Related papers: On classical uniformization theorems for higher di…

In this paper, we study the structure of the quantum cohomology ring of a projective hypersurface with non-positive 1st Chern class. We prove a theorem which suggests that the mirror transformation of the quantum cohomology of a projective…

We resolve the Grothendieck-Serre question over an arbitrary base field $k$: for a smooth $k$-group scheme $G$ and a smooth $k$-variety $X$, we show that every generically trivial $G$-torsor over $X$ trivializes Zariski semilocally on $X$.…

As is known, the irreducible projective representations (Reps) of anti-unitary groups contain three different situations, namely, the real, the complex and quaternion types with torsion number 1,2,4 respectively. This subtlety increases the…

We develop a theory of higher order structures in compact abelian groups. In the frame of this theory we prove general inverse theorems and regularity lemmas for Gowers's uniformity norms. We put forward an algebraic interpretation of the…

The Kestelman-Borwein-Ditor Theorem asserts that a non-negligible subset of $\mathbb{R}$ which is Baire (=has the Baire property, BP) or measurable is shift-compact: it contains some subsequence of any null sequence to within translation by…

Let K be a subfield of the real field, D be a discrete subset of K and f : D^n -> K be a function such that f(D^n) is somewhere dense. Then (K,f) defines the set of integers. We present several applications of this result. We show that K…

A non-linear backward equation with diffusive terms is postulated for the probability density that depends on the Bohmian quantum potential. An associated nonlinear Schr\"{o}dinger equation is also introduced and extension of the analysis…

We continue the development of the computability of the second real Johnson-Wilson theory. As ER(2) is not complex orientable, this gives some difficulty even with basic spaces. In this paper we compute the second real Johnson-Wilson theory…

Let $k$ a field of characteristic zero. Let $X$ be a smooth, projective, geometrically rational $k$-surface. Let $\mathcal{T}$ be a universal torsor over $X$ with a $k$-point et $\mathcal{T}^c$ a smooth compactification of $\mathcal{T}$.…

We develop a general theory of higher semiadditive Fourier transforms that includes both the classical discrete Fourier transform for finite abelian groups at height $n=0$, as well as a certain duality for the $E_n$-(co)homology of…

We state two recent results concerning the linearization of integrable systems on generalised Jacobians. Then we apply this to the (complexified) spherical pendulum.

We consider the equivariant Kasparov category associated to an \'etale groupoid, and by leveraging its triangulated structure we study its localization at the "weakly contractible" objects, extending previous work by R. Meyer and R. Nest.…

We prove the conjectures of Graham-Kumar and Griffeth-Ram concerning the alternation of signs in the structure constants for torus-equivariant K-theory of generalized flag varieties G/P. These results are immediate consequences of an…

Kleinian singularities, i.e., the varieties corresponding to the algebras of invariants of Kleinian groups are of fundamental importance for Algebraic geometry, Representation theory and Singularity theory. The filtered deformations of…

We show that the special unitary group associated to an involution of the second kind on a central division algebra of degree three does not contain hermitian or skew-hermitian elements. Especially, there are no reflections. For Albert's…

Paper withdrawn. There is a gap in the proof of Proposition 4.3 (its conclusion ``d'o\`{u} la proposition.'' is incorrect). Therefore theorems 1.1 and 3.1, which were the main results of the paper, are not proved.

We give a new proof of the theorem stating that for any connected linear algebraic group G over an algebraically closed field k of characteristic 0 and for any closed connected subgroup H of G, the unramified Brauer group of G/H vanishes.

As time passes, once simple quantum states tend to become more complex. For strongly coupled k-local Hamiltonians, this growth of computational complexity has been conjectured to follow a distinctive and universal pattern. In this paper we…

Recently representation theory has been used to provide atomic decompositions for a large collection of classical Banach spaces. In this paper we extend the techniques to also include projective representations. As our main application we…

Let $k$ be a finitely generated field of characteristic $p>0$ and $X$ a smooth and proper scheme over $k$. Recent works of Cadoret, Hui and Tamagawa show that, if $X$ satisfies the $\ell$-adic Tate conjecture for divisors for every prime…