Related papers: A Groupoid Proof of the Lefschetz fixed point form…

In this note, we present a probabilistic proof of the well-known finite geometric series. The proof follows by taking the moments of the sum and the difference of two independent exponentially distributed random variables.

We generalize the fixed-point property for discrete groups acting on convex cones given by Monod in \cite{monod} to topological groups. At first, we focus on describing this fixed-point property from a functional point of view, and then we…

In Proposition I of "Memoire sur les conditions de resolubilite des equations par radicaux", Galois established that any intermediate extension of the splitting field of a polynomial with rational coefficients is the fixed field of its…

The main result of this note is a hard Lefschetz theorem for the Chow groups of generalized Kummer varieties. The same argument also proves hard Lefschetz for Chow groups of Hilbert schemes of abelian surfaces. As a consequence, we obtain…

The purpose of this paper is to propose a version of the notion of convenient Lie groupoid as a generalization of this concept in finite dimension. The authors point out which obstructions appear in the infinite dimensional context and how…

In this paper we develop the functional calculus for elliptic operators on compact Lie groups without the assumption that the operator is a classical pseudo-differential operator. Consequently, we provide a symbolic descriptions of complex…

We present a general fixed point theorem which can be seen as the quintessence of the principles of proof for Banach's Fixed Point Theorem, ultrametric and certain topological fixed point theorems. It works in a minimal setting, not…

This paper concerns a formula which relates the Lefschetz number L(f) for a map f:M --> M' to the fixed point index I(f) summed with the fixed point index of a derived map on part of the boundary of M. Here M is a compact manifold and M' is…

We give a proof of the Erd\H{o}s-Ko-Rado Theorem using the Borel Fixed Point Theorem from algebraic group theory. This perspective gives a strong analogy between the Erd\H{o}s-Ko-Rado Theorem and (generalizations of) the Gerstenhaber…

The goal of this article is to establish local Lipschitz continuity of weak solutions for a class of degenerated elliptic equations of divergence form, in the Heisenberg Group. The considered hypothesis for the growth and ellipticity…

A general Lefschetz formula for the geodesic action on locally symmetric spaces is proven.

We prove formulas for power moments for point counts of elliptic curves over a finite field $k$ such that the groups of $k$-points of the curves contain a chosen subgroup. These formulas express the moments in terms of traces of Hecke…

We give a self-contained algebraic description of a formal symplectic groupoid over a Poisson manifold M. To each natural star product on M we then associate a canonical formal symplectic groupoid over M. Finally, we construct a unique…

We will prove the following theorems. The first theorem posits the existence of a fixed point for the actions of nilpotent Lie groups on nonpositively curved compact manifolds. The second theorem states that actions of solvable Lie groups…

Motivated by some alternatives to the classical logical model of boolean algebra, this paper deals with algebraic structures which extend skew lattices by locally invertible elements. Following the meme of the Ehresmann-Schein-Nambooripad…

In this article, we develop a calculus of Shubin type pseudodifferential operators on certain non-compact spaces, using a groupoid approach similar to the one of van Erp and Yuncken. More concretely, we consider actions of graded Lie groups…

We prove a Noether--Lefschetz-type result for certain linear systems on a projective threefold with isolated singularities.

We prove a topological rigidity theorem for closed hypersurfaces of the Euclidean sphere and of an elliptic space form. It asserts that, under a lower bound hypothesis on the absolute value of the principal curvatures, the hypersurface is…

In this paper, we show the new fixed point theorem in metric spaces. Furthermore, for this fixed point theorem, we apply to the Collatz conjecture.

A homeomorphism of the $2$-torus with Lefschetz number different from zero has a fixed point. We give a version of this result for nilpotent groups of diffeomorphisms. We prove that a nilpotent group of $2$-torus diffeomorphims has finite…