course

INFO

We are announcing a program in geometric analysis, which will take place over the last two weeks of June 2023 (from 19th to 30th). It will be held at the Institute of Mathematics of the University of Granada (IMAG), downtown Granada. This International Doctoral Summer School is associated and partially funded by the Doctorate School in Sciences, Technologies and Engineering of the University of Granada.

ONLINE ATTENDANCE

The talks of this Doc-Course will be broadcast via Google Meet and they can be followed at meet.google.com/zop-oeov-dve

PROGRAM

The program consists of the following two parts:

First week:

Summer School consisting of the following 4 mini-courses and 3 talks aimed at PhD students and young postdocs:

Mini-courses:

• Sun-Yung Alice Chang (Princeton University): Fractional GJMS operators and applications
• Xavier Cabré (ICREA and Universitat Politècnica de Catalunya): On the nonlocal mean curvature (lecture notes)
• Moritz Kassmann (Universität Bielefeld): Exterior value problems and regularity for nonlocal operators
• Rafe Mazzeo (Stanford University): Toward a geometric theory of fractional Laplacians

Talks:

• L. Battaglia (Roma Tre): Prescribing almost constant curvatures on the half-plane
• J.C Fernández-Morelos (UNAM): Optimal Partitions and prescribed Q-curvature equations
• Samuel Pérez-Ayala (Princeton): TBA

The videos of these talks can be found on our YouTube channel: https://www.youtube.com/watch?v=PsfEwLWdex0&list=PL3Qr8EnGl1O-uWV8lwG2yjGWLI-v14RTY&pp=iAQB

Schedule for the first week:

Second week:

Specialized research conference, with the following speakers:

• V. Agostiniani (U. di Trento): A PDE proof of the Riemannian Penrose inequality (Abstract)
• R. Bettiol (CUNYl): Bifurcating minimal surfaces in ellipsoids of revolution
• E. Cabezas Rivas (U. de Valencia): Characterization of the subdifferential and minimizers for the anisotropic p-capacity
• J. Case (Penn State U.): A Gauss-Bonnet formula for renormalized areas (Abstract)
• E. Cinti (U. di Bologna): Optimal regularity for isoperimetric sets with density (Abstract)
• F. Colasuonno (U di Bologna): Critical double phase problems (Abstract)
• J. Espinar (U. de Granada): Min-Oo conjecture for fully nonlinear conformally invariant equations (Abstract)
• P. Esposito (Roma Tre U.): Exponential PDEs in high dimensions (Abstract)
• R. Graham (U. of Washington): Extrinsic GJMS Operators for Submanifolds (Abstract)
• M. Grossi (La Sapienza, U. di Roma): The number of critical points of the Robin function in domains with a small hole (Abstract)
• R. Gover (U. Auckland): Some linear and non-linear (conformal) Dirichlet-Neumann maps ( Abstract)
• M. Gursky (Notre Dame U.): The ASD deformation complex and a conjecture of Singer (Abstract)
• I. Ianni (La Sapienza, U. di Roma): Uniqueness results for local and non-local Dirichlet problems (Abstract)
• E. Kuwert (Freiburg U.): Curvature varifolds with free boundary
• Y.-J. Lin (Wichita State U.): Conformally covariant polydifferential operators associated with CVIs and its applications (Abstract)
• A. Maalaoui (Clark U.): Compactness of Dirac-Einstein Structures in Dimensions 3 and 4 (Abstract)
• F. de Marchis (La Sapienza, U. di Roma): On critical points of the Moser-Trudinger functional (Abstract)
• V. Martino (U. Bologna): On the conformal Dirac-Einstein equations (Abstract)
• S. McKeown (U. of Texas at Dallas): A fourth-order Escobar-Yamabe problem on a half-ball (Abstract)
• A. Pistoia (La Sapienza, U. di Roma): Conformal metrics with prescribed curvatures(Abstract)
• J. Qing (U. de California Santa Cruz): \(p\)-Laplace equations, \(p\)-superharmonic functions, and their applications in conformal geometry (Abstract)
• J. Ratzkin (Würzburg U.): Compactness of singular constant \(Q\)-curvature metric on punctured spheres (Abstract)
• D. Ruiz (U. Granada): Steady solutions for the 2D Euler equations and overdetermined elliptic problems ( Abstract)
• B. Sharp (Leeds U.): Degree-one \(\alpha\)-harmonic maps with low energy
• S. Terracini (U. Torino): Boundary Harnack principles and degenerate equations on singular sets (Abstract)
• G. Wang (U. Freiburg): Geometric inequalities for capillary hypersurfaces (Abstract)
• P. Yang (Princeton U.): Variation of the Einstein-Hilbert action for pseudohermitian manifolds
• Y. Wang (Johns Hopkins): Yamabe flow of asymptotically flat metrics (Abstract)
• J. Wei (U. British Columbia): Optimal Beckner Inequality for Axially Symmetric Functions on \(S^4\) and \(S^6\) (Abstract)

