Description 

Organised in partnership with the Clay Mathematics Institute

Please note that School related material (abstracts, slides/notes as received by lectureres, and video recording of most School lectures) can be viewed & downloaded directly from this site, see list of links on the left of this page, as follows:  either by clicking on the link "Programme" and scrolling it down (i.e. in chronological order), or  by clicking on the link "Speakers" (i.e. sets of lectures grouped by lecturer). In addition, video recording of lectures is also available on a dedicated playlist on ICTP YouTube Channel: https://www.youtube.com/watch?v=2msDseBIAeI&list=PLLq_gUfXAnknsgmI5B1OmZfOuqZls0dK * * *
The School aims at introducing students both to the basic ideas and to the most recent breakthroughs in the field of extrinsic curvature flows, a fundamental research direction at the intersection of Analysis and Geometry, with deep connections to the theories of minimal surfaces and of diffusive partial differential equations.
Extrinsic flows have important applications to the geometry of submanifolds, as their study provides an effective strategy for obtaining topological classification results and for proving sharp geometric inequalities. In a broader context, extrinsic flows arise in describing the dynamics of interfaces in physical and biological sciences, a fact that provides a strong scientific motivation for their mathematical inquiry. Virtually all the different approaches to mean curvature flows will be accounted for, with particular emphasis on the fundamental problem of singularities formation. A major goal of the School will indeed be putting the best students in the position of understanding the many open problems in the field. LIST OF LECTURERS S. Angenent, University of WisconsinMadison P. Daskalopoulos, Columbia University G. Huisken, Universität Tübingen C. Mantegazza, Università di Napoli Federico II F. Otto, MPI for Mathematics in the Sciences C. Sinestrari, Università di Roma Tor Vergata T. Souganidis, University of Chicago Y. Tonegawa, Tokyo Institute of Technology Interested candidates should apply online (see link "Apply here" on the lefthand menu). * DEADLINE FOR APPLICATION: EXPIRED * ICTP Secretariat contact: smr3209@ictp.it 
International School on Extrinsic Curvature Flows  (smr 3209)
Go to day


08:30  17:00
DAY 1
Location: Leonardo Building  Budinich Lecture Hall 
08:30
Financial issues at the Fermi Building for paid participants  in parallel, at the Leonardo Building registration of faculty and of participants not lodging at ICTP guesthouses.
1h50'
(
Leonardo Building  Lobby
)
For full information please refer to the General Information Sheet.

10:20
Welcome remarks and opening
10'

10:30
Monotonicity formulae and noncollapsing estimates for mean curvature flow with applications  1
1h0'
Speaker: Gerhard Huisken (Tübingen University) Material: Abstract Video 
11:30
Nonlinear extrinsic flows and ancient solutions  1
1h0'
Speaker: Panagiota Daskalopoulos (Columbia University) Material: Abstract Slides  12:30 Lunch 2h0'

14:30
Existence and regularity theories of Brakke flow  1
1h0'
Speaker: Yoshihiro Tonegawa (Tokyo Institute of Technology) Material: Abstract Video  15:30 Coffee break 30' ( Leonardo Building  Lobby )

16:00
Singularities of the mean curvature flow of mean convex hypersurfaces  1
1h0'
Speaker: Carlo Sinestrari (University of Rome Tor Vergata) Material: Abstract Video

08:30
Financial issues at the Fermi Building for paid participants  in parallel, at the Leonardo Building registration of faculty and of participants not lodging at ICTP guesthouses.
1h50'
(
Leonardo Building  Lobby
)

08:30  17:00
DAY 1


09:00  17:00
DAY 2

09:00
Monotonicity formulae and noncollapsing estimates for mean curvature flow with applications  2
1h15' (
Leonardo Building  Budinich Lecture Hall
)
Speaker: Gerhard Huisken (Tübingen University) Material: Video  10:15 Coffee break 30' ( Leonardo Building  Lobby )

10:45
Existence and regularity theories of Brakke flow  2
1h15' (
Leonardo Building  Budinich Lecture Hall
)
Speaker: Yoshihiro Tonegawa (Tokyo Institute of Technology) Material: Video  12:00 Lunch 2h0'

14:00
Nonlinear extrinsic flows and ancient solutions  2
1h15' (
Leonardo Building  Budinich Lecture Hall
)
Speaker: Panagiota Daskalopoulos (Columbia University) Material: Slides  15:15 Coffee break 30' ( Leonardo Building  Budinich Lecture Hall )

15:45
Monotonicity formulae and noncollapsing estimates for mean curvature flow with applications  3
1h15' (
Leonardo Building  Budinich Lecture Hall
)
Speaker: Gerhard Huisken (Tübingen University) Material: Video

09:00
Monotonicity formulae and noncollapsing estimates for mean curvature flow with applications  2
1h15' (
Leonardo Building  Budinich Lecture Hall
)

19:30  21:00
DAY 2: RECEPTION  All participants are cordially invited to an informal reception on the Terrace of the Adriatico Guesthouse.
Location: Adriatico Guesthouse

