Wednesday September 13, 2017 4:00 PM Math Tower 5127
 Silvia Ghinassi, Jack Burkart, Stony Brook University
Organizational meetingAll are invited to discuss possible topics.

Wednesday September 20, 2017 4:00 PM Math Tower 5127
 Silvia Ghinassi, Stony Brook University
Introduction to Minimal SurfacesFirst meeting and general introduction to minimal surfaces.

Wednesday September 27, 2017 4:00 PM Math Tower 5127
 Silvia Ghinassi, Stony Brook University
Some examples of minimal surfacesWe will keep following the first chapter of ColdingMinicozzi, providing some examples of minimal surfaces. If time allows we will move on to discuss consequences of the First Variation formula.

Wednesday October 04, 2017 4:00 PM Math Tower 5127
 JinCheng Guu, Stony Brook University
Consequences of the first variation formulaWith the aim of proving Bernstein's theorem, which states that the only entire solutions to the minimal surface equation in R^2 are affine functions, we prove harmonicity of the coordinate functions, monotonicity formula of volume for minimal submanifolds and the mean value inequality.
If time allows, we will introduce the Gauss map and prove Bernstein's theorem, otherwise these will be topics for the next seminar.
Note: last time we discussed, after a brief introduction to Riemannian geometry, the minimal submanifold equation. Please take a look at the relevant examples in 1.2 in ColdingMinicozzi as they won't be covered in the seminar.

Wednesday October 11, 2017 4:00 PM Math Tower 5127
 Ben Sokolowsky, Stony Brook University
Bernstein's Theorem

Wednesday October 18, 2017 4:00 PM Math Tower 5127
 Edward Bryden, Stony Brook University
TBA

Wednesday October 25, 2017 4:00 PM Math Tower 5127

CANCELEDThe seminar has been canceled to allow those interested to attend Dusa McDuff's talk, part of the Workshop "Geometry of Manifolds".

Wednesday November 01, 2017 4:00 PM Math Tower 5127
 Jack Burkart, Stony Brook University
Weierstrass Representation and The Strong Maximum PrincipleWe will discuss some complex analysis tools which are of interest in the study of minimal submanifolds. More specifically, we will discuss the following things:
1. The Weierstrass representation of a minimal surface.
2. The Schwarz Reflection Principle
3. The Strong Maximum Principle for minimal hypersurfaces.

Wednesday November 08, 2017 4:00 PM Math Tower 5127
 Edward Bryden, Stony Brook University
Second Variation Formula, Morse Index, and Stability (continued)We continue our discussion on minimal submanifolds. Having introduced the second variation formula, we are gonna discuss stability and Morse index. Moreover we will prove a characterization of stability for minimal hypersurfaces.

Wednesday November 15, 2017 4:00 PM Math Tower 5127
 Jae Ho Cho, Stony Brook University
Simons' InequalityWe will prove Simons' inequality, which gives the way to control the Laplacian of the norm of the 2nd fundamental form on a minimal hypersurface. Using this theorem, we can see that there is a canonical way to get a flat metric(possibly singular) on any 2dimensional minimal hypersurfaces by observing the fact that Simons' inequality becomes the equality in the surface case.

Wednesday November 29, 2017 4:00 PM Math Tower 5127
 Matthew Dannenberg, Stony Brook University
TBA

Wednesday December 06, 2017 4:00 PM Math Tower 5127
 JinCheng Guu, Stony Brook University
TBA