* Special talk by Susanna Terracini (U. di Torino) to explain the role of the EWM in the Mathematics community.

Schedule for the second week:


PARTICIPANTS

(both weeks)

• Virginia Agostiniani (Università degli Studi di Trento)
• Aubrey Sophie Aiken (University of California, Santa Cruz)
• Antonio Alarcón (Universidad de Granada)
• Joao Henrique Andrade (University of British Columbia)
• Pêdra Andrade (Instituto Superior Técnico- University of Lisbon)
• Luigi Appolloni (University of Leeds)
• Francesco Balducci (Università di Roma "La Sapienza")
• Itahisa Barrios Cubas (Universidad Autónoma de Madrid)
• Luca Battaglia (Università degli Studi Roma Tre)
• Fatima Bengrine (Universidad Autónoma de Madrid)
• Chiara Bernardini (Università di Padova)
• Renato Bettiol (CUNY)
• Francesca Bianchi (University of Ferrara)
• Juan Pablo Cabeza (Universidad de Chile)
• Esther Cabezas-Rivas (Universitat de València)
• Xavier Cabré (ICREA and UPC, Barcelona)
• Jeffrey Case (Penn State University)
• Sun-Yung Alice Chang (Princeton University)
• Xuezhang Chen (Nanjing University)
• Eleonora Cinti (Università di Bologna)
• Francesca Colasuonno (Università di Bologna)
• Sergio Cruz Blázquez (Universidad de Granada)
• Davide Dameno (Università degli Studi di Milano)
• Azahara De la Torre (Sapienza Università di Roma)
• Francesca De Marchis (Sapienza Università di Roma
• Luca Di Beo (University of Udine)
• Gianmichele Di Matteo (Karlsruher Institut für Technologie KIT)
• José Espinar (Universidad de Cádiz)
• Pierpaolo Esposito (Università degli Studi Roma Tre)
• Juan Carlos Fernández (Universidad Nacional Autónoma de México)
• Benjy Firester (Harvard)
• Carlos Fuertes Morán (Universidad Autónoma de Madrid)
• Alba Dolores García Ruiz (ICMAT-UAM) ​(email)
• Marco Gipo Ghimenti (University of Pisa)
• Gianmarco Giovannardi (University of Florence)
• María del Mar González (Universidad Autónoma de Madrid)
• Irene Gonzálvez Martínez (Universidad Autónoma de Madrid)
• Rod Gover (University of Auckland)
• Robin Graham (University of Washington)
• Massimo Grossi (Università di Roma Sapienza)
• Florian Grube (Bielefeld University)
• Yaoting Gui (Beijing institute center for mathematical research)
• Matthew Gursky (University of Notre Dame)
• Thorben Hensiek (Bielefeld University)
• Jorge Hidalgo (Universidad de Granada) (email)
• Isabella Ianni (La Sapienza Università di Roma)
• Peio Ibarrondo (Universidad Autónoma de Madrid)
• Mikel Ispizua (Universidad Autónoma de Madrid)
• Moritz Kassmann (Bielefeld University)
• Ayush Khaitan (Penn State University)
• Michał Kijaczko (Wrocław University of Science and Technology)
• Seongtag Kim (Inha University)
• Tzu-Mo Kuo (University of California, Santa Cruz)
• Sri Rama Chandra Kushtagi (University of Texas at Dallas)
• Ernst Kuwert (University of Freiburg, Germany)
