Geometric insights in Partial Differential Equations: advances and challenges
 Organizer(s):
Name:
Affiliation:
Country:
Luca Vilasi
University of Messina
Italy
Giovanni Molica Bisci
San Raffaele University of Rome
Italy
Vicentiu Radulescu
University of Craiova
Romania
 Introduction:  
  Partial Differential Equations (PDEs) play a fundamental role in addressing a wide range of geometric problems, both in pure mathematics and applied sciences. Recent developments have unveiled new connections between geometric structures and PDE techniques, leading to significant advances in the understanding of existence, uniqueness, and qualitative properties of solutions. However, crucial challenges remain, particularly concerning regularity issues, where singularities and lack of smoothness pose significant obstacles in various contexts. This session aims to explore recent breakthroughs in geometric PDEs, highlighting novel methods and open problems while fostering collaboration among researchers working at the intersection of analysis and geometry.