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Maximal surfaces, Born-Infeld solitons and Ramanujan’s identities

Harish-Chandra Research Institute, Allahabad, India

In this talk, we will explain how one can obtain the Weierstrass- Enneper representation for maximal graphs( assuming that the Gauss map is one-one) in hodographic coordinates by making an observation that the maximal surface equation and Born-Infeld equation are related upto a wick rotation. This observation also gives us a way to construct a one parameter family of complex Born-Infeld solitons( solutions of Born-Infeld equation) from a given one parameter family of maximal surfaces. We also show that a Born-Infeld soliton can be realised either as a spacelike minimal graph or timelike minimal graph over a timelike plane or a combination of both away from singular points. Next we show the existence of a maximal surface containing a given spacelike closed curve and having a special singularity. Finally, we show the connection of maximal surfaces to analytic number theory through certain Ramanujan’s identities.

Seminario 1ª planta, IEMath

On neutral 4-manifolds (survey) and counterexamples to Goldberg Conjecture in indefinite metric spaces

Osaka City University Advanced Mathematical Institute

My talk will begin with a survey on the existence theorem of a neutral metric on a 4-manifold. The existence of a neutral metric on a 4-manifold is equivalent to the existence of a field 2-planes, and also to that of a pair of two kinds of almost complex structures. These facts are proved on the basis of a theorem of Hirzebruch and Hopf (1958), and of Donaldson’s classification of definite intersection forms (1983). I then consider the Goldberg Conjecture (1969) of indefinite metric version, and I report some counterexamples to the Conjecture of indefinite metric version. Also, future problems will be discussed.

Seminario primera planta, IEMATH

Isometric Reeb flow on Real Hypersurfaces in Hermitian Symmetric Spaces.

Kyungpook National University

In this talk. first, from the histrorical view point we introduce some works on isometric Reeb flow on real hypersurfaces in complex projective space, complex hyperbolic space, complex two-plane Grassmannians, and complex quadrics. Next we want to give a recent classification of isometric Reeb flow on real hypersurfaces in generalized complex k-plane Grassamnnians.

Seminario 1ª planta, IEMath

Every meromorphic function is the Gauss map of a conformal minimal surface

Univerza v Ljubljani

We prove that every meromorphic function on an open Riemann surface \(M\) is the complex Gauss map of a conformal minimal immersion \(f:M\to \mathbb R^3\); furthermore, \(f\) may be chosen as the real part of a holomorphic null curve \(F:M\to\mathbb C^3\). Analogous results are proved for conformal minimal immersions \(M\to\mathbb R^n\) for any \(n>3\). We also show that every conformal minimal immersion \(M\to\mathbb R^n\) is isotopic to a flat one, and we identify the path connected components of the space of all conformal minimal immersions \(M\to\mathbb R^n\) for any \(n\ge 3\). (Joint work with Antonio Alarcón and Francisco J. López,

Seminario 1ª planta, IEMath

Lawson correspondence for minimal and constant mean curvature surfaces

Université Paris-Est Marne-la-Vallée

Lawson correspondence between minimal surfaces in \(\mathbb{S}^3\) and constant mean curvature (CMC) surfaces in \(\mathbb{R}^3\) is instrumental in building examples of surfaces, but also reveals a lot about the structure of underlying PDEs. In discrete geometry, simple definitions of CMC surfaces are not obvious (many have been given) and an analog to Lawson correspondence has eluded researchers for a long time. We will present here a natural and computation-friendly definition, based on Lax pairs, which showcases the analogy between the two types of surfaces, as well as proposes a construction method. We will try to outline the similarities and differences between the smooth and discrete realms. Joint work with Alexander Bobenko (TU Berlin)

Seminario primera planta, IEMATH

On a solution for a fourth-order nonlinear partial differential equation in a compact manifold

The purpose of this article is to provide sufficient conditions for having a positive weak solution for a fourth-order non-linear partial differential equation in M, a compact Riemannian manifold, and this solution is harmonic on the boundary of M.

