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:

Click here for talks – title and abstract

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

Participant List:
Ben Andrews (Australian National University)
Steven Buchanan (Australian National University)
Nathan Burns (University of Tennessee)
Beomjun Choi (POSTECH)
Julie Clutterbuck (Monash University)
Jose Espinar (Universidad de Granada)
Brett Kotschwar (Arizona State University)
Kwok-Kun Kwong (University of Wollongong)
Vishnu Mangalath (Australian National University)
James McCoy (University of Newcastle)
Huy The Nguyen (Queen Mary University of London)
Devesh Rajpal (Australian National University)
Mariel Saez (P. Universidad Catolica de Chile)
Yong Wei (University of Science and Technology of China)
Glen Wheeler (University of Wollongong)
Haotian Wu (University of Sydney)
Theodora Bourni (University of Tennessee Knoxville)
Mat Langford (Australian National University)
Qiyu Zhou (Australian National University)
Cale Rankin (Monash University)
Sean Wynn (University of Newcastle)

Registration:

• Registration is now closed
• Arrival date: 23 February 2025
• Departure date: 1 March 2025

ASSOCIATED EVENTS

MATRIX Wine and Cheese Afternoon 26 February 2025
A pre-dinner wine and cheese afternoon. Produce is locally-sourced to showcase delicacies from the region.