 Lecturer
 Professor Tristan Rivière
 Coordinator
 Alexis Michelat
Official website :
Link
Fundamental notions of Geometric Measure Theory and Differential Geometry of Minimal Submanifolds from respectively :
The study of minimal surfaces takes its origins in the works of Euler and Bernouilli from the eigtheen century. Since then, minimal surfaces have become central objects in mathematics much beyond the field of geometry with applications in analysis, applied mathematics, theoretical physics and natural sciences.
There have been tremendous developments in the field in the last few years, with a particular emphasis on the variational methods, which permitted to solve several old problems.
In the seminar we shall concentrate first on the AlmgrenPitts minmax theory for the construction of codimension one minimal surfaces in arbitrary closed manifolds as well as on the GromovGuth minmax widths. We will then carefully study a series of recent works by Marques and Neves about the realization of these widths by minimal hypersurfaces. The paramount of the seminar will be the presentation of their very recent proof of a conjecture by Yau asserting the existence of infinitely many embedded minimal hypersurfaces on any closed manifold of dimension strictly less than 8 for generic metrics.
Date 
Lectures 
Speaker 
28 February 2018 
Introduction to Geometric Measure Theory I

Alexis Michelat

7 March 2018 
Introduction to Geometric Measure Theory II

Alexis Michelat

14 March 2018 
Gromov and Guth pSweepOuts for Hypersurfaces

Alexis Michelat

21 March 2018 
Existence of infinitely many minimal hypersurfaces in positive Ricci curvature I

Alessandro Pigati

28 March 2018 
Existence of infinitely many minimal hypersurfaces in positive Ricci curvature II

Alessandro Pigati

11 April 2018 
Geometric aspects of semilinear elliptic PDEs and minimal hypersurfaces on closed manifolds II

Dr. Marco Guaraco

18 April 2018 
No Lecture

25 April 2018 
No Lecture

2 May 2018 
Bumpy Metric Theorem and Morse Index of Minimal Hypersurfaces

Yang Liu and Jaume De Dios

9 May 2018 
Weyl Law for the Volume Spectrum I

Alexis Michelat

16 May 2018 
Weyl Law for the Volume Spectrum II

Alessandro Pigati

23 May 2018 
Denseness and equidistribution of minimal hypersurfaces

Prof. Dr. Alessandro Carlotto
