Models for higher categories

• Applicant: Dr. Viktoriya Ozornova
• Subject Area: Mathematics
• Term: Funded in 2020
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 442418934

Mathematics deals with structures and patterns. In the 1950s, the idea of looking for pattern and structures inside those structures began to conquer the minds of the mathematicians: category theory was born. The successful organization of mathematical objects allowed to make proofs clearer, simpler and more transparent. This clarity was key to a few advances in the modern algebraic topology and algebraic geometry. Extracting the essence of the methods also allowed to transfer them into adjacent areas of mathematics.Within the last 25 years, it has become more and more clear that category theory has too little flexibility for several applications in homotopy theory, which were partially inspired by problems from computer science and physics. The goal of this project is the comparison and further development of models for "higher" category theory.

• DFG Programme: Research Fellowships
• International Connection: USA
• Host: Professorin Dr. Emily Riehl