Conference: Geometric flows and applications

Rutgers University New Brunswick, New Brunswick NJ

Investigators

Abstract

The award will support US participants attending the conference 'Geometric Flows and Applications', which will take place on July 10-14th at ICMS, Bayes Center in Edinburgh, UK. The event will bring together researchers in geometry and topology whose research interests are closely aligned to topics where geometric flows either already or are expected to play a key role, and will include experts in the analysis of geometric flows. Specific topics will include aspects of complex geometry, Hermitian geometry, symplectic and contact topology, special holonomy, calibrated geometry and gauge theory, as well as Riemannian geometry and low-dimensional topology. A major goal of this conference is to support, train and encourage the next generation of mathematicians in the fields of analysis, complex geometry and mathematical physics. The distinguished and well-known speakers will draw in junior participants from all over the US. By inviting promising junior people to attend, some contributing talks, this conference will help to nurture and support the future leaders of the field. New collaborations and research papers are expected to emerge from this meeting. The theme of this conference is the study of geometric flows and their applications to diverse topics in geometry and topology. Geometric flows are powerful tools for tackling important problems across diverse areas in geometry and topology, and beyond. Spectacular successes go back at least to Donaldson’s work on the Hitchin–Kobayashi correspondence, and continue to the present, with the proofs of the Poincar\'e and Geometrization Conjectures, the Differentiable Sphere Theorem, and the Generalized Smale Conjecture. There are still many key open problems of fundamental importance in a range of areas for which geometric flows provide a natural approach, and for which other methods have proved unsuccessful thus far. Geometric flows are nonlinear, parabolic evolution equations for key geometric quantities, which lie at the heart of a rich and developing theory combining the study of partial differential equations and differential geometry. The most well-known examples of these flows are the Ricci flow and the mean curvature flow, both of which have significant applications, particularly to topology. By using additional data on the manifold (for example, a complex structure), one can define geometric flows which now can now be used to study these more refined geometries. This has proved extremely fruitful, for example in applications (both potential and realised) to gauge theory, the study of the minimal model programme and related problems in complex and algebraic geometry, symplectic topology, Mirror Symmetry and exceptional holonomy. The website for the conference is: https://www.icms.org.uk/workshops/2023/geometric-flows-and-applications This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.