Varifolds

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Next lectures
14.10.2026, 15:00 (E2 10 (Leon-Lichtenstein))
16.10.2026, 15:00 (E2 10 (Leon-Lichtenstein))
21.10.2026, 15:00 (E2 10 (Leon-Lichtenstein))
23.10.2026, 15:00 (E2 10 (Leon-Lichtenstein))
28.10.2026, 15:00 (A3 01 (Sophus-Lie room))
30.10.2026, 15:00 (E2 10 (Leon-Lichtenstein))
04.11.2026, 15:00 (E2 10 (Leon-Lichtenstein))
06.11.2026, 15:00 (E2 10 (Leon-Lichtenstein))
11.11.2026, 15:00 (E2 10 (Leon-Lichtenstein))
13.11.2026, 15:00 (E2 10 (Leon-Lichtenstein))
18.11.2026, 15:00 (E2 10 (Leon-Lichtenstein))
20.11.2026, 15:00 (E2 10 (Leon-Lichtenstein))
25.11.2026, 15:00 (E2 10 (Leon-Lichtenstein))
27.11.2026, 15:00 (E2 10 (Leon-Lichtenstein))
02.12.2026, 15:00 (E2 10 (Leon-Lichtenstein))
04.12.2026, 15:00 (E2 10 (Leon-Lichtenstein))
09.12.2026, 15:00 (E2 10 (Leon-Lichtenstein))
11.12.2026, 15:00 (E2 10 (Leon-Lichtenstein))
16.12.2026, 15:00 (E2 10 (Leon-Lichtenstein))
18.12.2026, 15:00 (E2 10 (Leon-Lichtenstein))
23.12.2026, 15:00 (E2 10 (Leon-Lichtenstein))
30.12.2026, 15:00 (E2 10 (Leon-Lichtenstein))
06.01.2027, 15:00 (E2 10 (Leon-Lichtenstein))
08.01.2027, 15:00 (E2 10 (Leon-Lichtenstein))
13.01.2027, 15:00 (E2 10 (Leon-Lichtenstein))
15.01.2027, 15:00 (E2 10 (Leon-Lichtenstein))
20.01.2027, 15:00 (E2 10 (Leon-Lichtenstein))
22.01.2027, 15:00 (E2 10 (Leon-Lichtenstein))
27.01.2027, 15:00 (E2 10 (Leon-Lichtenstein))
29.01.2027, 15:00 (E2 10 (Leon-Lichtenstein))

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This course aims at introducing the theory of Varifolds, focusing on the following topics.

Part 1: Introduction to Varifolds:
----- definitions, basic properties, monotonicity formula, rectifiability, constancy theorem, compactness theorems (integer rectifiability).

Part 2: Strong constancy lemma:
----- integer rectifiability revisited, A-free measures and application to the Rank 1 Theorem for BV functions.

Part 3: Regularity of (almost stationary) Varifolds:
----- \(C^{1, \alpha}\) regularity for Varifolds with bounded curvature.

Part 4: Application to phase transition problems (Allen-Cahn)

No particular prerequisites are needed, except some basic knowledge in (Geometric) Measure Theory, Functional Analysis and PDE.
The goals are certainly ambitious, but the course is mostly self-contained.
Detailed notes and references will be provided.
Online streaming will be available.
The choice of topics can be adapted to the interest of the audience.
We will focus mostly on ideas, strategies and direct proofs, rather than the most advanced results in the very specific fields under consideration.
The ideas presented in the course have been used in multiple and rather different mathematical contexts.
Given the chance to present some advanced (and beautiful) mathematics, this course is ment to be an open space to share mathematical discussions.
Everyone is more than welcome to follow actively.

Keywords
Varifolds

Prerequisites
Standard (Geometric) Measure Theory and Functional Analysis