18 jan 2027 - 22 jan 2027   [open in google calendar]

Westlake University (Yungu Campus), Hangzhou, Zhejiang, China

In the early 1980s Almgren introduced multiple-valued functions minimizing the Dirichlet energy in order to describe the behaviour of area-minimizing currents near branch points, where an approximation through single valued continuous functions was not suitable. With this tool he proved that the singular set of an m-dimensional area-minimizing integral current in codimension at least two has Hausdorff dimension at most $m-2$. His results have been later reproved by De Lellis and Spadaro in "$Q$-valued functions revisited" and in the series "Regularity of area minimizing currents I - gradient $L^p$ estimates", "Regularity of area minimizing currents II - center manifold" and "Regularity of area minimizing currents III - blow-up" with new ideas and tools, including the frequency function, the center manifold and the approximation of currents by multiple-valued graphs.

From that point, there has been a proliferation of work relating to the regularity of multiple-valued functions, or which make use of them in some way. Some of them investigate regularity properties of $Q$-valued functions themselves, with a particular emphasis for $\texttt{Dir}$-minimizing functions (see for example "Improved estimate of the singular set of $\texttt{Dir}$-minimizing $Q$-valued functions via an abstract regularity result" and "Rectifiability and upper Minkowski bounds for singularities of harmonic $Q$-valued maps"), other instead apply regularity properties of $Q$-valued functions to retrieve regularity results involving minimal varifolds and currents (see for example "On the boundary behavior of mass-minimizing integral currents" and the series of works of De Lellis, Minter, Skorobogatova and Krummel, Wickramasekera).

Much remains unknown, including the finer structure of the singular set, the uniqueness of tangent cones at every point, and the extension of these methods to generic stationary varifolds and other variational problems.

The main topics of this program include:

1. multiple-valued functions;

2. minimal surfaces immersed in Euclidean and in Riemannian spaces;

3. theory of currents, with a particular emphasis on area-minimizing currents;

4. rectifiability;

5. links with Calculus of Variations and Geometric Measure Theory.

We particularly welcome early-career scholars and those with a strong interest in these topics to participate in this event.

Registration

Please note that applications are reviewed on a rolling basis, and offers are sent out as we go. Once all available spots are filled, we will stop accepting applications.

Application Deadline: December 20, 2026.

Participants should provide the following documents in English:

• curriculum vitae;

• academic transcripts;

• motivation letter (written by a human);

• contact information (email) for at least (one) referee for a potential recommendation letter (which should be sent from the referee's academic email address directly to $\texttt{its_programs@westlake.edu.cn}$);

• proof of English proficiency (e.g. IELTS or TOEFL scores, transcripts from English courses, study experiece in an English-speaking country);

• relevant scientific materials (e.g. articles).

Organizers: Paolo De Donato, Thierry De Pauw, Changyou Wang.

Speakers: Hsin-Chuang Chou, Daniele De Gennaro, Changyu Guo, Aria Halavati, Jonas Hirsh, Sanghoon Lee, Stefano Nardulli, Roberto Ognibene, Adam Parusiński, Armin Rainer, Anna Skorobogatova, Elefterios Soultanis, Emanuele Spadaro, Salvatore Stuvard, Kelei Wang, Ling Wang, Zhengyi Xiao, Zihui Zhao.

• Student (including PhD) registration
• Faculty ( including Postdoctoral and other researcher) registration
• event webpage