Gradient flows in geometry and PDE

David Wood

  •  20 Jan 2025 - 31 Jan 2025
     8:00 am - 5:00 pm

Organisers:
Yoshikazu Giga (University of Tokyo, Japan)
Shinya Okabe (Tohoku University, Japan)
Philip Schrader (Murdoch University, Australia)
Glen Wheeler (University of Wollongong, Australia)
Valentina Wheeler (University of Wollongong, Australia)

Program Description: Gradient flows represent the evolution of mathematical objects in the direction of their steepest descent relative to a certain (energy, metric space) pair. They depict how systems move towards an energy minimising state, symbolising the “path of least resistance.” As a research field, gradient flows is extremely active and quite broad. For our research program, we highlight some specific themes: (a) new choices of metric space; (b) convergence results, especially with rough or arbitrary data; (c) higher-order equations; and (d) geometric flows.

This research program seeks to explore part of the multifaceted world of gradient flows, focusing on four principal domains: new metric space choices, convergence results with arbitrary data, higher-order equations, and geometric evolution equations. Gradient flows are ubiquitous in mathematics, appearing in geometry, topology, and analysis. Research on gradient flows remains extremely active, with many unanswered questions, with our choice of themes motivated by what is current in research and in the interest of our community.

This research program will bring together key researchers working in these areas to stimulate new progress and facilitate collaboration. It also aims to encourage greater connection between the Australian and Japanese mathematics communities.

Program Structure: TBD

Registration:

  • Deadline: TBD
  • Registration is by invitation only. If you are interested to participate in this program, please contact one of the organisers with your CV and research background.
  • Arrival date: 19 January 2025

ASSOCIATED EVENTS
MATRIX Wine and Cheese Afternoon 21 January 2025
On the first Tuesday of each program, MATRIX provides a pre-dinner wine and cheese afternoon. Produce is locally-sourced to showcase delicacies from the region.