Seminario 1ª planta IEMATH


Geometric Analysis Workshop 2017

Valencia (España)


Del 5 al 8 de septiembre tendrá lugar en la Facultat de Ciències Matemàtiques de la Universitat de València el workshop con título Geometric Analysis en homenaje a Olga Gil Medrano, catedrática del Departamento de Geometría y Topología, antigua vicerrectora de Relaciones Internacionales y Cooperación de la Universitat de València y expresidenta de la RSME.

Durante las mañanas habrá conferencias plenarias y las tardes se dedicarán a grupos de trabajo y discusiones informales sobre temas propuestos por los asistentes. Los conferenciantes invitados son Pacelli Bessa (Universidade Federal do Ceará, Brasil), Vincent Borrelli (Université de Lyon, Francia), Esther Cabecas-Rivas (Goethe-Universität Frankfurt, Alemania), Pablo Chacón (Universidad de Salamanca), Leonor Ferrer (Universidad de Granada), Anna Fino (Università di Torino, Italia), Luquesio Jorge (Universidade Federal do Ceará, Brasil), Ilkka Holopainen (University of Helsinki, Finlandia), Ana Hurtado (Universidad de Granada), Steen Markvosen (Danmarks Tekniske Universitet, Dinamarca), Peter Minchor (Universität Wien, Austria) y Luigi Vezzoni (Università di Torino, Italia).

La asistencia al workshop es gratuita.

Differential Geometry conference at Banach Conference Center

Bedlewo (Poland)

Dear professor, Dear geometry researcher, We are pleased to invite you to the conference 'Differential Geometry' that will take place in the Banach Conference Center at Bedlewo, Poland, from June 18th till June 24th 2017. This conference is the sixth in a series organized in a Polish-European co-operation. It is sponsored by the Banach Center and the Warsaw Center of Mathematics and Computer Science. The purpose of this conference is to bring together researchers in geometry and to provide for them a forum to present their recent work to colleagues from different nationalities. This way we aim to stimulate discussion about the latest findings in differential geometry and to increase international collaboration.
The conference will cover the following topics:
- Riemannian and pseudo-Riemannian geometry,
- classical differential geometry,
- manifolds with special structures (Kaehler, Sasakian etc.),
- submanifolds,
- affine differential geometry,
- relations between geometry and PDE's,
- global problems,
- classification results.

BCAM-PV/EHU Graduate School: Introduction To Geometric Analysis: The Atiyah-Singer Index Theorem

Basque Centre of Applied Mathematics (Spain)

Geometric Analysis consists in applying PDE tools in order to prove deep theorems in Geometry. It is one of the areas mathematics with more spectacular results in the last half a century.
The school is primarily aimed for Master and beginning Ph. D. students, and hence prerequisites will be kept to a minimum. The objective is to develop the tools and some working knowledge in Geometric Analysis, that is the interaction of manifold theory with PDE analysis. We hope to bring together students in analysis and geometry and establish a fruitful interaction between them.
We have chosen as a guiding goal of the school, to develop the tools and explain a proof of one of the most classic and striking theorems in geometric analysis, namely the Atiyah-Singer Index Theorem. Besides the importance of the theorem, we feel that developing the tools, assembling a proof and explaining some applications (Hirzebruch-Riemann-Roch and Hirzebruch signature theorems) will help the students in learning useful techniques in geometry and analysis, and learning how they can be combined in order to prove deep results.
The school will last for three weeks. The first two weeks will be devoted to develop basic techniques in geometry and analysis of PDE’s, which are needed for the proof of the theorem, but which are completely central by themselves. In the third one Atiyah-Singer index theorem will be proved, some applications will be derived, and in addition some topics of modern geometric analysis will be surveyed, in order to let the participants taste some topics of current research.

