Organisers:
MATRIX
Theodora Bourni (University of Tennessee Knoxville)
Mat Langford (Australian National University )

MFO
Julian Scheuer (Goethe Universität Frankfurt)
Miles Simon (Universität Magdeburg)

Program Description:

Geometric flows such as the harmonic map heat flow, the Ricci flow, and the mean curvature flow exploit the power of diffusion to canonically deform geometric structures towards equilibria (possibly after rescaling). This is both a natural procedure for proving the existence and regularity of such equilibrium states, as well as a powerful method for characterizing and organizing the permitted initial states (the equilibrium states being typically much easier to characterize than the initial ones). The diffusive nature of such equations also often allows even very rough initial data to be “instantaneously smoothed”; the ability to canonically smooth rough geometric objects is highly desirable for numerous geometric applications.

The theme of this workshop will be singularity formation and resolution in nonlinear parabolic partial differential equations arising in geometry. It will be guided by significant recent progress, related geometric and topological applications, and a number of difficult outstanding open problems.

Program Structure: TBD

MFO webpage: https://www.mfo.de/occasion/2509b/www_view

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: 23 February 2025
• Departure date: 28 February 2025

ASSOCIATED EVENTS

MATRIX Wine and Cheese Afternoon 25 February 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.