples of stratified spaces, such as…
Recent developments in the theory of stability conditions and its relation to Teichmuller theory have revealed a deep connection between triangulated categories and surfaces. Motivated by this, we prove a categorical analogue of the…
Using $p$-adic local Langlands correspondence for $\operatorname{GL}_2(\mathbb{Q}_2)$ and an ordinary $R = \mathbb{T}$ theorem, we prove that the support of patched modules for quaternionic forms meet every irreducible component of the…
In this short note, we provide a broad class of examples of stability conditions on the category of coherent sheaves which generalise Gieseker stability. We refer to them as "adapted to coherent sheaves" and they admit Harder--Narasimhan…
Recently, Nitzan and Olsen showed that Balian-Low theorems (BLTs) hold for discrete Gabor systems defined on $\mathbb{Z}_d$. Here we extend these results to a multivariable setting. Additionally, we show a variety of applications of the…
We give a variant of Artin algebraization along closed subschemes and closed substacks. Our main application is the existence of \'etale, smooth, or syntomic neighborhoods of closed subschemes and closed substacks. In particular, we prove…
The relationship between overparameterization, stability, and generalization remains incompletely understood in the setting of discontinuous classifiers. We address this gap by establishing a generalization bound for finite function classes…
We study a broad class of qudit stabilizer codes, termed $\mathbb{Z}_N$ bivariate-bicycle (BB) codes, arising either as two-dimensional realizations of modulated gauge theories or as $\mathbb{Z}_N$ generalizations of binary BB codes. Our…
In this paper we initiate the study of enriched $\infty$-operads. We introduce several models for these objects, including enriched versions of Barwick's Segal operads and the dendroidal Segal spaces of Cisinski and Moerdijk, and show these…
In this report, we investigate the stabilization of saddle fixed points in coupled oscillators where individual oscillators exhibit the saddle fixed points. The coupled oscillators may have two structurally different types of suppressed…
We reexamine the N=1 supersymmetric gauge theories with product gauge groups by adding the mass terms and the quartic terms for the flavors: two gauge group theory with fundamentals, bifundamentals and adjoints, three gauge group theory…
In this work we prove convergence of renormalised models in the framework of regularity structures [Hai14] for a wide class of variable coefficient singular SPDEs in their full subcritical regimes. In particular, we provide for the first…
We investigate the Hurwitz action of the braid group Br_n on the n-fold Cartesian product of Br_3 and determine some stabilisers of its Artin systems. Our algebraic result is complemented by a geometric study of families of plane polynomial…
We investigate the Berezin integral of non-compactly supported quantities. In the framework of supermanifolds with corners, we give a general, explicit and coordinate-free repesentation of the boundary terms introduced by an arbitrary…
We prove a general representation stability result for polynomial coefficient systems which lets us prove representation stability and secondary homological stability for many families of groups with polynomial coefficients. This gives two…
We prove a new kind of homological stability theorem for automorphism groups of finitely-generated projective modules over Dedekind domains, which takes into account all possible stabilisation maps between these, rather than only…
We prove Berezin--Li--Yau-type lower bounds with additional term for the eigenvalues of the Stokes operator and improve the previously known estimates for the Laplace operator. Generalizations to higher-order operators are given.