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We describe a method of computing equivariant and ordinary intersection cohomology of certain varieties with actions of algebraic tori, in terms of structure of the zero- and one-dimensional orbits. The class of varieties to which our…

In this paper we give a new and simplified proof of the variational Hodge conjecture for complete intersection cycles on a hypersurface in projective space.

In this article, we introduce the study of a class of finite groups $G$ which admits a subgroup which intersects all non-trivial subgroups of $G$. We also explore a subclass of it consisting of all groups $G$ in which the prime order…

This is the second in a series of papers. Here we develop here an intersection theory for manifolds equipped with an action of a finite group. As in our previous paper, our approach will be homotopy theoretic, enabling us to circumvent the…

We prove an existence theorem for jet differentials on complete intersection varieties that generalizes a theorem of S. Diverio. We also show that one can readily deduce hyperbolicity for generic complete intersections of high multidegree…

The authors establish a relation of the theory of varieties with degenerate Gauss maps in projective spaces with the theory of congruences and pseudocongruences of subspaces and show how these two theories can be applied to the construction…

We build a variant of Collatz Conjecture for polynomials over $\mathbb{F}_2$ and we prove that it is solved. By the way, we give several examples.

We generalize several comparison results between algebraic, semi-topological and topological K-theories to the equivariant case with respect to a finite group.

The Malle-Navarro conjecture relates central block theoretic invariants in two inequalities. In this paper, we prove the conjecture for the 2-blocks and the unipotent 3-blocks of the general linear and unitary groups in non-defining…

We give a Belyi-type characterisation of smooth complete intersections of general type over $\mathbb{C}$ which can be defined over $\bar{\mathbb{Q}}$. Our proof uses the higher-dimensional analogue of the Shafarevich boundedness conjecture…

Both the Klein-Williams invariant $\ell_G(f)$ from \cite{KW2} and the generalized equivariant Lefschetz invariant $\lambda_G(f)$ from \cite{weber07} serve as complete obstructions to the fixed point problem in the equivariant setting. The…

We establish a theory of complexes of relative correspondences. The theory generalizes the known theory of complexes of correspondences of smooth projective varieties. It will be applied in the sequel of this paper to the construction of…

We extend the notion of intersection graphs for knots in the theory of finite type invariants to string links. We use our definition to develop weight systems for string links via the adjacency matrix of the intersection graph, and show…

We introduce a new graph invariant of finite groups that provides a complete characterization of the splitting types of unramified prime ideals in normal number field extensions entirely in terms of the Galois group. In particular, each…

A conjecture due to Zassenhaus asserts that if $\ G$ is a finite group then any torsion unit in $\mathbb{Z}G$ is conjugate in $\mathbb{Q}G$ to an element of $\ G$. We present a weaker form of this conjecture for some infinite groups.

A multivariate Gauss-Lucas theorem is proved, sharpening and generalizing previous results on this topic. The theorem is stated in terms of a seemingly new notion of convexity. Applications to multivariate stable polynomials are given.

We study generalized splines from the perspective of the representation theory of the category of graphs with contractions. Our main theorem proves a kind of finite generation, which in turn implies the existence of a ``universal generating…

We consider the conjecture of Brutman and Pasow on a totality divided differences and prove the conjecture for continuous functions.

Let A_1,...,A_k be a collection of families of subsets of an n-element set. We say that this collection is cross-intersecting if for any i,j in [k] with i not equal to j, A in A_i and B in A_j implies that the intersection of A and B is…

It is shown that any finitely generated non-elementary Fuchsian group has among its homomorphic images all but finitely many of the alternating groups. This settles in the affirmative a conjecture of Graham Higman.