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The Calabi-Yau problem for Riemann surfaces with finite genus and countably many ends

Univerza v Ljubljani

We show that if R is a compact Riemann surface and M is a domain in R whose complement is a union of countably many pairwise disjoint smoothly bounded closed discs, then M is the complex structure of a complete bounded minimal surface in \(\mathbb{R}^3\). More precisely, we prove that there is a complete conformal minimal immersion \(X:M→\mathbb{ℝ}^3\) extending to a continuous map from the closure of \(M\) such that \(X(\partial M)\) is a union of pairwise disjoint Jordan curves. This extends a result for finite bordered Riemann surfaces proved in 2015. (Joint work with Antonio Alarcon.)

Seminario 1ª planta, IEMath-GR

Asimptotic Plateau problem for prescribed mean curvature hypersurfaces

University of Helsinki

I will talk on a recent joint preprint with Jean-Baptiste Casteras and Jaime Ripoll. We prove the existence of solutions to the asymptotic Plateau problem for hypersurfaces of prescribed mean curvature in Cartan-Hadamard manifolds N. More precisely, given a suitable subset L of the asymptotic boundary of N and a suitable function H on N, we are able to construct a set of locally finite perimeter whose boundary has generalized mean curvature H and asymptotic boundary L provided that N satisfies the so-called strict convexity condition and that its sectional curvatures are bounded from above by a negative constant. We also obtain a multiplicity result in low dimensions.

Seminario de la primera planta, IEMathUGR

Superficies CMC de género arbitrario en \(\mathbb{M}^2(\epsilon) \times \mathbb{R}\)

Universidad de Granada

Se presentará una extensión de la técnica conjugada de Plateau para la construcción de superficies de curvatura media constante en espacios homogéneos. Usando dicha técnica se construirán superficies de curvatura media constante compactas de género arbitrario simétricas con respecto al grupo de simetrías de una teselación de \(\mathbb{M}^2(\epsilon) \times \mathbb{R}\) para H menor que cierta cota superior que depende de la teselación. En el caso \(\mathbb{S}^2\times \mathbb{R}\) (i.e. \(\epsilon=1\)) se probará que dichas superficies son embebidas para \(H < 1/2\).

Seminario 1ª planta, IEMath-GR

Scherk-like translators for the Mean Curvature Flow

Universidad de Granada

We prove existence and uniqueness for a two-parameter family of translators for mean curvature flow. We get additional examples by taking limits at the boundary of the parameter space. Some of the translators resemble well-known minimal surfaces (Scherk's doubly periodic minimal surfaces, helicoids), but others have no minimal surface analogs. This is a joint work with D. Hoffman and B. White.

Seminario 1ª planta, IEMath-GR

The wedge theorem for ancient mean curvature flows

University of Copenhagen

We show that a wedge theorem (also called a bi-halfspace theorem) holds for properly immersed ancient solutions to the mean curvature flow in n-dimensional Euclidean space. This adds to a long story, as it generalizes our own wedge theorem for self-translators from 2018, which implies the minimal surface case by Hoffman-Meeks (1990) that in turn contains the classical cone theorem by Omori (1967). Another application of the wedge theorem is to classify the convex hulls of the sets of reach of all proper ancient flows, hence posing restrictions on the possible singularities that can occur in mean curvature flow. The proof uses a parabolic Omori-Yau maximum principle for proper ancient flows. This is joint work with Francesco Chini (Univ. Copenhagen).

Seminario 1ª Planta, IEMATH

Jenkins-Serrin problem for translating graphs

Universidad de Granada

I will discuss about recent joint works with E.S. Gama, J. de Lira and F. Martín concerning Jenkins-Serrin type problems for the graphical translators of the mean curvature flow in Riemannian product manifolds \(M\times R\). We prove, for example, the existence of Jenkins-Serrin type translators that can be described as horizontal graphs "over" suitable domains in a vertical plane.

Some results of invariant theory for CR-manifolds

Xinyang Normal University

In this talk, I will introduce some recent works of invariant theory on CR manifolds. After a briefing of CR manifolds, some integral invariants will be introduced in the Heisenberg groups (regarded as a flat model of CR manifolds). The invariants are not changed in the sense of the pseudo-hermitian transformations which can be regarded as the rigid motions in the Heisenberg groups. We take the approach from Integral Geometry for convex bodies, but in our case, the assumption of convexity is not necessary. The applications can be implemented to the CR-version of the Crofton's formula and the containment problems with other related. Some recent development in the invariant theory for CR manifolds will also be discussed in the end of the talk.

Seminario 1ª planta, IEMath-GR

Isoparametric surfaces in \(\mathbb{E}(\kappa,\tau)\)-spaces

Universidad Complutense de Madrid

We provide an explicit classification of the following four families of surfaces in any homogeneous 3-manifold with 4-dimensional isometry group:

  • isoparametric surfaces,
  • surfaces with constant principal curvatures,
  • extrinsically homogeneous surfaces,
  • \(H\)-surfaces with vanishing Abresch-Rosenberg differential.
This is a joint work with Miguel Domínguez Vázquez.

