Geometric Problems in Linear and Nonlinear PDEs

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Geometric Problems in Linear and Nonlinear PDEs

 16 - 20 Jun 2025

Sabhal Mor Ostaig, the Isle of Skye

  • Monica Musso, University of Bath
  • Massimo Grossi, Universita' di Roma La Sapienza
  • Asma Hassannezhad, University of Bristol
  • Alessandro Savo, Universita' di Roma La Sapienza

About:

Geometric analysis has intrigued mathematicians for centuries and remains a vibrant area of modern mathematics. Central to this field are the formulation of both linear and nonlinear partial differential equations (PDEs) on manifolds and the minimization of energy functionals in infinite-dimensional spaces. Our workshop will focus on four closely interconnected areas within geometric analysis: characterizing solutions to PDEs, Euler equations, minimal surface theory, and spectral geometry. The event aims to bring together leading experts and early-career researchers from around the world to discuss the latest advancements, exchange ideas, and explore major challenges and open problems in the field. 

We acknowledge the support of the London Mathematical Society and Glasgow Mathematical Journal Trust. The event is organised in partnership with the Clay Mathematics Institute.

 

Programme

MONDAY 16 JUNE 2025
09.00–09.15 Housekeeping and welcome by ICMS
09.15-09:45 Introduction by organisers
09.45-10.30 Juan Dávila, University of Bath Overhanging water waves in the presence of vorticity
10.30-11.00 Coffee Break
11.00-11.45 Manuel del Pino, University of Bath Delaunay-type compact equilibria in the liquid drop model
11.45-12.30 Katie Gittins, Durham University Nodal counts for the Robin problem on Lipschitz domains
12.30-14.00 Lunch
14.00-14.45 Rowan Juneman, University of Bath Vortex dynamics for the Gross-Pitaevskii equation
14.45-15.30 Angela Pistoia, Sapienza University of Rome On some properties of Steklov eigenfunctions
15.30-16.00 Coffee Break
16.00-17.00 Michael Struwe, ETH Zurich The prescribed curvature flow on the disc
18:00-19:00 Welcome reception
TUESDAY 17 JUNE 2025
09.00-09.45 Melanie Rupflin, University of Oxford Quantitative estimates for almost harmonic maps
09.45-10.30 Michael Levitin, University of Reading
10.30-11.00 Coffee Break
11.00-11.45 Michail Karpukhin, UCL Eigenvalues and minimal surfaces
11.45-12.30 Jean Lagacé, King's College London A canonical foliation for the bubble-sheet singularities of geometric flows
12.30-14.00 Lunch
14.00-14.45 Andrea Bisterzo, Università degli Studi di Milano-Bicocca ON SOME PROPERTIES OF STEKLOV EIGENFUNCTIONS
14.45-15.30 Francesca Gladiali, 'Centro di Ricerca Ennio De Giorgi, Pisa Two characterizations of embedded minimal helicoids and totally geodesic hypersurfaces on space-forms
15.30-16.00 Coffee Break
16.00-18.00 Informal discussion
18.00 Dinner
WEDESDAY 18 JUNE 2025
09.00-09.45 Bruno Colbois, University of Neuchâtel Title
09.45-10.30 Luigi Provenzano, Sapienza Università di Roma Can one hear the conformal class of a surface?
10.30-11.00 Coffee Break
11.00-11.45 Giusi Vaira, Università degli Studi di Bari Aldo Moro The Brezis - Nirenberg problem in low dimensions
11.45-12.30 Open session
12.30-14.00 Lunch
14.00-18.00 Free afternoon
18.00 Dinner
THURSDAY 19 JUNE 2025
09.00-09.45 Samuel Perez-Ayala, Haverford College Eigenvalue estimates on asymptotically hyperbolic spaces and their submanifolds
09.45-10.30 Romain Petrides, Université Paris Cité
10.30-11.00 Coffee Break
11.00-11.45 Iosif Polterovich, Université de Montréal
11.45-12.30 David Ruiz, University of Granada Compactly supported solutions to the stationary 2D Euler equations with noncircular streamlines
12.30-14.00 Lunch
14.00-15.30 Informal discussion
18.00 Conference Dinner

Sponsors and Funders:

  • CMI
  • London
  • Glasgow