Related papers: Uniform sum-product phenomenon for algebraic group…

The main result of this paper is the following: for all $b \in \mathbb Z$ there exists $k=k(b)$ such that \[ \max \{ |A^{(k)}|, |(A+u)^{(k)}| \} \geq |A|^b, \] for any finite $A \subset \mathbb Q$ and any non-zero $u \in \mathbb Q$. Here,…

We prove an all genera version of the Crepant Resolution Conjecture of Ruan and Bryan-Graber for type A surface singularities. We are based on a method that explicitly computes Hurwitz-Hodge integrals described in an earlier paper and some…

We prove a version of uniqueness theorem for Cuntz-Pimsner algebras of discrete product systems over semigroups of Ore type. To this end, we introduce Doplicher-Roberts picture of Cuntz-Pimsner algebras, and the semigroup dual to a product…

We prove that the $abc$-Conjecture implies upper bounds on Zsigmondy sets that are uniform over families of unicritical polynomials over number fields. As an application, we use the $abc$-Conjecture to prove that there exist uniform bounds…

For Lebesgue generic $(x_1,x_2)\in \mathbb{R}^2$, we investigate the distribution of small values of products $q\cdot \|qx_1\| \cdot \|qx_2\|$ with $q\in\mathbb{N}$, where $\|\cdot \|$ denotes the distance to the closest integer. The main…

In this paper we establish a Steinberg-Lusztig tensor product theorem for abstract Fock space. This is a generalization of the type A result of Leclerc-Thibon and a Grothendieck group version of the Steinberg-Lusztig tensor product theorem…

We prove quantitative versions of Borel and Harish-Chandra's theorems on reduction theory for arithmetic groups. Firstly, we obtain polynomial bounds on the lengths of reduced integral vectors in any rational representation of a reductive…

On a reduced analytic space $X$ we introduce the concept of a generalized cycle, which extends the notion of a formal sum of analytic subspaces to include also a form part. We then consider a suitable equivalence relation and corresponding…

We study general properties of exotic crossed-product functors and characterise those which extend to functors on equivariant C*-algebra categories based on correspondences. We show that every such functor allows the construction of a…

We describe an effective method for calculating certain infinite sums, generalizations of the classical Bernoulli polynomials. As shown by Edward Witten in his papers on two-dimensional gauge theories, the correlation functions of…

We prove very general formulae for the generating series of (Hodge) genera of symmetric products with coefficients, which hold for complex quasi-projective varieties with any kind of singularities, and which include many of the classical…

We give a combinatorial expansion of the stable Grothendieck polynomials of skew Young diagrams in terms of skew Schur functions, using a new row insertion algorithm for set-valued semistandard tableaux of skew shape. This expansion unifies…

Based on the reduction of degree in polynomial mappings and some known results in algebraic geometry, by introducing the Brouwer degree, a tool from differential topology, algebraic topology and algebraic geometry, we completely prove the…

We present a general abstract framework for combinatorial Dyson-Schwinger equations, in which combinatorial identities are lifted to explicit bijections of sets, and more generally equivalences of groupoids. Key features of combinatorial…

We study graph products of groups from the viewpoint of measured group theory. We first establish a full measure equivalence classification of graph products of countably infinite groups over finite simple graphs with no transvection and no…

In a recent paper, Ayyer and Behrend present for a wide class of partitions factorizations of Schur polynomials with an even number of variables where half of the variables are the reciprocals of the others into symplectic and/or orthogonal…

There is a well-known combinatorial definition, based on ordered set partitions, of the semigroup of faces of the braid arrangement. We generalize this definition to obtain a semigroup Sigma_n^G associated with G wr S_n, the wreath product…

In this paper we show that counting Grothendieck's dessins d'enfants is universal in the sense that some other enumerative problems are either special cases or directly related to it. Such results provide concrete examples that support a…

We introduce an elliptic version of the Grothendieck-Springer sheaf and establish elliptic analogues of the basic results of Springer theory. From a geometric perspective, our constructions specialize geometric Eisenstein series to the…

We associate convex bodies to a wide class of graded G-algebras where G is a connected reductive group. These convex bodies give information about the Hilbert function as well as multiplicities of irreducible representations appearing in…