相关论文: A Constructive Approach to Zauner's Conjecture via…

We develop a full 6-functor formalism for $p$-torsion \'etale sheaves in rigid-analytic geometry. More concretely, we use the recently developed condensed mathematics by Clausen--Scholze to associate to every small v-stack (e.g.…

Investigating a recent positive solution of a conjecture of Grunewald and O'Halloran for complex finite dimensional nilpotent Lie algebras, we are in the position to find results of existence and uniqueness for the construction of complex…

We establish a precise relationship between the $G\Sigma$ collective field theory of the double scaled SYK model and the worldsheet theory of the complex Liouville string a.k.a. sine dilaton gravity. The relationship is similar to the…

The Symmetric Informationally Complete Positive Operator-Valued Measures (SIC-POVMs) are known to exist in all dimensions $\leq 151$ and few higher dimensions as high as $1155$. All known solutions with the exception of the Hoggar solutions…

We give a new proof of Zariski's multiplicity conjecture in the case of isolated hypersurface singularities; this was first proved by de Bobadilla-Pe\l ka \cite{BobadillaPelka}. Our proof uses the TQFT structure of fixed-point Floer…

We prove that the length function for perverse sheaves and algebraic regular holonomic D-modules on a smooth complex algebraic variety Y is an absolute Q-constructible function. One consequence is: for "any" fixed natural (derived) functor…

By the theory of Eisenstein series, generating functions of various divisor functions arise as modular forms. It is natural to ask whether further divisor functions arise systematically in the theory of mock modular forms. We establish,…

For a reductive group $G$, we introduce a notion of singular support for cocomplete dualizable DG-categories equipped with a strong $G$-action. This is done by considering the singular support of the sheaves of matrix coefficients arising…

In this paper, we introduce a general family of sequent-style calculi over the modal language and its fragments to capture the essence of all constructively acceptable systems. Calling these calculi \emph{constructive}, we show that any…

We show that the cyclotomic conjecture on the characteristic polynomial of T-ramified S-split Iwasawa modules introduced in a previous paper and satisfied by abelian fields governs the Z${\ell}$-rank of the submodule of fixed points for all…

We construct a lift of the $p$-complete sphere to the universal height $1$ higher semiadditive stable $\infty$-category tsade-$1$ of Carmeli--Schlank--Yanovski, providing a counterexample, at height $1$, to their conjecture that the natural…

This article has two purposes. In \cite{R3} (math.KT/0405211) we showed that the FIC (Fibered Isomorphism Conjecture for pseudoisotopy functor) for a particular class of 3-manifolds (we denoted this class by \cal C) is the key to prove the…

In this paper we extend a conjecture of Ash and Sinnott relating niveau one Galois representation to the mod p cohomology of congruence subgroups of SL(n,Z) to include Galois representations of higher niveau. We then present computational…

We state and verify up to weight 172 a conjecture on the existence of a certain generating set for spaces of classical Siegel modular forms. This conjecture is particularly useful for calculations involving Fourier expansions. Using this…

The manuscript is devoted to the construction of $\Psi^\star$- algebras containing the Bergman projection on the unit ball $B_n$ of $\mathbb C^n$. We consider the $C^\star$-algebra $\mathcal{L}(L^2(B_n))$ of bounded operator acting on the…

The magic triangle due to Cvitanovi\'c and Deligne--Gross is an extension of the Freudenthal--Tits magic square of semisimple Lie algebras. In this paper, we identify all two-dimensional rational conformal field theories associated to the…

A recently proposed correspondence between 4-dimensional N=2 SUSY SU(k) gauge theories on R^4/Z_m and SU(k) Toda-like theories with Z_m parafermionic symmetry is used to construct four-point N=1 super Liouville conformal block, which…

We develop a generally applicable method for constructing functions, $C$, which have properties similar to Zamolodchikov's $C$-function, and are geometrically natural objects related to the theory space explored by non-perturbative…

Let $R$ be the power series ring or the polynomial ring over a field $k$ and let $I $ be an ideal of $R.$ Macaulay proved that the Artinian Gorenstein $k$-algebras $R/I$ are in one-to-one correspondence with the cyclic $R$-submodules of the…

We make progress towards understanding the structure of Littlewood-Richardson coefficients $g_{\lambda,\mu}^{\nu}$ for products of Jack symmetric functions. Building on recent results of the second author, we are able to prove new cases of…