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I give a simpler proof of the generalisation of Engel's Theorem to Leibniz algebras.

We study the coinduction functor on the category of FI-modules and its variants. Using the coinduction functor, we give new and simpler proofs of (generalizations of) various results on homological properties of FI-modules. We also prove…

We prove estimates for the Gowers uniformity norms of functions over $\Zz/p\Zz$ which are trace functions of certain $\ell$-adic sheaves, and establish in particular a strong inverse theorem for these functions.

We develop the global moduli theory of symplectic varieties in the sense of Beauville. We prove a number of analogs of classical results from the smooth case, including a global Torelli theorem. In particular, this yields a new proof of…

Let F be a field of characteristic 2. In this paper we determine the Kato-Milne cohomology of the rational function field F(x) in one variable x. This will be done by proving an analogue of the Milnor exact sequence [4] in the setting of…

We develop cohomological and homological theories for a profinite group $G$ with coefficients in the Pontryagin dual categories of pro-discrete and ind-profinite $G$-modules, respectively. The standard results of group (co)homology hold for…

We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.

In this paper we prove several inequalities by means of diagrammatic expansions, a technique already used in [BG13]. This time we show that iterations of the folding of a probability leads to the proof of some in- equalities by means of a…

The result of this paper is proved in arXiv:1112.1163

In this paper, we will give an extension of Mok's theorem on the generalized Frankel conjecture under the condition of the orthogonal bisectional curvature.

We establish axiomatic characterizations of $K$-theory and $KK$-theory for real C*-algebras. In particular, let $F$ be an abelian group-valued functor on separable real C*-algebras. We prove that if $F$ is homotopy invariant, stable, and…

We generalize several classical theorems in extremal combinatorics by replacing a global constraint with an inequality which holds for all objects in a given class. In particular we obtain generalizations of Tur\'an's theorem, the…

We prove an induction theorem for the higher algebraic K-groups of group algebras $kG$ of finite groups $G$ over characteristic $p$ finite fields $k$. For a certain class of finite groups, which we call $p$-isolated, this reduces…

We give a combinatorial proof of the skew Kostka analogue of the K-saturation theorem. More precisely, for any positive integer k, we give an explicit injection from the set of skew semistandard Young tableaux with skew shape…

We prove a global uniform Artin-Rees lemma type theorem for sections of ample line bundles over smooth projective varieties. This result is used to prove an Artin-Rees lemma for the polynomial ring with uniform degree bounds. The proof is…

\begin{abstract} We apply the theory of generalized Watson transforms developed in \cite{zheng00} to construct the complementary series of $GL(2,\R)$. \end{abstract}

We give two generalizations of the Clifford theorem to algebraic surfaces. As an application, we obtain some bounds for the number of moduli of surfaces of general type.

We give a simple proof of the Fourier Inversion Theorem, using the methods of nonstandard analysis.

In this paper, we shall prove the Chung-Feller Theorem in several ways. We provide an inductive proof, bijective proof, and proofs using generating functions, and the Cycle Lemma of Dvoretzky and Motzkin.

We prove Faltings Finiteness Theorem using Rieffel's classification of the noncommutative tori.