Analysis Student Seminar

from Thursday
June 01, 2017 to Sunday
December 31, 2017
Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars

Wednesday
September 13, 2017

4:00 PM
Math Tower 5-127
Silvia Ghinassi, Jack Burkart, Stony Brook University
Organizational meeting

All are invited to discuss possible topics.


Wednesday
September 20, 2017

4:00 PM
Math Tower 5-127
Silvia Ghinassi, Stony Brook University
Introduction to Minimal Surfaces

First meeting and general introduction to minimal surfaces.


Wednesday
September 27, 2017

4:00 PM
Math Tower 5-127
Silvia Ghinassi, Stony Brook University
Some examples of minimal surfaces

We will keep following the first chapter of Colding-Minicozzi, 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 5-127
Jin-Cheng Guu, Stony Brook University
Consequences of the first variation formula

With 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 Colding-Minicozzi as they won't be covered in the seminar.


Wednesday
October 11, 2017

4:00 PM
Math Tower 5-127
Ben Sokolowsky, Stony Brook University
Bernstein's Theorem


Wednesday
October 18, 2017

4:00 PM
Math Tower 5-127
Edward Bryden, Stony Brook University
TBA


Wednesday
October 25, 2017

4:00 PM
Math Tower 5-127

CANCELED

The 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 5-127
Jack Burkart, Stony Brook University
Weierstrass Representation and The Strong Maximum Principle

We 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 5-127
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 5-127
Jae Ho Cho, Stony Brook University
Simons' Inequality

We 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 2-dimensional 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 5-127
Matthew Dannenberg, Stony Brook University
TBA


Wednesday
December 06, 2017

4:00 PM
Math Tower 5-127
Jin-Cheng Guu, Stony Brook University
TBA


Show events for:
Instructions for subscribing to Stony Brook Math Department Calendars