Related papers: Luigi Cremona and cubic surfaces

Gabrio Piola's scientific papers have been underestimated in the mathematical-physics literature. Indeed a careful reading of them proves that they are original, deep and far reaching. Actually -even if his contribution to mechanical…

For Legendre curves, we consider surfaces of revolution of frontals. The surface of revolution of a frontal can be considered as a framed base surface. We give the curvatures and basic invariants for surfaces of revolution by using the…

A cubic polyhedron is a polyhedral surface whose edges are exactly all the edges of the cubic lattice. Every such polyhedron is a discrete minimal surface, and it appears that many (but not all) of them can be relaxed to smooth minimal…

These notes grew out of two lectures I have given on CAT(0) cube complexes. I've tried to keep the material elementary and self-contained in order to keep the material easily accessible and to provide an elementary introduction on the topic…

This is a survey of results on the construction of holomorphic cusp forms on tube domains originally initiated by Ikeda. Besides a survey it includes conjectures and possible applications of our work.

Glickenstein \cite{Glickenstein} and Glickenstein-Thomas \cite{GT} introduced the discrete conformal structures on surfaces in an axiomatic approach and studied its classification. In this paper, we give a full classification of the…

The theory of surfaces in Euclidean space can be naturally formulated in the more general context of Legendre surfaces into the space of contact elements. We address the question of deformability of Legendre surfaces with respect to the…

Our aim in this note is to present some of the crucial contributions of Jean-Christophe Yoccoz to the theory of circle diffeomorphisms. We start with a short historical account before exposing Yoccoz' work. Then we give a brief description…

We explore algebraic properties of noncommutative frames. The concept of noncommutative frames is due to Le Bruyn, who introduced it in connection with noncommutative covers of the Connes-Consani arithmetic site.

The aim of the note is to illustrate some of the ideas introduced by Luis Caffarelli in his groundbreaking works on the regularity theory for elliptic free boundary problems, in a way which can be understood by non-experts.

The purpose of this essay is to trace the historical development of geometry while focusing on how we acquired mathematical tools for describing the "shape of the universe." More specifically, our aim is to consider, without a claim to…

We present a restriction theorem for the Fourier transform to a 2-dimensional conical surface of finite type, obtaining a sharp result, which improves previous work by Barcelo.

This article is based on the author's inaugural lecture at the University of Cologne on 24 January 2003.

The goal of these lectures is to give an introduction to the study of the fundamental group of a Klein surface. We start by reviewing the topological classification of Klein surfaces and by explaining the relation with real algebraic…

In this paper we prove that the generalized version of the Minimal Resolution Conjecture stated by Mustata holds for certain general sets of points on a smooth cubic surface $X \subset \mathbb{P}^3$. The main tool used is Gorenstein liaison…

We give an overview of the existence and regularity results for curvature flows and how these flows can be used to solve some problems in geometry and physics.

We survey Mirzakhani's work relating to Riemann surfaces, which spans about 20 papers. We target the discussion at a broad audience of non-experts.

It has long been known that to a complex cubic surface or threefold one can canonically associate a principally polarized abelian variety. We give a construction which works for cubics over an arithmetic base. This answers, away from the…

We show that the Kulikov surfaces form a connected component of the moduli space of surfaces of general type with p_g=0 and K^2=6. We also give a new description for the surfaces, extending ideas of Inoue. Finally we calculate the…

The aim of these notes is to explain main ideas of the theory of complements. Basically we will follow Shokurov's work alg-geom/9711024.