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Let $A$ be a special biserial algebra over an algebraically closed field. We show that the first Hohchshild cohomology group of $A$ with coefficients in the bimodule $A$ vanishes if and only if $A$ is representation finite and simply…

Questions related to Brauer-Manin obstructions to the Hasse principle and weak approximation for homogeneous spaces of tori over a number field are well-studied, generally using arithmetic duality theorems, starting with works of Sansuc and…

We study the interplay between holomorphic conformal field theory and dualities of 3D topological quantum field theories generalizing the paradigm of level-rank duality. A holomorphic conformal field theory with a Kac-Moody subalgebra…

In this note we prove that the fouth bounded cohomology of non-abelian free groups with trivial real coefficients is non-zero. In order to prove this, we establish a splitting argument whose simplest form is as follows: Let $M$ denote an…

We define, for any group $G$, finite approximations ; with this tool, we give a new presentation of the profinite completion $\hat{\pi} : G \to \hat{G}$ of an abtract group $G$. We then prove the following theorem : if $k$ is a finite prime…

We study the L-infinity-formality problem for the Hochschild complex of the universal enveloping algebra of some examples of Lie algebras such as Cartan-3-regular quadratic Lie algebras (for example semisimple Lie algebras and in more…

We show that compatible systems of $\ell$-adic sheaves on a scheme of finite type over the ring of integers of a local field are compatible along the boundary up to stratification. This extends a theorem of Deligne on curves over a finite…

Arithmetic of K3 surfaces defined over finite fields is investigated. In particular, we show that any K3 surface of finite height over a finite field k of characteristic p > 3 has a quasi-canonical lifting to characteristic 0, and that for…

We compare by a very elementary approach the second adjoint and trivial Leibniz cohomology spaces of a Lie algebra to the usual ones. Examples are given of coupled cocycles. Some properties are deduced as to Leibniz deformations. We also…

Let A be a basic connected finite dimensional algebra over an algebraically closed field, let G be a group, let T be a basic tilting A-module and let B the endomorphism algebra of T. Under a hypothesis on T, we establish a correspondence…

C*-algebras generalizing Cuntz-Krieger algebras can be associated to hyperbolic homeomorphisms of compact metric spaces. They satisfy a non-commutative form of Spanier-Whitehead duality with respect to K-theory. We prove this for the case…

Our contribution is a bounded cubic compilation theorem. For each fixed resource parameter $k$, syntactic proof checking at resource level $k$ is faithfully represented by a finite bounded-domain system of cubic polynomial equations. Every…

Atiyah and Hirzebruch gave examples ofeven degree torsion classes in the singularcohomology of a smooth complex projective manifold, which arenot Poincar\'{e} dual to an algebraiccycle. We notice that the order ofthese classes are small…

Any action of a group $\Gamma$ on $\mathbb H^3$ by isometries yields a class in degree three bounded cohomology by pulling back the volume cocycle to $\Gamma$. We prove that the bounded cohomology of finitely generated Kleinian groups…

With every reduced $E$-Fountain semigroup $S$ which satisfies the generalized right ample condition we associate a category with zero morphisms $\mathcal{C}(S)$. Under some assumptions we prove an isomorphism of $\Bbbk$-algebras $\Bbbk…

We prove that Floer theory induces a filtration by ideals on equivariant quantum cohomology of symplectic manifolds equipped with a $\mathbb{C}^*$-action. In particular, this gives rise to Hilbert-Poincar\'e polynomials on ordinary…

Let $n$ be a positive integer. The main result of this manuscript is a construction of a filtration on the cohomology ring of a regular nilpotent Hessenberg variety in $GL(n,{\mathbb{C}})/B$ such that its associated graded ring has graded…

We explore the Fourier transform of the Heegaard Floer $d$-invariants, which is particularly well-behaved with respect to connected sum. As corollaries, we show that lens spaces are cancellable in the monoid of 3-manifolds up to integer…

For a pair of finite relational structures $(\mathfrak{A},\mathfrak{B})$ such that $\mathfrak{A}$ homomorphically maps to $\mathfrak{B}$ we denote by $K_{(\mathfrak{A},\mathfrak{B})}$ the following statement: for all structures…

In this paper, we study the Andr\'e-Quillen homology of simplicial commutative $\ell$-algebras, $\ell$ a field, having certain vanishing properties. When $\ell$ has non-zero characteristic, we obtain an algebraic version of a theorem of…