Mathematics is not a static field of knowledge, but rather a multifaceted, dynamic, and expanding discipline, in which areas seemingly far from applications suddenly become indispensable and applications stimulate challenging foundational mathematical research. Moreover, many application-driven mathematical developments are also motivated and triggered by developments in other scientific and humanities fields.

The research agenda for MATH+ has not been fixed in advance for several years, but is designed to be dynamic. New fields and opportunities emerge over time, or need to be actively developed. The *Topic Development Lab (TDL) *is a central part of MATH+ that, based on this dynamic view of mathematics, provides a platform for developing new topics, for building bridges between different fields of mathematics (e.g., between “pure” and “applied”), and for reaching out to other areas of science and potential cooperation partners outside of mathematics. The main activity of the TDL consists of Thematic Einstein Semesters funded by the Einstein Foundation Berlin.

**The current Thematic Einstein Semester (Summer 2024):**

Mathematics for Quantum Technologies

This Thematic Einstein semester aims to shed light on the mathematical aspects of the rapidly developing fields of quantum information processing, quantum cryptography, and quantum metrology. The related novel quantum technologies, which will vastly outperform their classical counterparts in certain tasks, rely to a significant extent on complex mathematical theory that closely links numerous areas of applied mathematics. During the semester it is intended to bring together young researchers and experienced scholars from mathematics, theoretical physics, engineering and related disciplines in a number of workshops, a summer school and further activities.

**Past Thematic Einstein Semesters:**

- Network Games, Tropical Geometry, and Quantum Communication (Summer 2019)
- Algebraic Geometry: Varieties, Polyhedra, Computation (Winter 2019/20)
- Energy-Based Mathematical Methods for Reactive Multiphase Flows (Winter 2020/21)
- Geometric and Topological Structure of Materials (Summer 2021)
- Mathematics of Imaging in Real-Word Challenges (Winter 2021/22)
- The Mathematics of Complex Social Systems: Agent-based and Data-driven Modeling (Summer 2022)
- Scales of Temporality: Modeling Time and Predictability in the Literary and in the Mathematical Sciences (Winter 2022/23)
- Mathematical Optimization for Machine Learning (Summer 2023)
- Small Data Analysis (Winter 2023/24)