Masterclass:

Recent Progress on Singularity Analysis and Applications of the Mean Curvature Flow

Copenhagen Centre for Geometry & Topology (GeoTop),
University of Copenhagen,
April 29 - May 3, 2024

The event will consist of minicourses by our speakers, going in depth into their cutting edge work on the behavior of singularities under the MCF and its applications, in particular with the low entropy Schoenflies problem in mind. With the topics and time constraint in consideration the target audience will be mathematicians and students already working/studying in the field or adjacently.

Lecturers/Invited speakers with course descriptions

Jacob Bernstein (Johns Hopkins U)

Course title: Self-expanders of mean curvature flow and applications

Description: We discuss some recent developments in the theory of self-expanders of mean curvature flow. These are special solutions of the flow that model how it smooths out conical points. Applications to the topology and geometry of hypersurfaces will be highlighted. Largely based on joint work with Lu Wang.

Felix Schulze (Warwick U)

Course title: Generic mean curvature flow and applications

Description: We will give an overview on recent work on the existence of generic mean curvature flows and discuss some topological applications. We will also point out connections to the problem of generic regularity of area minimizing hypersurfaces. This is based on joint works with Otis Chodosh, Kyeongsu Choi and Christos Mantoulidis.

Ao Sun (Lehigh U)

Course title: Morse theory perspective of mean curvature flow: dynamics, and interpolation method

Description: Morse theory is a fundamental theory in the study of geometry and topology. I will discuss a Morse theory perspective of mean curvature flow. In particular, I will discuss how to study the dynamics of singularities of mean curvature flow (based on joint work with Jinxin Xue), and how to use the interpolation method to construct special mean curvature flow solutions (based on joint work with Adrian Chu and joint work with Jingwen Chen).

Programme

Reading material for the course can be found here.

	MO 29/4	TU 30/5	WE 1/5	TH 2/5	FR 3/5
8:30					Coffee
09:00-10:00	Registration + Coffee				Lecture 13 (Schulze, A110)
9:30	Registration + Coffee	Coffee	Coffee	Coffee
10:00-12:00	Lecture 1 (Sun, Aud 10)	Lecture 4 ( Schulze, Aud 05)	Lecture 7 (Bernstein, Aud 05) Lecture 8 (Schulze, Aud 05)	Lecture 10 (Sun, A110)	Lecture 14 (Sun, A110) Lecture 15 (Bernstein, A110)
12:00-13:00	Lunch	Lunch	Lecture 9 (Sun, Aud 05)	Lunch	Lunch
13:00-14:45	Lecture 2 (Schulze, A110)	Lecture 5 (Bernstein, A104)		Lecture 11 (Bernstein, Aud 01)
14:45-15:15	Coffee	Coffee		Coffee
15:15-17:00	Lecture 3 (Bernstein. Aud 05)	Lecture 6 (Sun, A104)		Lecture 12 (Schulze, Aud 01)
17:30				Walk to Dinner
18:00	Reception			Dinner

Venue and transportation

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. More detailed information about the rooms will be posted here as the date of the masterclass is approached.

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.

Accommodation

We kindly ask the participants to arrange their own accommodation.

We recommend Hotel 9 Små Hjem, which is pleasant and inexpensive and offers rooms with a kitchen. Other inexpensive alternatives are CabInn, which has several locations in Copenhagen: the Hotel City (close to Tivoli), Hotel Scandinavia (Frederiksberg, close to the lakes), and Hotel Express (Frederiksberg) are the most convenient locations; the latter two are 2.5-3 km from the math department. Somewhat more expensive – and still recommended – options are Hotel Nora and Ibsen's Hotel.

An additional option is to combine a stay at the CabInn Metro Hotel with a pass for Copenhagen public transportation (efficient and reliable). See information about tickets & prices.