The basis for the ambitious research program pursued in the Appplication Areas and Emerging Fields is provided by the broad mathematical expertise assembled in the MATH+ community. Berlin mathematics is known for its collaborative and interactive approach, which not only disregards traditional boundaries between mathematical subfields but also actively pursues exchange and research with disciplines that may or may not be traditionally viewed as being close to mathematics. The Topic Development Lab (TDL), as part of the IC, shall provide the forum for this scientific exchange, building bridges between different fields of mathematics, and reaching out to potential scientific cooperation partners outside of mathematics. Its activities include the Thematic Semesters and the Method Development Unit.
The current Thematic Semester (Winter 2026/27):
The Multiplicative Weights Update Method
During the winter semester 2026/27, we are organizing a thematic semester on the Multiplicative Weights Update Method, a basic algorithmic technique that has been as been discovered and rediscovered at least six or seven times over the last decades, in diverse fields such as economics, combinatorics, discrete and online optimization, computational and discrete geometry, machine learning, metric embeddings, bioinformatics, computational complexity theory, game theory, and statistics.
In 2012, Arora, Hazan, and Kale published a survey, in which they popularized the technique. However, we believe that this survey only scratches the surface, and that much more on the topic can be discovered.
The goal of the thematic semester is threefold:
- to provide a systematic overview of the basics and the many applications of the multiplicative weights update method in various fields of mathematics and computer science;
- to achieve a deeper understanding of the method, its extensions and generalizations;
- to bring together experts from the different fields and to make the underlying techniques and theory more widely known.
Further details and a complete overview of all its activities can be found here.
Documentations on the previous Thematic Semesters from the first funding period (2019 – 2025) can be found here.