Mathematics Lab

The Lab explores computational and experimental techniques for advancing research in mathematics.

Computational and Experimental Mathematics

Group organizers: Zach Greenberg, Abhiram Kidambi, Max Riestenberg

This discussion group is dedicated to using computation to explore theoretical mathematics. We are interested in sharing computational techniques and concrete experiments across diverse areas of mathematics.

The lab serves as a think tank to explore the growing interaction between mathematics and AI/machine learning at various levels (mathematical foundations, use of mathematical structures in AI, use of AI in mathematical research), as well as the appearance and the use of mathematics in other sciences.

Mathematics and Complex Structures

Group organizers: Alvaro Diaz, Duc Luu, Guillermo Restrepo, Daniel Spitz, Dia Taha

This discussion group aims to study and explore complex systems through the lens of mathematics and artificial intelligence (AI). Our research interests cover various domains, including Physics, Chemistry, Finance, Biology, Neuroscience, Social Sciences, and History, reflecting our dedication to interdisciplinary research. The core methodological basis lies in mathematics, statistics, machine learning, topological data analysis (TDA), simulations, and visualization. Two main objectives guide our mission. First, we aim to develop mathematical and AI-based methods and techniques for studying complex systems, targeting both theory and practice. Second, we aim to rigorously apply these and other existing methods directly to concrete problems arising from complex systems. A key component of our approach is the synthesis of data-driven and analytical techniques for analyzing and identifying patterns, trends, and causal relationships within complex systems.

Mathematical Foundations of AI

Group organizers: Alvaro Diaz, Marzieh Eidi, Benjamin Gess, Parvaneh Johari, Francesca Tombari, Angelica Torres

The lab is involved in outreach activities at Leipzig, including school workshops and visits, high school students (BeLL), internships, REUs, public talks, cooperation with museums, artists, and exhibitions. Through its outreach activities, the lab brings mathematics to the public and opens up new ways to engage with mathematics.

Group organizers: Jana Gregor, Joerg Lehnert, Erika Roldan, Dia Taha