09:00  17:00
DAY 2


09:00  17:00
DAY 3
Location: Leonardo Building  Budinich Lecture Hall 
09:00
Existence and regularity theories of Brakke flow  3
1h15'
Speaker: Yoshihiro Tonegawa (Tokyo Institute of Technology) Material: Video  10:15 Coffee break 30' ( Leonardo Building  Lobby )

10:45
Singularities of the mean curvature flow of mean convex hypersurfaces  2
1h15'
Speaker: Carlo Sinestrari (University of Rome Tor Vergata) Material: Video  12:00 Lunch 2h0'

14:00
Monotonicity formulae and noncollapsing estimates for mean curvature flow with applications  4
1h15'
Speaker: Gerhard Huisken (Tübingen University) Material: Video  15:15 Coffee break 30' ( Leonardo Building  Lobby )

15:45
Nonlinear extrinsic flows and ancient solutions  3
1h15'
Speaker: Panagiota Daskalopoulos (Columbia University)

09:00
Existence and regularity theories of Brakke flow  3
1h15'

09:00  17:00
DAY 3


09:00  17:00
DAY 4
Location: Leonardo Building  Budinich Lecture Hall 
09:00
Nonlinear extrinsic flows and ancient solutions  4
1h15'
Speaker: Panagiota Daskalopoulos (Columbia University) Material: Slides  10:15 Coffee break 30' ( Leonardo Building  Lobby )

10:45
Monotonicity formulae and noncollapsing estimates for mean curvature flow with applications  5
1h15'
Speaker: Gerhard Huisken (Tübingen University) Material: Video  12:00 Lunch 2h0'

14:00
Singularities of the mean curvature flow of mean convex hypersurfaces  3
1h15'
Speaker: Carlo Sinestrari (University of Rome Tor Vergata) Material: Video  15:15 Coffee break 30' ( Leonardo Building  Lobby )

15:45
Existence and regularity theories of Brakke flow  4
1h15'
Speaker: Yoshihiro Tonegawa (Tokyo Institute of Technology) Material: Video

09:00
Nonlinear extrinsic flows and ancient solutions  4
1h15'

09:00  17:00
DAY 4


09:00  17:00
DAY 5
Location: Leonardo Building  Budinich Lecture Hall 
09:00
Singularities of the mean curvature flow of mean convex hypersurfaces  4
1h15'
Speaker: Carlo Sinestrari (University of Rome Tor Vergata) Material: Video  10:15 Coffee break 30' ( Leonardo Building  Lobby )

10:45
Existence and regularity theories of Brakke flow  5
1h15'
Speaker: Yoshihiro Tonegawa (Tokyo Institute of Technology) Material: Video  12:00 Lunch 2h0'

14:00
Singularities of the mean curvature flow of mean convex hypersurfaces  5
1h15' (
Leonardo Building  Budinich Lecture Hall
)
Speaker: Carlo Sinestrari (University of Rome Tor Vergata) Material: Video  15:15 Coffee break 30' ( Leonardo Building  Lobby )

15:45
Nonlinear extrinsic flows and ancient solutions  5
1h15' (
Leonardo Building  Budinich Lecture Hall
)
Speaker: Panagiota Daskalopoulos (Columbia University) Material: Slides

09:00
Singularities of the mean curvature flow of mean convex hypersurfaces  4
1h15'

09:00  17:00
DAY 5


09:00  17:00
DAY 6
Location: Leonardo Building  Budinich Lecture Hall 
09:00
Phasefield models for motion by mean curvature  1
1h15'
Speaker: Panagiotis Souganidis (University of Chicago) Material: Abstract Video  10:15 Coffee break 30' ( Leonardo Building  Lobby )

10:45
Dynamics, Symmetry and Asymmetry of Ancient Solutions to Mean Curvature Flow 1: ODE techniques in curvature flows
1h15' (
Leonardo Building  Budinich Lecture Hall
)
Speaker: Sigurd Angenent (University of WisconsinMadison) Material: Abstract Video  12:00 Lunch 2h0'

14:00
Phasefield models for motion by mean curvature  2
1h15'
Speaker: Panagiotis Souganidis (University of Chicago) Material: Video  15:15 Coffee break 30' ( Leonardo Building  Lobby )

15:45
Motion by curvature of networks in the plane  1
1h15'
Speaker: Carlo Mantegazza (University of Naples Federico II) Material: Abstract Appendix: 1000 grains in motion More course references Slides Video

09:00
Phasefield models for motion by mean curvature  1
1h15'

09:00  17:00
DAY 6


09:00  18:15
DAY 7
Location: Leonardo Building  Budinich Lecture Hall 
09:00
Phasefield models for motion by mean curvature  3
1h15' (
Leonardo Building  Budinich Lecture Hall
)
Speaker: Panagiotis Souganidis (University of Chicago) Material: Video  10:15 Coffee break 30' ( Leonardo Building  Lobby )

10:45
Dynamics, Symmetry and Asymmetry of Ancient Solutions to Mean Curvature Flow 2: Uniqueness and Nonuniqueness of MCF from cones
1h15' (
Leonardo Building  Budinich Lecture Hall
)
Speaker: Sigurd Angenent (University of WisconsinMadison) Material: Video  12:00 Lunch 2h0'

