Geometric Analysis, which historically consists in using tools from analysis — and in particular PDEs and variational methods — to solve problems with a purely geometric statement, has now become a central area of mathematics. The field was shaped in the 1980’s by fundamental contributions from Schoen, Yau, Uhlenbeck, Hamilton and many others. Classical milestones include the resolution of the Yamabe problem (Aubin–Schoen), the positive mass theorem (Schoen–Yau), the foundational results of Uhlenbeck on Yang–Mills equations and Donaldson’s applications to 4-manifold topology, and Perelman’s proof of Thurston’s geometrization conjecture via Hamilton’s Ricci flow. Today Geometric Analysis is an extremely active area where analytic techniques and geometric intuition mutually reinforce each other. Recent advances include, for instance, the regularity theory of minimal surfaces, Allen–Cahn interfaces, Yang–Mills–Higgs fields, the study of singularities of variational problems arising in geometry and mathematical physics, high-dimensional counterexamples to the Milnor conjecture.
The JAG 2027 will be the third edition of this series, following the pilot meeting in Marne (2025) and JAG 2026 in Roscoff, which successfully gathered around 80 participants from France and abroad and fostered new collaborations. The aim of JAG 2027 is to consolidate this annual meeting into a permanent gathering in the French mathematical landscape, offering a regular opportunity for the community to meet, exchange ideas, and initiate new projects.