Dates

January 18-22nd, 2027;

Location

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

1 Presentation

We are delighted to announce the Short-term Program in "Multiple-valued functions", which will take place at the Institute for Theoretical Sciences, Westlake University, from January 18th-22nd, 2027.

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 Dir-minimizing functions (see for example "Improved estimate of the singular set of 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.

2 Speakers

Mini courses

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Individual lectures

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• Hsin-Chuang Chou (University of Wien);

• Daniele De Gennaro (Bocconi University);

• Changyu Guo (Shandong University);

• Aria Halavati (Bocconi University);

• Sanghoon Lee (Seoul National University);

• Stefano Nardulli (Federal University of ABC);

• Roberto Ognibene (University of Milan Bicocca);

• Armin Rainer (Vienna University of Technology);

• Elefterios Soultanis (University of Jyvaskyla);

• Kelei Wang (Wuhan University);

• Ling Wang (Bocconi University);

• Zhengyi Xiao (University of Vienna);

• Zihui Zhao (Johns Hopkins University).

3 Registration

The short-term program is designed for PhD and graduate students in Mathematics with a background in Mathematical Analysis, preferably in measure theory and Sobolev spaces.

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

4 Application material

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 its_programs@westlake.edu.cn);

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

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

5 Application submission

Please submit your application via:

• Student registration:

https://v.wjx.cn/vm/PAmgGt9.aspx#

• Faculty ( including Postdoctoral and other researcher) registration:

https://v.wjx.cn/vm/YanJuBg.aspx#