Seminario 1ª planta, IEMath-GR

Carleman type theorems in complex analysis and minimal surface theory

Universidad de Liubliana

Carleman’s approximation theorem (1927) was ostensibly the first result concerning approximation of continuous functions defined on an unbounded closed set of C, namely R, by entire functions. The approximation is stronger than uniform approximation as the error at x can be made to taper off as x approaches infinity (from within R). An essential property of R for such an approximation to exist is that it has bounded exhaustion hulls, that is, the complement of R in the one point compactification of C is locally connected at infinity. Bounded exhaustion hulls play an important role in the characterisation of totally real sets admitting Carleman approximation and Carleman approximation of jets; see Manne et al (2011), Magnusson and Wold (2016). In this talk I will discuss some recent generalisations of Carleman’s theorem including preliminary results from ongoing joint work with Ildefonso Castro-Infantes where the problem of approximating by directed holomorphic immersions, for example by null curves, is being considered.

Seminario de la primera planta, IEMath


Bringing Young Mathematicians Together

ICMAT (Spain)

Welcome to the 2nd BYMAT Conference – Bringing Young Mathematicians Together. This conference aims to:
  • Strengthen the links between PhD students in all disciplines where mathematics is relevant, nationally and internationally.
  • Encourage researchers of different institutions, disciplines and countries to start building a network of contacts soon into their careers.
  • Provide a warm and open space for researchers in the early stages of their career to present their work to peers of similar experience.
  • Promote cross-disciplinary training during the PhD stage, favouring interaction with students from different areas, and boosting scientific outreach and the transfer of knowledge between academia and industry.
  • Favour the use of English as a working language to make BYMAT an inclusive conference.

The conference is especially directed at PhD students in all areas of mathematics and related disciplines, and indeed any young people who use mathematics in their daily lives/jobs. Everyone, from undergraduates to university professors or industry professionals, is more than welcome to attend!

We expect contributed talks and posters to come mainly from PhD students, young industry professionals, master’s students and recent PostDoc. The official language of the conference will be English. We will have short talks (15-20 minutes), distributed in thematic parallel sessions, a poster session, 7 plenary talks given by young professors and industry professionals, workshops and plenty of social activities.

Registration is open until 30th April. Talk and grant applications can be submitted until 11th March.

Topics in Geometric Analysis

Princeton (USA)

The Women and Mathematics Program (WAM) at the Institute for Advanced Study is an annual program with the mission to recruit and retain more women in mathematics. WAM aims to counter the initial imbalance in the numbers of men and women entering mathematics training as well as the higher attrition rate of female mathematicians compared to their male counterparts at every critical transition stage in mathematical careers. WAM encourages female mathematicians to form collaborative research relationships and to become active in a vertical mentoring network spanning a continuum from undergraduates to emerita professors, which provides support and reduces the sense of isolation experienced by many women in mathematics. While there are a number of women's programs targeted solely at undergraduates, or graduate students, or postdocs, very few programs provide the depth and breadth that come from simultaneously including features tailored for undergraduate students, graduate students, and researchers from a broad spectrum of US institutions, all in one united community of scholars, as WAM does.

Taller y Encuentro de la Red Española de Análisis Geométrico

Murcia (España)


El encuentro de investigadores de la REAG es una de las actividades programadas de la Red Española de Análisis Geométrico. Sus objetivos principales son favorecer el intercambio de ideas y fomentar la cooperación entre investigadores, tanto miembros de la Red como de grupos afines cuya investigación se desarrolla en el campo del Análisis Geométrico.

Esta edición se celebrará en la Universidad de Murcia. Durante los días 8 y 9 de abril tendrá lugar el taller de jóvenes investigadores donde los siguientes miembros impartirán una serie de conferencias

  • Antonio Bueno (Universidad de Granada).
  • Verónica L. Cánovas (Universidad de Murcia).
  • Ildefonso Castro-Infantes (Universidad de Granada).
  • Jesús Castro-Infantes (Universidad de Granada).
  • Juan Luis Durán (Universidad Autónoma de Barcelona).
  • Ixchel Gutiérrez Rodríguez (Universidad de Santiago de Compostela).
  • David Iglesias (Universidad de Murcia).
  • Antonio Martínez-Triviño (Universidad de Granada).
  • Julián Pozuelo (Universidad de Granada).
  • Jaime Santos Rodríguez (Universidad Autónoma de Madrid).
  • Erik Sarrión (Universidad Jaume I).
  • Miriam Tárraga (Universidad de Murcia).

Tras el taller se celebrará el día 10 de abril el encuentro de la REAG donde los siguientes investigadores impartirán una conferencia:

  • Teresa Arias Marco (Universidad de Extremadura).
  • Marcos Dajczer (IMPA, Rio de Janeiro, Brasil).
  • Miguel Domínguez-Vázquez (Universidad Autónoma de Madrid).
  • Pablo Mira (Universidad Politécnica de Cartagena).
  • Roberto Rubio (Universidad Autónoma de Barcelona).
  • Francisco Torralbo (Universidad de Granada).
  • Fran Viñado (Universidad Jaume I)

IX Workshop on Differential Geometry

Maceió (Brazil)

The Workshop on Differential Geometry of the Institute of Mathematics of the Federal University of Alagoas has become a traditional event that takes place every year in Maceio-Alagoas, during the Brazilian summer. The aim of this workshop is to gather in Maceio national and international researchers of high scientific level in the field of differential geometry. In this 9th edition, the event will be held in two weeks. From 11 to 15 March, the activities will occur on the Mathematics Institute of the Federal University of Alagoas, and the program is dedicated to young researchers and graduate students, including a minicourse, 30min contributed talks and two sections of open problems. From 18 to 22 March, the activities will occur at Hotel Ponta Verde at Praia do Francês and keeps the traditional program with one minicourse and invited lectures.