Publication

Quasiconformal Embeddings of Y-Pieces

Publications associées (20)

Voss surfaces: A design space for geodesic gridshells

Olivier Baverel, Corentin Jean Dominique Fivet, Nicolas Robin Montagne

The design of envelopes with complex geometries often leads to construction challenges. To overcome these difficulties, resorting to discrete differential geometry proved successful by establishing close links between mesh properties and the existence of g ...

2021

Serre-Tate theory for Calabi-Yau varieties

Maciej Emilian Zdanowicz

Classical Serre-Tate theory describes deformations of ordinary abelian varieties. It implies that every such variety has a canonical lift to characteristic zero and equips the base of its universal deformation with a Frobenius lifting and canonical multipl ...

WALTER DE GRUYTER GMBH2021

Energy distribution of harmonic 1-forms and Jacobians of Riemann surfaces with a short closed geodesic

Jürgpeter Buser, Robert Silhol

We study the energy distribution of harmonic 1-forms on a compact hyperbolic Riemann surface S where a short closed geodesic is pinched. If the geodesic separates the surface into two parts, then the Jacobian variety of S develops into a variety that split ...

2021

Voss Surfaces: A Design Space for Geodesic Gridshells

Olivier Baverel, Corentin Jean Dominique Fivet, Nicolas Robin Montagne

2020

Primary invariants of Hurwitz Frobenius manifolds

Nicolas Gerson Orantin

Hurwitz spaces parameterizing covers of the Riemann sphere can be equipped with a Frobenius structure. In this review, we recall the construction of such Hurwitz Frobenius manifolds as well as the correspondence between semisimple Frobenius manifolds and t ...

AMER MATHEMATICAL SOC2018

Isogeny graphs of ordinary abelian varieties

Benjamin Pierre Charles Wesolowski, Dimitar Petkov Jetchev, Ernest Hunter Brooks

Fix a prime number l. Graphs of isogenies of degree a power of l are well-understood for elliptic curves, but not for higher-dimensional abelian varieties. We study the case of absolutely simple ordinary abelian varieties over a finite field. We analyse gr ...

Springer Heidelberg2017

The geometry of the universal Teichmuller space and the Euler-Weil-Petersson equation

Tudor Ratiu, François Gay-Balmaz

On the identity component of the universal Teichmuller space endowed with the Takhtajan-Teo topology, the geodesics of the Weil Petersson metric are shown to exist for all time. This component is naturally a subgroup of the quasisymmetric homeomorphisms of ...

Elsevier2015

Cohomology Of Large Semiprojective Hyperkahler Varieties

Tamás Hausel

In this paper we survey geometric and arithmetic techniques to study the cohomology of semiprojective hyperkahler manifolds including toric hyperkahler varieties, Nakajima quiver varieties and moduli spaces of Higgs bundles on Riemann surfaces. The resulti ...

Soc Mathematique France2015

Computational Approach to the Geometry of Compact Riemann Surfaces

Manuel Racle

The goal of this document is to provide a generalmethod for the computational approach to the topology and geometry of compact Riemann surfaces. The approach is inspired by the paradigms of object oriented programming. Our methods allow us in particular to ...

EPFL2013

Hecke modifications, wonderful compactifications and moduli of principal bundles

Michael Lennox Wong

In this paper we obtain parametrizations of the moduli space of principal bundles over a compact Riemann surface using spaces of Hecke modifications in several cases. We begin with a discussion of Hecke modifications for principal bundles and give construc ...

Scuola Normale Superiore2013

On the second successive minimum of the Jacobian of a Riemann surface

Björn Mützel

To a compact Riemann surface of genus g can be assigned a principally polarized abelian variety (PPAV) of dimension g, the Jacobian of the Riemann surface. The Schottky problem is to discern the Jacobians among the PPAVs. Buser and Sarnak showed that the s ...

Springer Netherlands2012

Closing Large Hyperbolic 2g-gons : a Way to Study Hyperelliptic Riemann Surfaces of Genus g

Poincaré's uniformisation theorem says that any Riemann surface is conformally equivalent to a unique (up to isometry) surface of constant Gauss curvature 0, 1 or –1. The (topologically) richest of these three worlds is for curvature –1 formed of hyperboli ...

EPFL2012

Finite Element Method on Riemann Surfaces and Applications to the Laplacian Spectrum

Marc Maintrot

The objective of this PhD thesis is the approximate computation of the solutions of the Spectral Problem associated with the Laplace operator on a compact Riemann surface without boundaries. A Riemann surface can be seen as a gluing of portions of the Hype ...

EPFL2012

A class of Neumann type systems and its application

Jinbing Chen

A class of Neumann type systems are derived separating the spatial and temporal variables for the 2+1 dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada (CDGKS) equation and the modified Korteweg-de Vries (mKdV) hierarchy. The Lax-Moser matrix of Neumann type s ...

International Press2012

Capacities, Systoles and Jacobians of Riemann Surfaces

Björn Mützel

To any compact Riemann surface of genus g one may assign a principally polarized abelian variety (PPAV) of dimension g, the Jacobian of the Riemann surface. The Jacobian is a complex torus and we call a Gram matrix of the lattice of a Jacobian a period Gra ...

EPFL2011

Totally geodesic subgraphs of the pants complex

Hugo Parlier

In recent work of Brock's, the pants graph is shown to be a combinatorial model for the completion of the Weil-Petersson metric on Teichmuller space. We prove that every Farey graph embedded in the pants graph is totally geodesic, in analogy with the extri ...

2008

Fixed point free involutions on Riemann surfaces

Hugo Parlier

In this paper, involutions without fixed points on hyperbolic closed Riemann surface are discussed. For an orientable surface X of even genus with an arbitrary Riemannian metric d admitting an involution tau, it is known that min (p is an element of X) d(p ...

The Hebrew University Magnes Press, Springer2008

Trace coordinates of Teichmüller spaces of Riemann surfaces

Thomas Gauglhofer

Using an algebraic formalism based on matrices in SL(2,R), we explicitly give the Teichmüller spaces of Riemann surfaces of signature (0,4) (X pieces), (1,2) ("Fish" pieces) and (2,0) in trace coordinates. The approach, based upon gluing together two build ...

EPFL2006

Trace coordinates of Teichmüller space of Riemann surfaces of signature $(0,4)$

Klaus-Dieter Semmler, Thomas Gauglhofer

Summary: We explicitly give

calT

, the Teichmüller space of four-holed spheres (which we call

X

pieces) in trace coordinates, as well as its modular group and a fundamental domain for the action of this group on

calT

which is its moduli space. As a co ...

2005

On the geometry of simple closed geodesics

Hugo Parlier

The leitmotif of this dissertation is the search for length formulas and sharp constants in relation with simple closed geodesics on hyperbolic compact Riemann surfaces. The main tools used are those of hyperbolic trigonometry, topological properties of si ...

EPFL2004