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The Geometry of Singular Sets August 2–13, 2027 Buenos Aires

The Geometry of Singular Sets: School on Geometric Measure Theory, Harmonic Analysis and PDE 

From August 2–13, 2027, the second two-week school in our inaugural IAS/South America season, The Geometry of Singular Sets, will take place exclusively at the Universidad de Buenos Aires.

All of the courses in this school work, from different sides, on a single question: how much structure a set or a solution must have, and where it can fail to have it — dimension, rectifiability, and the geometry of singular sets. Harmonic measure and free-boundary problems read the analysis of an elliptic equation off the geometry of a boundary; the singular sets of minimal surfaces and other variational problems are governed by rectifiability; regularity theory for nonlocal and degenerate equations asks what survives when classical geometry breaks down; and the dimension theory of fractal sets, together with projection, Fourier-analytic and multifractal methods, supplies the measuring tools common to all of them.

Format at a Glance

  • Two weeks, Monday to Friday, with both Wednesday and Friday afternoons kept free for research and informal discussion.
  • Six minicourses of three 90-minute lectures each — three in Week 1, three in Week 2.
  • Two distinguished plenary lecturers — François Ledrappier and Carlos Kenig — will give 90-minute lectures.
  • Six 60-minute plenary lectures: Stéphane Jaffard, Stéphane Seuret, Malabika Pramanik, Joshua Zahl, Pablo Lessa, and Tatiana Toro.
  • A semiplenary tier of 50-minute lectures and 25-minute invited talks, drawing on the Argentine community and a partner group in Uruguay, plus a contributed-talk session and two poster sessions.
  • Teaching blocks: 10:00–11:30, 12:00–13:30, and 15:00–16:30
    • Lunch: 13:30–15:00
    • Evening session: 17:00
    • Coffee breaks

Week 1: August 2–6, 2027

  • Eugenia Malinnikova* (Stanford University): Unique Continuation, Nodal Sets, and Eigenfunctions
  • Camillo De Lellis (Institute for Advanced Study, Princeton): Singular Sets and Rectifiability in the Calculus of Variations
  • Luis Silvestre (University of Chicago): Regularity Theory for Nonlocal and Degenerate Equations

Week 2: August 9–13, 2027

  • Pablo Shmerkin (University of British Columbia): Fractal Dimension, Projections, and Fourier-Analytic Methods
  • Xavier Tolsa (ICREA & Universitat Autònoma de Barcelona): Rectifiability, Harmonic Measure and Analytic Capacity
  • Francesco Maggi (University of Texas at Austin): Sets of Finite Perimeter, Minimal Surfaces, and Capillarity

Distinguished Plenary Lectures

  • François Ledrappier [CNRS / Sorbonne Université & Notre Dame (emeritus)]: Dimension of Invariant and Stationary Measures; the Ledrappier–Young Formula
  • Carlos Kenig (University of Chicago): Harmonic Measure, Free Boundaries, and Unique Continuation

Plenary Lectures

  • Stéphane Jaffard (LAMA, Université Paris-Est Créteil): Multifractal Analysis and Wavelet Methods
  • Stéphane Seuret (LAMA, Université Paris-Est Créteil): Multifractal Analysis, Dimension, and Diophantine Approximation
  • Malabika Pramanik (University of British Columbia): Configurations and Patterns in Fractal Sets; Fourier Dimension
  • Joshua Zahl (Chern Institute of Mathematics, Nankai University): Kakeya Sets, Restriction, and Incidence Geometry
  • Pablo Lessa (Universidad de la República, Montevideo): Random Walks, Stationary Measures and Dimension

  • Tatiana Toro (University of Washington / SLMath): Free Boundary Problems, Quantitative Unique Continuation, and Epsilon-Regularity

    (*) To be confirmed.

2027 Programs and Applications

Explore Higher Categories and Applications and The Geometry of Singular Sets: School on Geometric Measure Theory, Harmonic Analysis and PDE, and apply.

The deadline to apply to Higher Categories and Applications (July 5–16, 2027) and to The Geometry of Singular Sets: School on Geometric Measure Theory, Harmonic Analysis and PDE (August 2–13, 2027) via MathPrograms.org is February 15, 2027, at 11:59 pm (Eastern Standard Time).

Applications to each school are linked in the right sidebar.

Also in the right sidebar is the Travel & Participant Information [link to online PDF form], covering questions related to travel, accommodations, meals, and other administrative matters. If you need help or have questions, email [email protected].

 

APPLICATION Information
  • Application deadline is February 15, 2027, at 11:59 pm (Eastern Standard Time).
    • Application: Higher Categories and Applications (July 5–16, 2027) [insert MathPrograms.org link]
    • Application: The Geometry of Singular Sets: School on Geometric Measure Theory, Harmonic Analysis and PDE (August 2–13, 2027) [insert MathPrograms.org link]
IAS/South America and Participant Information