Related papers: Finite symmetry groups in complex geometry

Finite (or Discrete) Fourier Transforms (FFT) are essential tools in engineering disciplines based on signal transmission, which is the case in most of them. FFT are related with circulant matrices, which can be viewed as group matrices of…

This is the third and final installment of an exposition of an ACL2 formalization of finite group theory. Part I covers groups and subgroups, cosets, normal subgroups, and quotient groups. Part II extends the theory in the developmnent of…

This text is an introduction to a few selected areas of Alain Connes' noncommutative geometry written for the volume of the school/conference "Noncommutative Geometry 2005" held at IPM Tehran. It is an expanded version of my lectures which…

This is mainly a review of my results related to the title. We discuss, how many elliptic fibrations and elliptic fibrations with infinite automorphism group (or the Mordell-Weil group) an algebraic K3 surface over an algebraically closed…

These notes provide an introduction to Giroux's theory of convex surfaces in contact 3-manifolds and its simplest applications. They put a special emphasis on pictures and discussions of explicit examples. The first goal is to explain why…

Physical theories grounded in mathematical symmetries are an essential component of our understanding of a wide range of properties of the universe. Similarly, in the domain of machine learning, an awareness of symmetries such as rotation…

This is a short presentation of some classical results on finite dimensional complex Lie algebras (classification of nilpotent Lie algebras, deformations and perturbations, contractions and rigidity). We present some applications to…

In this work, we study symplectic structures on graded manifolds and their global counterparts, higher Lie groupoids. We begin by introducing the concept of graded manifold, starting with the degree 1 case, and translating key geometric…

If a (possibly finite) compact Lie group acts effectively, locally linearly, and homologically trivially on a closed, simply-connected four-manifold with second Betti number at least three, then it must be isomorphic to a subgroup of S^1 x…

Motivated by Felix Klein's notion that geometry is governed by its group of symmetry transformations, Charles Ehresmann initiated the study of geometric structures on topological spaces locally modeled on a homogeneous space of a Lie group.…

This is an expanded version of the lecture notes for a minicourse that I gave at a summer school called "Advanced Course on Geometry and Dynamics of Integrable Systems" at CRM Barcelona, 9--14/September/2013. In this text we study the…

The special linear groups, the mapping class groups of surfaces, the outer autormorphism groups of free groups appear in numerous domains. Their analogies, developped in particular in K. Vogtmann's work, have been written about a lot. In…

We study abelian varieties and K3 surfaces with complex multiplication defined over number fields of fixed degree. We show that these varieties fall into finitely many isomorphism classes over an algebraic closure of the field of rational…

In this paper we provide the final steps in the proof, announced by Eskin-Fisher-Whyte, of quasi-isometric rigidity of a class of non-nilpotent polycyclic groups. To this end, we prove a rigidity theorem on the boundaries of certain…

This paper is the third in a series dedicated to the fundamentals of sub-Riemannian geometry and its implications in Lie groups theory: "Sub-Riemannian geometry and Lie groups. Part I", math.MG/0210189, available at…

We extend the theory of complete minimal surfaces in $\mathbb{R}^3$ of finite total curvature to the wider class of elliptic special Weingarten surfaces of finite total curvature; in particular, we extend the seminal works of L. Jorge and…

This habilitation memoir (in French, submitted in May 2014) is made up of five chapters, each being an introduction to work of the author between 2006 and 2014. The core of the memoir consists of the first three chapters, pertaining to…

Extending the results of [Asian J. Math. 2019], in [Doc. Math. \textbf{21}, 2016] we calculated explicitly the number of isomorphism classes of superspecial abelian surfaces over an arbitrary finite field of \textit{odd} degree over the…

This is the text of the Hermann Weyl Prize lecture given by the author at the XXIV Colloquium on Group Theoretical Methods in Physics, Paris, July 2002 (to appear in the Proceedings of the Colloquium).

The exterior degree of a finite group has been introduced in [P. Niroomand and R. Rezaei, On the exterior degree of finite groups, Comm. Algebra 39 (2011), 335--343] and the present paper is devoted to study the exterior degree of infinite…