# ERC School on Analysis in Metric Spaces and Geometric Measure Theory

## Jan. 10, 2011 - Jan. 14, 2011

The school is organized for PhD students and postdocs interested in Geometric Measure Theory and Analysis in Metric Spaces. Special emphasis will be put on the theory of currents, isoperimetric and filling problems, and regularity theory. The school will be funded by the ERC Advanced Grant GeMeThnES, Geometric Measure Theory in non-Euclidean Spaces.

Lecturers

Dimitri Burago (Pennsylvania State University): From Asymptotic Volume of Tori to Minimal Surfaces in Normed Spaces and Boundary Rigidity, with a Few Digressions

Robert Hardt (Rice University): Rectifiable and Flat Chains and Charges in a Metric Space

Emanuele Spadaro (Hausdorff Center for Mathematics, Bonn): The Role of Multi-Valued Functions in the Regularity Theory of Minimal Currents

Robert Young (IHES, Paris): Asymptotics of Filling Problems

Jan 10, 2011:

9.00: Robert Hardt (Rice University): Rectifiable and Flat Chains and Charges in a Metric Space, I

10.00: Dmitri Burago (Pennsylvania State University): From Asymptotic Volume of Tori to Minimal Surfaces in Normed Spaces and Boundary Rigidity, with a Few Digressions, I

11.30: Robert Young (New York University): Asymptotics of Fillings Problems, I

3.00: Emanuele Spadaro (MPI Leipzig): The role of Multiple Valued Functions in the Regularity Theory of Minimal Currents, I

4.00: Robert Hardt (Rice University): Rectifiable and Flat Chains and Charges in a Metric Space, II

Jan 11, 2011:

9.00: Dmitri Burago (Pennsylvania State University): From Asymptotic Volume of Tori to Minimal Surfaces in Normed Spaces and Boundary Rigidity, with a Few Digressions, II

10.00: Robert Young (New York University): Asymptotics of Fillings Problems, II

11.30: Emanuele Spadaro (MPI Leipzig): The role of Multiple Valued Functions in the Regularity Theory of Minimal Currents, II

2.30: Robert Hardt (Rice University): Rectifiable and Flat Chains and Charges in a Metric Space, III

3.30: Dmitri Burago (Pennsylvania State University): From Asymptotic Volume of Tori to Minimal Surfaces in Normed Spaces and Boundary Rigidity, with a Few Digressions, III

4.50: Robert Young (New York University): Asymptotics of Fillings Problems, III

Jan 12, 2011:

9.00: Emanuele Spadaro (MPI Leipzig): The role of Multiple Valued Functions in the Regularity Theory of Minimal Currents, III

10.00: Robert Hardt (Rice University): Rectifiable and Flat Chains and Charges in a Metric Space, IV

11.30: Dmitri Burago (Pennsylvania State University): From Asymptotic Volume of Tori to Minimal Surfaces in Normed Spaces and Boundary Rigidity, with a Few Digressions, IV

Jan 13, 2011:

9.00: Robert Young (New York University): Asymptotics of Fillings Problems, IV

10.00: Emanuele Spadaro (MPI Leipzig): The role of Multiple Valued Functions in the Regularity Theory of Minimal Currents, IV

11.00: Dmitri Burago (Pennsylvania State University): From Asymptotic Volume of Tori to Minimal Surfaces in Normed Spaces and Boundary Rigidity, with a Few Digressions, V

2.30: Enrico Le Donne (ETH Zurich): Some new embedding results for subRiemannian manifolds

3.10: Sara Daneri (SISSA Trieste): A disintegration technique for locally affine partitions of $\mathbb{R}^d$ and related divergence formulas

3.50: Colin Carroll (Rice University): Currents and Differential Forms in Metric Spaces

4.50: Riikka Korte (University of Helsinki): The equivalence between the pointwise Hardy inequality and the uniform capacity density condition

5.30: Davide Vittone (Dip. Matematica, Univ. di Padova): Isodiametric sets in the Heisenberg group

6.10: Stefan Suhr (Regensburg University): Aubry-Mather Theory for Lorentzian Manifolds

6.50: Costante Bellettini (ETH Zurich): Some minimal integral currents in geometry: the calibrated ones

Jan 14, 2011:

9.00: Robert Hardt (Rice University): Rectifiable and Flat Chains and Charges in a Metric Space, V

10.00: Robert Young (New York University): Asymptotics of Fillings Problems, V

11.30: Emanuele Spadaro (MPI Leipzig): The role of Multiple Valued Functions in the Regularity Theory of Minimal Currents, V