Geometry - in honour of Mario Micallef's 60th birthday

Warwick (United Kingdom)


Local Organiser: Peter Topping

Speakers will include:

  • Claudio Arezzo (ICTP)
  • Ailana Fraser (UBC)
  • Tobias Lamm (KIT)
  • Yng-Ing Lee (NTU/Oxford)
  • Martin Li (CUHK)
  • Davi Maximo (U Penn)
  • Vlad Moraru (L’Aquila)
  • Georgios Moschidis (Princeton/Cambridge)
  • Aaron Naber (Northwestern)
  • Andre Neves (Imperial/Chicago)
  • Rick Schoen (UC Irvine)
  • Ben Sharp (Warwick)

Registration deadline for those requesting any financial/accommodation support: noon, Monday 13 March 2017.Registration closes: noon, Monday 3 April 2017.

Talks start: 9am on Monday 8 May

Talks end: 4pm Wednesday 10 May (tentative plan)

All talks in MS.04, Mathematics Institute, University of Warwick. Workshop dinner to be held Tuesday 9th May, 6.30pm, at The Cross, Kenilworth. We expect to have a buffet dinner at the Mathematics Institute on Monday 8th May.

Supported by EPSRC through a symposium grant and the Warwick-Imperial-Cambridge geometric analysis seminar (with Dafermos, Neves, Wickramasekera, funded by a Programme grant).

Young Researcher Workshop on Differential Geometry in Minkowski Space

Granada (España)

The aim of this workshop is to bring together active young researchers on differential geometry in Lorentz-Minkowski space, specially on surfaces with constant curvature. The meeting addresses specially for graduate students, recent PhDs and other junior researchers, to meet and present their work to each other. The speakers are young researchers that will present their latest results and the lectures will be focused on familiarizing the participants with the background material leading up to specific problems.

Minimal Surfaces: Integrable Systems and Visualisation

Cork (Ireland)

Scientific Committee:
Franz Pedit (UMass) Antonio Ros (UGR)

Organising Committee:
Tim Hoffmann (TUM)
Martin Kilian (UCC)
Katrin Leschke (UoL)
Francisco Martin (UGR)
Katsuhiro Moriya (UTsukuba)

Confirmed Speakers:
Benoît Daniel (IECL), Isabel Fernández (USeville), Leonor Ferrer (UGR), Laurent Hauswirth (UPE), Barbara Nelli (UnivAQ), Pablo Mira (UPCT), Franz Pedit (UMass), Joaquín Pérez (UGR), Ulrich Pinkall (TUB), Martin Schmidt (UMA)

France-Italy meeting in Geometric Analysis

Pisa (Italy)

The aim of the meeting is to gather some experts, including young ones, working actively in Geometric Analysis. We would like especially to bring together people with more analytic and more geometric backgrounds in order to fruitfully exchange ideas and methods for applications of one field to another. This interaction has been quite successful over the past decades, and we hope to create new occasions for continuing in this.

James SERRIN: from His legacy to the new frontiers

Perugia (Italy)

The aim of the conference is to bring together leading experts and researchers in nonlinear partial differential equations and in subjects of pure and applied mathematics, in which James Serrin inspired generations of Mathematicians and continues to influence their ideas. The conference will promote research, stimulate interactions among the participants and continue the tradition of the previous meetings on PDEs methods and their applications held in Perugia in the last decades

Congreso Bienal de la Real Sociedad Matemática Española

Universidad de Zaragoza (Spain)

En nombre del Comité Organizador es un placer invitarte a participar en el congreso de la Real Sociedad Matemática Española que se celebrará en la Facultad de Educación de la Universidad de Zaragoza del 30 de enero al 3 de febrero de 2017.
En este congreso Bienal RSME 2017 se dará a conocer la reciente investigación en matemáticas, así como estrecharemos lazos de colaboración entre distintos grupos de investigación de nuestro país. La asistencia al congreso permitirá disfrutar de esta ciencia a través de variadas actividades programadas en la ciudad de Zaragoza.
Por todos estos motivos te animamos a participar en este evento y esperamos verte en la histórica ciudad de Zaragoza.
Juan Ignacio Montijano
Presidente del Comité Organizador