All Codimensions Mean Curvature Flow and Minimal Surfaces

Speaker: Theodora Bourni (University of Tennessee, Knoxville)

Course Title: Free boundary curve shortening flow.

Abstract: This mini-course offers an introduction to the free boundary curve shortening flow, centered on three interconnected themes: existence theory, stability and asymptotics, and ancient solutions. We will begin with short- and long-time existence results under natural geometric assumptions, emphasizing how boundary conditions shape the analytical framework. We then turn to more recent developments in the forward evolution, focusing on stability properties and convergence to self-similar solutions, including quantitative rates where available. The course concludes with the backward-in-time perspective, presenting classification results and structural features of ancient solutions.

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Speaker: Giada Franz (Université Gustave Eiffel, Paris)

Course Title: An introduction to Simon-Smith min-max theory for minimal surfaces.

Abstract: This minicourse introduces the Simon–Smith min–max framework for constructing minimal and free boundary minimal surfaces. After reviewing the necessary background and key definitions, we explain how these methods produce critical points of the area functional with prescribed topology. We illustrate the theory through several applications. Time permitting, we outline the main ideas behind the proof of the min–max theorem and discuss recent developments and open problems in the field.

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Speaker: Huy The Nguyen (Queen Mary University of London)

Course Title: Introduction to High Codimension Mean Curvature Flow.

Abstract:  In this series of lectures, we will introduce mean curvature flow from the perspective of high codmension emphasising results and techniques useful in this context. High codimension, that is codimension greater than or equal to two, differs from the well studied hypersurface case in a number of key ways, no preservation of embeddedness from the loss of the avoidance principle, a far more complicated curvature from the presence of a non flat normal bundle and unrestricted topology from Nash’s embedding theorem. Nevertheless, much progress has been made in recent years. After initial introductory material, this lecture course will survey these results. 

As you can see from the schedule below the courses will be spread out across a few buildings. Here are some GPS coordinates for the buildings where the talks will be: 

AKB: 55,70134° N, 12,55860° E | Google Maps | Map (JPG) |

HCØ: Main building: HCØ

Goth: Campus near Nørreport(!) Google Maps

Food club Nørrebro: Google maps

Room schedule (university page)

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The conference/masterclass will take place at the Department of Mathematical Sciences, University of Copenhagen. See detailed instructions on how to reach Copenhagen and the conference venue.

Tickets and passes for public transportation can be bought at the Copenhagen Airport and every train or metro station. You can find the DSB ticket office on your right-hand side as soon as you come out of the arrival area of the airport. DSB has an agreement with 7-Eleven, so many of their shops double as selling points for public transportation.

A journey planner in English is available.

More information on the "find us" webpage.