• Julia Lenczewska Wroclaw (University of Science and Technology)
• Yueh-Ju Lin (Wichita State University)
• Rafael López Soriano (Universidad de Granada)
• Ali Maalaoui (Clark University)
• Diego Alfonso Marín Muñoz (Universidad de Granada) (email)
• Juan Silverio Martínez Baena (Universidad de Granada)
• Vittorio Martino (University of Bologna)
• Dorian Martino (Université Paris Cité)
• Filippo Mastropietro (Università degli Studi di Milano)
• Rafe Mazzeo (University of Stanford)
• Lorenzo Mazzieri (Università degli Study di Trento)
• Stephen McKeown (University of Texas at Dallas)
• Rodrigo Morón Sanz (Universidad de Málaga)
• Najma Mosadegh kordmahaleh (Azarbaijan Shahid Madani University)
• Giulio Pascale (Università degli Studi di Napoli "Federico II")
• Samuel Pérez-Ayala (Princeton University)
• Angela Pistoia (Sapienza Università di Roma)
• Luigi Pollastro (Università degli Studi di Milano)
• Julián Pozuelo (Universidad de Granada)
• Jie Qing (UCSC)
• Abishek Rajan (UC Berkeley)
• Jesse Ratzkin (Universität Würzburg)
• Francisco Javier Reyes Sánchez (IMAG-UGR)
• Serena Rocci (Sapienza Università di Roma)
• Magdalena Rodríguez (Universidad de Granada)
• David Ruiz (Universidad de Granada)
• Jorge Ruiz Cases (Universidad Autónoma de Madrid)
• Miguel Sánchez Caja (Universidad de Granada)
• Daniel Raom Santiago (Sapienza Università di Roma)
• Makson Santos (Instituto Superior Tecnico - University of Lisbon)
• Waldemar Schefer (Bielefeld University)
• Delia Schiera (Instituto Superior Técnico)
• Luca Seemungal (University of Leeds)
• Benjamin Sharp (University of Leeds)
• Jinwoo Shin (Korea Institute for Advanced Study)
• Hepp Solveig (Bielefeld University)
• Romani Speciel (Stanford University)
• Susanna Terracini (University of Turin)
• Raphael Tsiamis (Harvard University)
• Aaron Tyrrell (Texas Tech University)
• Yi Wang (Johns Hopkins)
• Guofang Wang (University of Freiburg)
• Juncheng Wei (UBC Vancouver)
• Liangjun Weng (University of Rome Tor Vergata)
• Zetian Yan (Penn State University)
• Paul Yang (Princeton University)
• Ge Yuxin (University of Toulouse 3)
• Chaona Zhu (University of Rome "Tor Vergata")

REGISTRATION

The registration is now closed.


FINANCIAL SUPPORT

We are glad to announce that we will be able to provide some students and young postdocs with accommodation (in a shared room with another participant). Please indicate if you are applying for it when you register.

• Deadline (Financial support application): 1st March 2023.

Hotels

Some hotels close to IMAG (where the conference will take place) are:

• Hotel Catalonia
• Luna Granada
• Granada Center
• Hotel Reina Cristina

Some more hotels (a bit more expensive):

• Granada five sense
• Eurostar
• Sercotel

Cheaper option:

• Pensión San Joaquín

How to arrive

See general instructions here.

