I am organizing a learning seminar on Geometric Measure Theory (GMT) this summer. The goal is to follow Paul Minter’s lecture notes from his class last spring, which are available on his website. See his website for topics covered in his lecture notes. While I hope to cover the entire lecture notes, this might be too ambitious. A prerequisite for the seminar will be part of Leon Simon’s GMT book.

The seminar will be broadcast on Zoom, but those around Cambridge are encouraged to come to a seminar room and discuss together. Recordings will be available to attendees and may be deleted after a few weeks to encourage timely participation.

If you wish to be included in our mailing list, please send an email to me or add yourself with your email address on the sign up sheet.

Seminar Details

  • Time: Tuesday 1-3pm ET
  • Location: in-person 2-255, online zoom ID 965 1323 5547 1

Prerequisites

  • Basic Measure Theory
  • Basic Minimal Surface Theory
  • Leon Simon’s GMT
    • Geometric objects and operations for $C^k$ submanifolds and (locally) Lipschitz functions (Chapter 2)
      • (co)Area formula, Tangent space, Divergence
      • First and second variation
      • Monotonicity formula
    • Rectifiable varifolds
      • Approximate tangent space, (co)Area formula (Chapter 3.1, 3.2)
      • First variation (Chapter 4.2)

Schedule

Sign up sheet

DateSpeakerTopic
Jul 2Dain KimOverview + Stratification of the Singular Set
Jul 9Tang-Kai LeeBellettini’s PDE method to Schoen–Simon’s Regularity Theory
Jul 16Abhinav JhaAllard’s Regularity: PDE case study
Jul 23Xinrui ZhaoAllard’s Regularity: general case
Aug 6Dain KimSimon’s Cylindrical Tangent Cone: intro
Aug 20Shrey AryanSimon’s Cylindrical Tangent Cone: $L^2$ estimates
Aug 29Yuze JiangSimon’s Cylindrical Tangent Cone: blow-ups
Sep 4Dongyeong KoWickramasekera’s Regularity Theory I
Sep 16Paul MinterWickramasekera’s Regularity Theory II

  1. password: We say a varifold $V = \underline{v}(M, \theta)$ is ********** if the first variation vanishes. ↩︎