14:00
Motion by curvature of networks in the plane  2
1h15'
Speaker: Carlo Mantegazza (University of Naples Federico II) Material: Slides Video  15:15 Coffee break 30' ( Leonardo Building  Lobby )

15:45
The thresholding scheme for mean curvature flow as minimizing movement scheme  1
1h15' (
Leonardo Building  Budinich Lecture Hall
)
Speaker: Felix Otto (Max Planck Institute for Mathematics in the Sciences in Leipzig) Material: Abstract Video

09:00
Phasefield models for motion by mean curvature  3
1h15' (
Leonardo Building  Budinich Lecture Hall
)

19:30  21:00
DAY 7: RECEPTION  All participants are cordially invited to an informal reception on the Terrace of the Adriatico Guesthouse.
Location: Adriatico Guesthouse

09:00  18:15
DAY 7


09:00  18:15
DAY 8
Location: Leonardo Building  Budinich Lecture Hall 
09:00
Dynamics, Symmetry and Asymmetry of Ancient Solutions to Mean Curvature Flow 3: Velazquez' example, and asymptotics for ancient ovals
1h15' (
Leonardo Building  Budinich Lecture Hall
)
Speaker: Sigurd Angenent (University of WisconsinMadison) Material: Video  10:15 Coffee break 30' ( Leonardo Building  Lobby )

10:45
The thresholding scheme for mean curvature flow as minimizing movement scheme  2
1h15' (
Leonardo Building  Budinich Lecture Hall
)
Speaker: Felix Otto (Max Planck Institute for Mathematics in the Sciences in Leipzig) Material: Lecture notes Video  12:00 Lunch 2h0'

14:00
The thresholding scheme for mean curvature flow as minimizing movement scheme  3
1h15'
Speaker: Felix Otto (Max Planck Institute for Mathematics in the Sciences in Leipzig) Material: Video  15:15 Coffee break 30' ( Leonardo Building  Lobby )

15:45
Motion by curvature of networks in the plane  3
1h15'
Speaker: Carlo Mantegazza (University of Naples Federico II) Material: Appendix Slides Video

09:00
Dynamics, Symmetry and Asymmetry of Ancient Solutions to Mean Curvature Flow 3: Velazquez' example, and asymptotics for ancient ovals
1h15' (
Leonardo Building  Budinich Lecture Hall
)

09:00  18:15
DAY 8


09:00  18:15
DAY 9
Location: Leonardo Building  Budinich Lecture Hall 
09:00
Phasefield models for motion by mean curvature  4
1h15'
Speaker: Panagiotis Souganidis (University of Chicago) Material: Video  10:15 Coffee break 30' ( Leonardo Building  Lobby )

10:45
The thresholding scheme for mean curvature flow as minimizing movement scheme  4
1h15'
Speaker: Felix Otto (Max Planck Institute for Mathematics in the Sciences in Leipzig) Material: Slides Video  12:00 Lunch 2h0'

14:00
The thresholding scheme for mean curvature flow as minimizing movement scheme  5
1h15' (
Leonardo Building  Budinich Lecture Hall
)
Speaker: Felix Otto (Max Planck Institute for Mathematics in the Sciences in Leipzig) Material: Lecture notes Video  15:15 Coffee break 30' ( Leonardo Building  Lobby )

15:45
Motion by curvature of networks in the plane  4
1h15'
Speaker: Carlo Mantegazza (University of Naples Federico II) Material: Slides Video

09:00
Phasefield models for motion by mean curvature  4
1h15'

09:00  18:15
DAY 9


09:00  18:25
DAY 10
Location: Leonardo Building  Budinich Lecture Hall 
09:00
Phasefield models for motion by mean curvature  5
1h15' (
Leonardo Building  Budinich Lecture Hall
)
Speaker: Panagiotis Souganidis (University of Chicago) Material: Video  10:15 Coffee break 30' ( Leonardo Building  Lobby )

10:45
Motion by curvature of networks in the plane  5
1h15'
Speaker: Carlo Mantegazza (University of Naples Federico II) Material: Slides Video  12:00 Lunch 2h0'

14:00
Dynamics, Symmetry and Asymmetry of Ancient Solutions to Mean Curvature Flow 4: Ancient convex solutions to MCF
1h15' (
Leonardo Building  Budinich Lecture Hall
)
Speaker: Sigurd Angenent (University of WisconsinMadison) Material: Video  15:15 Coffee break 30' ( Leonardo Building  Lobby )

15:45
Dynamics, Symmetry and Asymmetry of Ancient Solutions to Mean Curvature Flow 5: Dynamics and symmetry of ancient convex mean curvature flows
1h15' (
Leonardo Building  Budinich Lecture Hall
)
Speaker: Sigurd Angenent (University of WisconsinMadison) Material: Video 
17:00
Closing remarks
10'

09:00
Phasefield models for motion by mean curvature  5
1h15' (
Leonardo Building  Budinich Lecture Hall
)

09:00  18:25
DAY 10