Spring 2019 Analysis Student Seminar

      This semester, we will learn about regularity of minimal surfaces in higher codimension. We will start with an introduction of Geometric Measure Theory, more specifically the Federer-Fleming theory of integral currents. Then, we will cover the classical theory of regularity in codimension 1. After understanding what are the obstructions to generalize this theory to higher condimensions, we will move onto regularity of minimal surfaces in codimension bigger than 1. There are no prerequisites besides basic knowledge of functional analysis, measure theory, and differential geometry.

      References

      • "The regularity theory of minimal surfaces in higher codimension" (a survey) by Camillo De Lellis. Link here.
      • "Almgren's center manifold in a simple setting" (PCMI Lectures) by Camillo De Lellis. Link here.

      Schedule

      All talks will be given in 5-127 on Wednesdays at 4:00, and we'll try to end around 5:15. The following is the tentative schedule, along with the references we will follow that day.


      Date

      Speaker

      Topic

      Reading

      Feb. 6

      Silvia Ghinassi

      Federer-Fleming theory of integral currents Part I

      De Lellis Survey Section 2

      Feb. 13

      Jack Burkart

      Federer-Fleming theory of integral currents Part II

      De Lellis Survey Section 2

      Feb. 20

      Jacob Mazor

      First considerations in the regularity theory

      De Lellis Survey Section 3

      Feb. 27

      TBA

      The regularity theory in codimension 1

      De Lellis Survey Section 4

      Mar. 6

      TBA

      Federer's theorem and the failure of ε-regularity in codimension >1

      De Lellis Survey Section 5

      Mar. 13

      TBA

      Almgren's stratification

      De Lellis Survey Section 5

      Mar. 20

      Enjoy your Spring break!

      Mar. 27

      TBA

      TBA

      Apr. 3

      TBA

      TBA

      Apr. 10

      TBA

      TBA

      Apr. 17

      TBA

      TBA

      Apr. 24

      TBA

      TBA

      May 1

      TBA

      TBA

      May 8

      TBA

      TBA