Poster

Download the poster here

Organizing Committee:

• Azahara DelaTorre Pedraza: azahara.delatorrepedraza@uniroma1.it
• María del Mar González: mariamar.gonzalezn@uam.es

Photos





Sponsors

• Main funding: Excellence Unit "María de Maeztu" at IMAG (grant CEX2020-001105-M, funded by MCIN/AEI/ 10.13039/501100011033)
• Other funding: European Mathematical Society, Escuela Internacional de Posgrado de la Universidad de Granada
  
  

  
  
  
  

Encuentro, abierto a cualquier investigador interesado en el tema, de los integrantes de los grupos de investigación:

El registro es gratuito, escribiendo un correo a fqm359@ugr.es. Tendrá lugar en el Seminario 1, IMAG

Más información en https://blogs.ugr.es/convex/jornada/

Erasmus + lectures for MSc and PhD students at Universidad de Granada, Spain

Abstract:
The aim of the serie of lectures is to bring an introduction to modern aspects and methods of hyperbolic geometry.We shall divide the topic into four parts:

Classical hyperbolic geometry. We shall recall some metric aspects of a hyperbolic space as one-sheeted hyperboloid including geodesics, trigonometry, isometries, and define the ideal boundary. Then we shall observe them via conformal models in the ball and in the upper half-space.
Hyperbolic manifolds. We shall show totally geodesic and totally umbilical hypersurfaces in a hyperbolic space. Moreover, we use de Sitter space for study geometry of them, including some properties of foliations. Finally, we shall show hyperbolic surfaces and 3-manifolds through discontinuous groups of hyperbolic isometries.
Gromov hyperbolicity. We shall start from CAT(0) space as the most natural extension of comparison methods in differential geometry. Then we study hypebolic spaces in the sense of Gromov with their properties focusing on the ideal boundary. As an application we look at finitely generated groups as metric space on which geometric group theory is founded.

Complex hyperbolic geometry and other generalizations. In this part we shall describe a complex hyperbolic space over complex numer and observe similaraties and differences with the real case. Then we mention on other generalizations like quaternionic and infinite-dimensional ones.

Lunes, martes y jueves (16, 17 y 18 de marzo de 2022): 11:30 a 14:00h

In this seminar we will present some facts about Morse theory of minimal surfaces in 3-manifolds

In this mini-course, we will present some facts about Morse theory of minimal surfaces in 3-manifolds that are useful in order to study some local geometric properties of minimal surfaces.

These results have interesting applications, not only in the study of minimal surfaces in Euclidean 3-space, but also in improving our knowledge about the local behavior of solitons of the mean curvature flow, like shrinkers and translators.

Impartido por:

Jose María Espinar, Universidad de Cádiz

Duración:

24 horas presenciales

Inscripción en:

https://posgrado.uca.es/web/short/cursodoc.php?idcurso=715

Descripción general

En este curso daremos los principales teoremas de clasificación de superficies completas con curvatura de Gauss o media constante.

Comenzaremos recordando algunas generalidades sobre superficies en el espacio euclídeo, como por ejemplo la obtención de las ecuaciones de estructura, que se usarán a lo largo del curso, o la noción de índice de un campo de vectores.

Seguiremos con la clasificación de superficies completas con curvatura de Gauss constante. Continuaremos con los principales resultados de clasificación de superficies de curvatura media constante, entre ellos, los Teoremas de Hopf y Alexandrov; Klotz-Ossermann y la teoría de clasificación de superficies de curvatura media constante propiamente embebidas de Korevaar-Kusner-Meeks-Solomon.

Se van a proceder a la defensas de los TFM del Programa Interuniversitario en Matemáticas correspondientes a las universidades de Granada y Sevilla, de forma virtual.




Las defensas tendrán lugar en las salas virtuales


ugr.zoom.us/my/mastermat1


ugr.zoom.us/my/mastermat2




Para las contraseñas de acceso a las salas virtuales, contactar con el Coordinador del Máster.

Conferenciantes: